Papers 2023

• Krylov complexity for non-local spin chains

  Aranya Bhattacharya, Pingal Pratyush Nath, Himanshu Sahu

  arXiv:2312.11677 · December 18, 2023 · quant-ph · Phys. Rev. D 109, 066010 (2024) · doi

  Abstract

  Building upon recent research in spin systems with non-local interactions, this study investigates operator growth using the Krylov complexity in different non-local versions of the Ising model. We find that the non-locality results in a faster scrambling of the operator to all sites. While the saturation value of Krylov complexity of local integrable and local chaotic theories differ by a significant margin, this difference is much suppressed when non-local terms are introduced in both regimes. This results from the faster scrambling of information in the presence of non-locality. In addition, we investigate the behavior of level statistics and spectral form factor as probes of quantum chaos to study the integrability breaking due to non-local interactions. Our numerics indicate that in the non-local case, late time saturation of Krylov complexity distinguishes between different underlying theories, while the early time complexity growth distinguishes different degrees of non-locality.

• Fracton models from product codes

  Yi Tan, Brenden Roberts, Nathanan Tantivasadakarn, Beni Yoshida, Norman Y. Yao

  arXiv:2312.08462 · December 13, 2023 · quant-ph · Phys. Rev. Research 7, L032062 (2025) · doi

  Abstract

  We explore a deep connection between fracton order and product codes. In particular, we propose and analyze conditions on classical seed codes which lead to fracton order in the resulting quantum product codes. Depending on the properties of the input codes, product codes can realize either Type-I or Type-II fracton models, in both nonlocal and local constructions. For the nonlocal case, we show that a recently proposed model of lineons on an irregular graph can be obtained as a hypergraph product code. Interestingly, constrained mobility in this model arises only from glassiness associated with the graph. For the local case, we introduce a novel type of classical LDPC code defined on a planar aperiodic tiling. By considering the specific example of the pinwheel tiling, we demonstrate the systematic construction of local Type-I and Type-II fracton models as product codes. Our work establishes product codes as a natural setting for exploring fracton order.

• Bulk reconstruction and non-isometry in the backwards-forwards holographic black hole map

  Oliver DeWolfe, Kenneth Higginbotham

  arXiv:2311.12921 · November 21, 2023 · hep-th

  Abstract

  The backwards-forwards map, introduced as a generalization of the non-isometric holographic maps of the black hole interior of Akers, Engelhardt, Harlow, Penington, and Vardhan to include non-trivial dynamics in the effective description, has two possible formulations differing in when the post-selection is performed. While these two forms are equivalent on the set of dynamically generated states -- states formed from unitary time evolution acting on well-defined initial configurations of infalling matter -- they differ on the generic set of states necessary to describe the apparent world of the infalling observer. We show that while both versions successfully reproduce the Page curve, the version involving post-selection as the final step, dubbed the backwards-forwards-post-selection (BFP) map, has the desirable properties of being non-isometric but isometric on average and providing state-dependent reconstruction of bulk operators, while the other version does not. Thus the BFP map is a suitable non-isometric code describing the black hole interior including interior interactions.

• Synthesis and Arithmetic of Single Qutrit Circuits

  Amolak Ratan Kalra, Michele Mosca, Dinesh Valluri

  arXiv:2311.08696 · November 15, 2023 · quant-ph · Quantum 9, 1647 (2025) · doi

  Abstract

  In this paper we study single qutrit circuits consisting of words over the Clifford$+D$ cyclotomic gate set, where $D=\text{diag}(\pmξ^{a},\pmξ^{b},\pmξ^{c})$, $ξ$ is a primitive $9$-th root of unity and $a,b,c$ are integers. We characterize classes of qutrit unit vectors $z$ with entries in $\mathbb{Z}[ξ, \frac{1}χ]$ based on the possibility of reducing their smallest denominator exponent (sde) with respect to $χ:= 1 - ξ,$ by acting an appropriate gate in Clifford$+D$. We do this by studying the notion of `derivatives mod $3$' of an arbitrary element of $\mathbb{Z}[ξ]$ and using it to study the smallest denominator exponent of $HDz$ where $H$ is the qutrit Hadamard gate and $D$. In addition, we reduce the problem of finding all unit vectors of a given sde to that of finding integral solutions of a positive definite quadratic form along with some additional constraints. As a consequence we prove that the Clifford$+D$ gates naturally arise as gates with sde $0$ and $3$ in the group $U(3,\mathbb{Z}[ξ, \frac{1}χ])$ of $3 \times 3$ unitaries with entries in $\mathbb{Z}[ξ, \frac{1}χ]$. We illustrate the general applicability of these methods to obtain an exact synthesis algorithm for Clifford$+R$ and recover the previous exact synthesis algorithm in \cite{kmm}. The framework developed to formulate qutrit gate synthesis for Clifford$+D$ extends to qudits of arbitrary prime power.

• A square-root speedup for finding the smallest eigenvalue

  Alex Kerzner, Vlad Gheorghiu, Michele Mosca, Thomas Guilbaud, Federico Carminati, Fabio Fracas, Luca Dellantonio

  arXiv:2311.04379 · November 7, 2023 · quant-ph

  Abstract

  We describe a quantum algorithm for finding the smallest eigenvalue of a Hermitian matrix. This algorithm combines Quantum Phase Estimation and Quantum Amplitude Estimation to achieve a quadratic speedup with respect to the best classical algorithm in terms of matrix dimensionality, i.e., $\widetilde{\mathcal{O}}(\sqrt{N}/ε)$ black-box queries to an oracle encoding the matrix, where $N$ is the matrix dimension and $ε$ is the desired precision. In contrast, the best classical algorithm for the same task requires $Ω(N)\text{polylog}(1/ε)$ queries. In addition, this algorithm allows the user to select any constant success probability. We also provide a similar algorithm with the same runtime that allows us to prepare a quantum state lying mostly in the matrix's low-energy subspace. We implement simulations of both algorithms and demonstrate their application to problems in quantum chemistry and materials science.

• NOON-state interference in the frequency domain

  Dongjin Lee, Woncheol Shin, Sebae Park, Junyeop Kim, Heedeuk Shin

  arXiv:2311.00338 · November 1, 2023 · quant-ph · Light: Science & Applications, 13, 90 (2024) · doi

  Abstract

  The examination of entanglement across various degrees of freedom has been pivotal in augmenting our understanding of fundamental physics, extending to high dimensional quantum states, and promising the scalability of quantum technologies. In this paper, we demonstrate the photon number path entanglement in the frequency domain by implementing a frequency beam splitter that converts the single-photon frequency to another with 50% probability using Bragg scattering four-wave mixing. The two-photon NOON state in a single-mode fiber is generated in the frequency domain, manifesting the two-photon interference with two-fold enhanced resolution compared to that of single-photon interference, showing the outstanding stability of the interferometer. This successful translation of quantum states in the frequency domain will pave the way toward the discovery of fascinating quantum phenomena and scalable quantum information processing.

• Generative Learning of Continuous Data by Tensor Networks

  Alex Meiburg, Jing Chen, Jacob Miller, Raphaëlle Tihon, Guillaume Rabusseau, Alejandro Perdomo-Ortiz

  arXiv:2310.20498 · October 31, 2023 · cs.LG

  Abstract

  Beyond their origin in modeling many-body quantum systems, tensor networks have emerged as a promising class of models for solving machine learning problems, notably in unsupervised generative learning. While possessing many desirable features arising from their quantum-inspired nature, tensor network generative models have previously been largely restricted to binary or categorical data, limiting their utility in real-world modeling problems. We overcome this by introducing a new family of tensor network generative models for continuous data, which are capable of learning from distributions containing continuous random variables. We develop our method in the setting of matrix product states, first deriving a universal expressivity theorem proving the ability of this model family to approximate any reasonably smooth probability density function with arbitrary precision. We then benchmark the performance of this model on several synthetic and real-world datasets, finding that the model learns and generalizes well on distributions of continuous and discrete variables. We develop methods for modeling different data domains, and introduce a trainable compression layer which is found to increase model performance given limited memory or computational resources. Overall, our methods give important theoretical and empirical evidence of the efficacy of quantum-inspired methods for the rapidly growing field of generative learning.

• Area laws and tensor networks for maximally mixed ground states

  Itai Arad, Raz Firanko, Rahul Jain

  arXiv:2310.19028 · October 29, 2023 · quant-ph · doi

  Abstract

  We show an area law in the mutual information for the maximally-mixed state $Ω$ in the ground space of general Hamiltonians, which is independent of the underlying ground space degeneracy. Our result assumes the existence of a `good' approximation to the ground state projector (a good AGSP), a crucial ingredient in previous area-law proofs. Such approximations have been explicitly derived for 1D gapped local Hamiltonians and 2D frustration-free locally-gapped Hamiltonians. As a corollary, we show that in 1D gapped local Hamiltonians, for any $\varepsilon>0$ and any bi-partition $L\cup L^c$ of the system, \begin{align*} \mathrm I_{\max}^\varepsilon (L:L^c)_Ω \le \mathrm O \big( \log (|L|\log(d))+\log(1/\varepsilon)\big), \end{align*} where $|L|$ represents the number of sites in $L$, $d$ is the dimension of a site and $\mathrm I_{\max}^\varepsilon (L:L^c)_Ω$ represents the $\varepsilon$-\emph{smoothed maximum mutual information} with respect to the $L:L^c$ partition in $Ω$. From this bound we then conclude $\mathrm I (L:L^c)_Ω \le \mathrm O\big(\log(|L|\log(d))\big)$ -- an area law for the mutual information in 1D systems with a logarithmic correction. In addition, we show that $Ω$ can be approximated in trace norm up to $\varepsilon$ with a state of Schmidt rank of at most $\mathrm{poly}(|L|/\varepsilon)$, leading to a good MPO approximation for $Ω$ with polynomial bond dimension. Similar corollaries are derived for the mutual information of 2D frustration-free and locally-gapped local Hamiltonians.

• Quantum-walk search in motion

  Himanshu Sahu, Kallol Sen

  arXiv:2310.14345 · October 22, 2023 · quant-ph · Scientific Reports 14, 2815 (2024) · doi

  Abstract

  In quantum computing, the quantum walk search algorithm is designed for locating fixed marked nodes within a graph. However, when multiple marked nodes exist, the conventional search algorithm lacks the capacity to simultaneously amplify the marked nodes as well as identify the correct chronological ordering between the marked nodes, if any. To address this limitation, we explore a potential extension of the algorithm by introducing additional quantum states to label the marked nodes. The labels resolve the ambiguity of simultaneous amplification of the marked nodes. Additionally, by associating the label states with a chronological ordering, we can extend the algorithm to track a moving particle on a two-dimensional surface. Our algorithm efficiently searches for the trajectory of the particle and is supported by a proposed quantum circuit. This concept holds promise for a range of applications, from real-time object tracking to network management and routing.

• Simulating 2D lattice gauge theories on a qudit quantum computer

  Michael Meth, Jan F. Haase, Jinglei Zhang, Claire Edmunds, Lukas Postler, Alex Steiner, Andrew J. Jena, Luca Dellantonio, Rainer Blatt, Peter Zoller … Christine Muschik … et al.

  arXiv:2310.12110 · October 18, 2023 · quant-ph · Nature Physics 21, 570-576 (2025) · doi

  Abstract

  Particle physics underpins our understanding of the world at a fundamental level by describing the interplay of matter and forces through gauge theories. Yet, despite their unmatched success, the intrinsic quantum mechanical nature of gauge theories makes important problem classes notoriously difficult to address with classical computational techniques. A promising way to overcome these roadblocks is offered by quantum computers, which are based on the same laws that make the classical computations so difficult. Here, we present a quantum computation of the properties of the basic building block of two-dimensional lattice quantum electrodynamics, involving both gauge fields and matter. This computation is made possible by the use of a trapped-ion qudit quantum processor, where quantum information is encoded in $d$ different states per ion, rather than in two states as in qubits. Qudits are ideally suited for describing gauge fields, which are naturally high-dimensional, leading to a dramatic reduction in the quantum register size and circuit complexity. Using a variational quantum eigensolver, we find the ground state of the model and observe the interplay between virtual pair creation and quantized magnetic field effects. The qudit approach further allows us to seamlessly observe the effect of different gauge field truncations by controlling the qudit dimension. Our results open the door for hardware-efficient quantum simulations with qudits in near-term quantum devices.

• Every quantum helps: Operational advantage of quantum resources beyond convexity

  Kohdai Kuroiwa, Ryuji Takagi, Gerardo Adesso, Hayata Yamasaki

  arXiv:2310.09154 · October 13, 2023 · quant-ph · Phys. Rev. Lett. 132, 150201 (2024) · doi

  Abstract

  Identifying what quantum-mechanical properties are useful to untap a superior performance in quantum technologies is a pivotal question. Quantum resource theories provide a unified framework to analyze and understand such properties, as successfully demonstrated for entanglement and coherence. While these are examples of convex resources, for which quantum advantages can always be identified, many physical resources are described by a nonconvex set of free states and their interpretation has so far remained elusive. Here we address the fundamental question of the usefulness of quantum resources without convexity assumption, by providing two operational interpretations of the generalized robustness measure in general resource theories. First, we characterize the generalized robustness in terms of a nonlinear resource witness and reveal that any state is more advantageous than a free one in some multicopy channel discrimination task. Next, we consider a scenario where a theory is characterized by multiple constraints and show that the generalized robustness coincides with the worst-case advantage in a single-copy channel discrimination setting. Based on these characterizations, we conclude that every quantum resource state shows a qualitative and quantitative advantage in discrimination problems in a general resource theory even without any specification on the structure of the free states.

• Robustness- and weight-based resource measures without convexity restriction: Multicopy witness and operational advantage in static and dynamical quantum resource theories

  Kohdai Kuroiwa, Ryuji Takagi, Gerardo Adesso, Hayata Yamasaki

  arXiv:2310.09321 · October 13, 2023 · quant-ph · Phys. Rev. A 109, 042403 (2024) · doi

  Abstract

  Quantum resource theories (QRTs) provide a unified framework to analyze quantum properties as resources for achieving advantages in quantum information processing. The generalized robustness and the weight of resource have been gaining increasing attention as useful resource quantifiers. However, the existing analyses of these measures were restricted to the cases where convexity of the set of free states is assumed, and physically motivated resources do not necessarily satisfy this restriction. In this paper, we give characterizations of robustness- and weight-based measures in general QRTs without convexity restriction through two different yet related approaches. On the one hand, we characterize the generalized robustness and the weight of resource by introducing a nonlinear witness. We show a general construction of new witness observables that detect the resourcefulness of a given state from multiple copies of the state and, using these witnesses, we provide operational interpretations of the above resource measures even without any convexity assumption. On the other hand, we find that the generalized robustness and the weight of resource can also be interpreted as the worst-case maximum advantage in variants of channel-discrimination and channel-exclusion tasks, respectively, where the set of free states consists of several convex subsets corresponding to multiple restrictions. We further extend these results to QRTs for quantum channels and quantum instruments. These characterizations show that every quantum resource exhibits an advantage for the corresponding tasks, even in general QRTs without convexity assumption. Thus, we establish the usefulness of robustness-based and weight-based techniques beyond the conventional scope of convex QRTs, leading to a better understanding of the general structure of QRTs.

• Streaming quantum state purification

  Andrew M. Childs, Honghao Fu, Debbie Leung, Zhi Li, Maris Ozols, Vedang Vyas

  arXiv:2309.16387 · September 28, 2023 · quant-ph · Quantum 9, 1603 (2025) · doi

  Abstract

  Quantum state purification is the task of recovering a nearly pure copy of an unknown pure quantum state using multiple noisy copies of the state. This basic task has applications to quantum communication over noisy channels and quantum computation with imperfect devices, but has only been studied previously for the case of qubits. We derive an efficient purification procedure based on the swap test for qudits of any dimension, starting with any initial error parameter. Treating the initial error parameter and the dimension as constants, we show that our procedure has sample complexity asymptotically optimal in the final error parameter. Our protocol has a simple recursive structure that can be applied when the states are provided one at a time in a streaming fashion, requiring only a small quantum memory to implement.

• The Generalized Capacity of a Quantum Channel

  Zahra Baghali Khanian

  arXiv:2309.14141 · September 25, 2023 · quant-ph

  Abstract

  The transmission of classical information over a classical channel gave rise to the classical capacity theorem with the optimal rate in terms of the classical mutual information. Despite classical information being a subset of quantum information, the rate of the quantum capacity problem is expressed in terms of the coherent information, which does not mathematically generalize the classical mutual information. Additionally, there are multiple capacity theorems with distinct formulas when dealing with transmitting information over a noisy quantum channel. This leads to the question of what constitutes a mathematically accurate quantum generalization of classical mutual information and whether there exists a quantum task that directly extends the classical capacity problem. In this paper, we address these inquiries by introducing a quantity called the generalized information, which serves as a mathematical extension encompassing both classical mutual information and coherent information. We define a transmission task, which includes as specific instances both classical information and quantum information capacity problems, and show that the transmission capacity of this task is characterized by the generalized information.

• Tight bounds on Pauli channel learning without entanglement

  Senrui Chen, Changhun Oh, Sisi Zhou, Hsin-Yuan Huang, Liang Jiang

  arXiv:2309.13461 · September 23, 2023 · quant-ph · Phys. Rev. Lett. 132, 180805 (2024) · doi

  Abstract

  Quantum entanglement is a crucial resource for learning properties from nature, but a precise characterization of its advantage can be challenging. In this work, we consider learning algorithms without entanglement to be those that only utilize states, measurements, and operations that are separable between the main system of interest and an ancillary system. Interestingly, we show that these algorithms are equivalent to those that apply quantum circuits on the main system interleaved with mid-circuit measurements and classical feedforward. Within this setting, we prove a tight lower bound for Pauli channel learning without entanglement that closes the gap between the best-known upper and lower bound. In particular, we show that $Θ(2^n\varepsilon^{-2})$ rounds of measurements are required to estimate each eigenvalue of an $n$-qubit Pauli channel to $\varepsilon$ error with high probability when learning without entanglement. In contrast, a learning algorithm with entanglement only needs $Θ(\varepsilon^{-2})$ copies of the Pauli channel. The tight lower bound strengthens the foundation for an experimental demonstration of entanglement-enhanced advantages for Pauli noise characterization.

• Classical simulation of peaked shallow quantum circuits

  Sergey Bravyi, David Gosset, Yinchen Liu

  arXiv:2309.08405 · September 15, 2023 · quant-ph

  Abstract

  An $n$-qubit quantum circuit is said to be peaked if it has an output probability that is at least inverse-polynomially large as a function of $n$. We describe a classical algorithm with quasipolynomial runtime $n^{O(\log{n})}$ that approximately samples from the output distribution of a peaked constant-depth circuit. We give even faster algorithms for circuits composed of nearest-neighbor gates on a $D$-dimensional grid of qubits, with polynomial runtime $n^{O(1)}$ if $D=2$ and almost-polynomial runtime $n^{O(\log{\log{n}})}$ for $D>2$. Our sampling algorithms can be used to estimate output probabilities of shallow circuits to within a given inverse-polynomial additive error, improving previously known methods. As a simple application, we obtain a quasipolynomial algorithm to estimate the magnitude of the expected value of any Pauli observable in the output state of a shallow circuit (which may or may not be peaked). This is a dramatic improvement over the prior state-of-the-art algorithm which had an exponential scaling in $\sqrt{n}$.

• Classifying fermionic states via many-body correlation measures

  Mykola Semenyakin, Yevheniia Cheipesh, Yaroslav Herasymenko

  arXiv:2309.07956 · September 14, 2023 · quant-ph · Quantum 9, 1705 (2025) · doi

  Abstract

  Understanding the structure of quantum correlations in a many-body system is key to its computational treatment. For fermionic systems, correlations can be defined as deviations from Slater determinant states. The link between fermionic correlations and efficient computational physics methods is actively studied but remains ambiguous. We make progress in establishing this connection mathematically. In particular, we find a rigorous classification of states relative to $k$-fermion correlations, which admits a computational physics interpretation. Correlations are captured by a measure $ω_k$, a function of $k$-fermion reduced density matrix that we call twisted purity. A condition $ω_k=0$ for a given $k$ puts the state in a class $G_k$ of correlated states. Sets $G_k$ are nested in $k$, and Slater determinants correspond to $k = 1$. Classes $G_{k=O(1)}$ are shown to be physically relevant, as $ω_k$ vanishes or nearly vanishes for truncated configuration-interaction states, perturbation series around Slater determinants, and some nonperturbative eigenstates of the 1D Hubbard model. For each $k = O(1)$, we give an explicit ansatz with a polynomial number of parameters that covers all states in $G_k$. Potential applications of this ansatz and its connections to the coupled-cluster wavefunction are discussed.

• Astronomical interferometry using continuous variable quantum teleportation

  Yunkai Wang, Yujie Zhang, Virginia O. Lorenz

  arXiv:2308.12851 · August 24, 2023 · quant-ph

  Abstract

  We propose a method to build an astronomical interferometer using continuous variable quantum teleportation to overcome the transmission loss between distant telescopes. The scheme relies on two-mode squeezed states shared by distant telescopes as entanglement resources, which are distributed using continuous variable quantum repeaters. We find the optimal measurement on the teleported states, which uses beam-splitters and photon-number-resolved detection. Compared to prior proposals relying on discrete states, our scheme has the advantages of using linear optics to implement the scheme without wasting stellar photons, and making use of multiphoton events, which are regarded as noise in previous discrete schemes. We also outline the parameter regimes in which our scheme outperforms the direct detection method, schemes utilizing distributed discrete-variable entangled states, and local heterodyne techniques.

• Correlation harvesting between particle detectors in uniform motion

  Lana Bozanic, Manar Naeem, Kensuke Gallock-Yoshimura, Robert B. Mann

  arXiv:2308.06329 · August 11, 2023 · quant-ph

  Abstract

  We investigate the correlation harvesting protocol using two Unruh-DeWitt particle detectors moving along four classes of uniformly accelerated trajectories categorized by Letaw: linear, catenary, cusped, and circular motions. For each trajectory, two types of configurations are carried out: one possesses a stationary (time-translation invariant) Wightman function and the other is nonstationary. We find that detectors undergoing linear, catenary, and cusped motions gain fewer correlations in the nonstationary configurations compared to those in stationary configurations. Detectors in circular motion have similar behavior in both configurations. We discuss the relative suppression of correlation harvesting due to high acceleration for each case. Remarkably we find that under certain circumstances detectors in both linear and circular states of motion can harvest genuine (non-communication assisted) entanglement even though they are in causal contact.

• Exploring causality in braneworld/cutoff holography via holographic scattering

  Takato Mori, Beni Yoshida

  arXiv:2308.00739 · August 1, 2023 · hep-th · JHEP10(2023)104 · doi

  Abstract

  Holography with branes and/or cutoff surfaces presents a promising approach to studying quantum gravity beyond asymptotically anti-de Sitter spacetimes. However, this generalized holography is known to face several inconsistencies, including potential violations of causality and fundamental entropic inequalities. In this work, we address these challenges by investigating the bulk scattering process and its holographic realization. Specifically, we propose that the information on a brane/cutoff surface $Q$ propagates according to the induced light cones originating from a fictitious asymptotic boundary behind $Q$, rather than the conventional ones originating from a point on $Q$. Additionally, we establish the validity of the connected wedge theorem for generalized holography with induced light cones. We also demonstrate that entropic inequalities remain valid within the induced causal diamonds. While the induced light cone seemingly permits superluminal signaling, we argue that this causality violation can be an artifact of state preparation for radially propagating excitations, rather than local operator excitations on $Q$.

• Complexity for one-dimensional discrete time quantum walk circuits

  Aranya Bhattacharya, Himanshu Sahu, Ahmadullah Zahed, Kallol Sen

  arXiv:2307.13450 · July 25, 2023 · quant-ph · Phys. Rev. A 109, 022223 (2024) · doi

  Abstract

  We compute the complexity for the mixed state density operator derived from a one-dimensional discrete-time quantum walk (DTQW). The complexity is computed using a two-qubit quantum circuit obtained from canonically purifying the mixed state. We demonstrate that the Nielson complexity for the unitary evolution oscillates around a mean circuit depth of $k$. Further, the complexity of the step-wise evolution operator grows cumulatively and linearly with the steps. From a quantum circuit perspective, this implies a succession of circuits of (near) constant depth to be applied to reach the final state.

• Fermionic Hamiltonians without trivial low-energy states

  Yaroslav Herasymenko, Anurag Anshu, Barbara Terhal, Jonas Helsen

  arXiv:2307.13730 · July 25, 2023 · quant-ph

  Abstract

  We construct local fermionic Hamiltonians with no low-energy trivial states (NLTS), providing a fermionic counterpart to the NLTS theorem. Distinctly from the qubit case, we define trivial states via finite-depth $\textit{fermionic}$ quantum circuits. We furthermore allow free access to Gaussian fermionic operations, provided they involve at most $O(n)$ ancillary fermions. The desired fermionic Hamiltonian can be constructed using any qubit Hamiltonian which itself has the NLTS property via well-spread distributions over bitstrings, such as the construction in [Anshu, Breuckmann, Nirkhe, STOC 2023]. We define a fermionic analogue of the class quantum PCP and discuss its relation with the qubit version.

• The Schmidt rank for the commuting operator framework

  Lauritz van Luijk, René Schwonnek, Alexander Stottmeister, Reinhard F. Werner

  arXiv:2307.11619 · July 21, 2023 · quant-ph · Commun. Math. Phys. 405, 152 (2024) · doi

  Abstract

  In quantum information theory, the Schmidt rank is a fundamental measure for the entanglement dimension of a pure bipartite state. Its natural definition uses the Schmidt decomposition of vectors on bipartite Hilbert spaces, which does not exist (or at least is not canonically given) if the observable algebras of the local systems are allowed to be general C*-algebras. In this work, we generalize the Schmidt rank to the commuting operator framework where the joint system is not necessarily described by the minimal tensor product but by a general bipartite algebra. We give algebraic and operational definitions for the Schmidt rank and show their equivalence. We analyze bipartite states and compute the Schmidt rank in several examples: The vacuum in quantum field theory, Araki-Woods-Powers states, as well as ground states and translation invariant states on spin chains which are viewed as bipartite systems for the left and right half chains. We conclude with a list of open problems for the commuting operator framework.

• Graphical CSS Code Transformation Using ZX Calculus

  Jiaxin Huang, Sarah Meng Li, Lia Yeh, Aleks Kissinger, Michele Mosca, Michael Vasmer

  arXiv:2307.02437 · July 5, 2023 · quant-ph · EPTCS 384, 2023, pp. 1-19 · doi

  Abstract

  In this work, we present a generic approach to transform CSS codes by building upon their equivalence to phase-free ZX diagrams. Using the ZX calculus, we demonstrate diagrammatic transformations between encoding maps associated with different codes. As a motivating example, we give explicit transformations between the Steane code and the quantum Reed-Muller code, since by switching between these two codes, one can obtain a fault-tolerant universal gate set. To this end, we propose a bidirectional rewrite rule to find a (not necessarily transversal) physical implementation for any logical ZX diagram in any CSS code. Then we focus on two code transformation techniques: code morphing, a procedure that transforms a code while retaining its fault-tolerant gates, and gauge fixing, where complimentary codes can be obtained from a common subsystem code (e.g., the Steane and the quantum Reed-Muller codes from the [[15,1,3,3]] code). We provide explicit graphical derivations for these techniques and show how ZX and graphical encoder maps relate several equivalent perspectives on these code-transforming operations.

• Effect of non-unital noise on random circuit sampling

  Bill Fefferman, Soumik Ghosh, Michael Gullans, Kohdai Kuroiwa, Kunal Sharma

  arXiv:2306.16659 · June 29, 2023 · quant-ph

  Abstract

  In this work, drawing inspiration from the type of noise present in real hardware, we study the output distribution of random quantum circuits under practical non-unital noise sources with constant noise rates. We show that even in the presence of unital sources like the depolarizing channel, the distribution, under the combined noise channel, never resembles a maximally entropic distribution at any depth. To show this, we prove that the output distribution of such circuits never anticoncentrates $—$ meaning it is never too "flat" $—$ regardless of the depth of the circuit. This is in stark contrast to the behavior of noiseless random quantum circuits or those with only unital noise, both of which anticoncentrate at sufficiently large depths. As consequences, our results have interesting algorithmic implications on both the hardness and easiness of noisy random circuit sampling, since anticoncentration is a critical property exploited by both state-of-the-art classical hardness and easiness results.

• Convergence of Dynamics on Inductive Systems of Banach Spaces

  Lauritz van Luijk, Alexander Stottmeister, Reinhard F. Werner

  arXiv:2306.16063 · June 28, 2023 · math-ph · Annales Henri Poincaré (2024) · doi

  Abstract

  Many features of physical systems, both qualitative and quantitative, become sharply defined or tractable only in some limiting situation. Examples are phase transitions in the thermodynamic limit, the emergence of classical mechanics from quantum theory at large action, and continuum quantum field theory arising from renormalization group fixed points. It would seem that few methods can be useful in such diverse applications. However, we here present a flexible modeling tool for the limit of theories: soft inductive limits constituting a generalization of inductive limits of Banach spaces. In this context, general criteria for the convergence of dynamics will be formulated, and these criteria will be shown to apply in the situations mentioned and more.

• Relating non-local quantum computation to information theoretic cryptography

  Rene Allerstorfer, Harry Buhrman, Alex May, Florian Speelman, Philip Verduyn Lunel

  arXiv:2306.16462 · June 28, 2023 · quant-ph · Quantum 8, 1387 (2024) · doi

  Abstract

  Non-local quantum computation (NLQC) is a cheating strategy for position-verification schemes, and has appeared in the context of the AdS/CFT correspondence. Here, we connect NLQC to the wider context of information theoretic cryptography by relating it to a number of other cryptographic primitives. We show one special case of NLQC, known as $f$-routing, is equivalent to the quantum analogue of the conditional disclosure of secrets (CDS) primitive, where by equivalent we mean that a protocol for one task gives a protocol for the other with only small overhead in resource costs. We further consider another special case of position verification, which we call coherent function evaluation (CFE), and show CFE protocols induce similarly efficient protocols for the private simultaneous message passing (PSM) scenario. By relating position-verification to these cryptographic primitives, a number of results in the cryptography literature give new implications for NLQC, and vice versa. These include the first sub-exponential upper bounds on the worst case cost of $f$-routing of $2^{O(\sqrt{n\log n})}$ entanglement, the first example of an efficient $f$-routing strategy for a problem believed to be outside $P/poly$, linear lower bounds on entanglement for CDS in the quantum setting, linear lower bounds on communication cost of CFE, and efficient protocols for CDS in the quantum setting for functions that can be computed with quantum circuits of low $T$ depth.

• Measurement-based infused circuits for variational quantum eigensolvers

  Albie Chan, Zheng Shi, Luca Dellantonio, Wolfgang Dür, Christine A. Muschik

  arXiv:2305.19200 · May 30, 2023 · quant-ph · Phys. Rev. Lett. 132, 240601 (2024) · doi

  Abstract

  Variational quantum eigensolvers (VQEs) are successful algorithms for studying physical systems on quantum computers. Recently, they were extended to the measurement-based model of quantum computing, bringing resource graph states and their advantages into the realm of quantum simulation. In this work, we incorporate such ideas into traditional VQE circuits. This enables novel problem-informed designs and versatile implementations of many-body Hamiltonians. We showcase our approach on real superconducting quantum computers by performing VQE simulations of testbed systems including the perturbed planar code, Z2 lattice gauge theory, 1D quantum chromodynamics, and the LiH molecule.

• Open system approach to Neutrino oscillations in a quantum walk framework

  Himanshu Sahu, C. M. Chandrashekar

  arXiv:2305.13923 · May 23, 2023 · quant-ph · Quantum Information Processing 23, 7 (2024) · doi

  Abstract

  Quantum simulation provides a computationally-feasible approach to model and study many problems in chemistry, condensed-matter physics, or high-energy physics where quantum phenomenon define the systems behaviour. In high-energy physics, quite a few possible applications are investigated in the context of gauge theories and their application to dynamic problems, topological problems, high-baryon density configurations, or collective neutrino oscillations. In particular, schemes for simulating neutrino oscillations are proposed using a quantum walk framework. In this study, we approach the problem of simulating neutrino oscillation from the perspective of open quantum systems by treating the position space of quantum walk as environment. We have obtained the recurrence relation for Kraus operator which is used to represent the dynamics of the neutrino flavor change in the form of reduced coin states. We establish a connection between the dynamics of reduced coin state and neutrino phenomenology, enabling one to fix the simulation parameters for a given neutrino experiment and reduces the need for extended position space to simulate neutrino oscillations. We have also studied the behavior of linear entropy as a measure of entanglement between different flavors in the same framework.

• Suggestions of decreasing dark energy from supernova and BAO data

  Mark Van Raamsdonk, Chris Waddell

  arXiv:2305.04946 · May 8, 2023 · astro-ph.CO

  Abstract

  The potential energy from a time-dependent scalar field provides a possible explanation for the observed cosmic acceleration. In this paper, we investigate how data from supernova and bary acoustic oscillation surveys constrain the possible evolution of a single scalar field over the period of time (roughly half the age of the universe) for which these data are available. Taking a linear approximation to the scalar potential $V(φ) = V_0 + V_1 φ$ around the present value, a likelihood analysis appears to significantly prefer models with a decreasing potential energy at present, with approximately $99.99 \%$ of the $\exp(-χ^2/2)$ distribution having $V_1 > 0$ in a convention where $\dotφ \le 0$ at present. The models favoured by the distribution typically have an order one decrease $\langle |{\rm Range}[V(φ(t))] / V(t_0)| \rangle \approx 0.36$ in the scalar potential energy over the time frame corresponding to $z < 2$. According to the likelihood analysis, the $Λ$CDM model with no variation in dark energy appears to be significantly disfavoured in the context of the linear potential model, but this should be interpreted cautiously since model selection criteria that make use of $Δχ^2$ while ignoring parameter space volumes still favour $Λ$CDM. Working with a second order approximation to the potential, the supernova data can be fit well for a wide range of possible potentials, including models where the universe has already stopped accelerating.

• Neural-Shadow Quantum State Tomography

  Victor Wei, W. A. Coish, Pooya Ronagh, Christine A. Muschik

  arXiv:2305.01078 · May 1, 2023 · quant-ph · Phys. Rev. Research 6, 023250 (2024) · doi

  Abstract

  Quantum state tomography (QST) is the art of reconstructing an unknown quantum state through measurements. It is a key primitive for developing quantum technologies. Neural network quantum state tomography (NNQST), which aims to reconstruct the quantum state via a neural network ansatz, is often implemented via a basis-dependent cross-entropy loss function. State-of-the-art implementations of NNQST are often restricted to characterizing a particular subclass of states, to avoid an exponential growth in the number of required measurement settings. To provide a more broadly applicable method for efficient state reconstruction, we present "neural-shadow quantum state tomography" (NSQST)-an alternative neural network-based QST protocol that uses infidelity as the loss function. The infidelity is estimated using the classical shadows of the target state. Infidelity is a natural choice for training loss, benefiting from the proven measurement sample efficiency of the classical shadow formalism. Furthermore, NSQST is robust against various types of noise without any error mitigation. We numerically demonstrate the advantage of NSQST over NNQST at learning the relative phases of three target quantum states of practical interest, as well as the advantage over direct shadow estimation. NSQST greatly extends the practical reach of NNQST and provides a novel route to effective quantum state tomography.

• Sufficiency of Rényi divergences

  Niklas Galke, Lauritz van Luijk, Henrik Wilming

  arXiv:2304.12989 · April 25, 2023 · quant-ph · IEEE Transactions on Information Theory, vol. 70 (7), pp. 5057-5076, (2024) · doi

  Abstract

  A set of classical or quantum states is equivalent to another one if there exists a pair of classical or quantum channels mapping either set to the other one. For dichotomies (pairs of states), this is closely connected to (classical or quantum) Rényi divergences (RD) and the data-processing inequality: If a RD remains unchanged when a channel is applied to the dichotomy, then there is a recovery channel mapping the image back to the initial dichotomy. Here, we prove for classical dichotomies that equality of the RDs alone is already sufficient for the existence of a channel in any of the two directions and discuss some applications. In the quantum case, all families of quantum RDs are seen to be insufficient because they cannot detect anti-unitary transformations. Thus, including anti-unitaries, we pose the problem of finding a sufficient family. It is shown that the Petz and maximal quantum RD are still insufficient in this more general sense and we provide evidence for sufficiency of the minimal quantum RD. As a side result of our techniques, we obtain an infinite list of inequalities fulfilled by the classical, the Petz quantum, and the maximal quantum RDs. These inequalities are not true for the minimal quantum RDs. Our results further imply that any sufficient set of conditions for state transitions in the resource theory of athermality must be able to detect time-reversal.

• Non-isometric codes for the black hole interior from fundamental and effective dynamics

  Oliver DeWolfe, Kenneth Higginbotham

  arXiv:2304.12345 · April 24, 2023 · hep-th

  Abstract

  We introduce a new holographic map for encoding black hole interiors by including both fundamental and effective dynamics. This holographic map is constructed by evolving a state in the effective, semiclassical gravity description of the interior backwards in time to pull the degrees of freedom outside the black hole, before evolving forwards in time in the fundamental description. We show this ``backwards-forwards'' map is equivalent to a post-selection map of the type introduced by Akers, Engelhardt, Harlow, Penington, and Vardhan, and in the case of trivial effective interactions reduces to their model, while providing a suitable generalization when those interactions are nontrivial. We show the map is equivariant with respect to time evolution, and independent of any interactions outside the black hole. This construction includes interactions with an infaller in a way that preserves the unitarity of black hole evolution exactly and does not allow for superpolynomial computational complexity.

• Quantum correlated photons via a passive nonlinear microcavity

  Mengdi Zhao, Yunkai Wang, Shanhui Fan, Kejie Fang

  arXiv:2304.11676 · April 23, 2023 · quant-ph

  Abstract

  Photons, by nature, typically do not exhibit interactions with each other. Creating photon-photon interactions holds immense importance in both fundamental physics and quantum technologies. Currently, such interactions have only been achieved indirectly as mediated by atomic-like quantum emitters with resonant photon-atom interactions. However, the use of these indirect interactions presents substantial fundamental challenges that impede scaling and practical applications. Here we demonstrate creation of non-classical photon correlations, including photon anti-bunching, via a passive InGaP photonic integrated circuit. Our approach employs the quantum interference between uncorrelated light and the two-photon bound state, the latter of which arises from the $χ^{(2)}$-mediated photon interaction. Our work opens a new route in controlling quantum light by harnessing highly-engineerable bulk optical nonlinearities, which has significant implications for nonlinear optical quantum information processing and quantum networking.

• Non-local computation and the black hole interior

  Alex May, Michelle Xu

  arXiv:2304.11184 · April 21, 2023 · hep-th

  Abstract

  In a two sided black hole, systems falling in from opposite asymptotic regions can meet inside the black hole and interact. This is the case even while the two CFTs describing each asymptotic region are non-interacting. Here, we relate these behind the horizon interactions to non-local quantum computations. This gives a quantum circuit perspective on these interactions, which applies whenever the interaction occurs in the past of a certain extremal surface that sits inside the black hole and in arbitrary dimension. Whenever our perspective applies, we obtain a boundary signature for these interior collisions which is stated in terms of the mutual information. We further revisit the connection discussed earlier between bulk interactions in one sided AdS geometries and non-local computation, and recycle some of our techniques to offer a new perspective on making that connection precise.

• Constraints on physical computers in holographic spacetimes

  Aleksander M. Kubicki, Alex May, David Pérez-Garcia

  arXiv:2304.09900 · April 19, 2023 · hep-th · SciPost Phys. 16, 024 (2024) · doi

  Abstract

  Within the setting of the AdS/CFT correspondence, we ask about the power of computers in the presence of gravity. We show that there are computations on $n$ qubits which cannot be implemented inside of black holes with entropy less than $O(2^n)$. To establish our claim, we argue computations happening inside the black hole must be implementable in a programmable quantum processor, so long as the inputs and description of the unitary to be run are not too large. We then prove a bound on quantum processors which shows many unitaries cannot be implemented inside the black hole, and further show some of these have short descriptions and act on small systems. These unitaries with short descriptions must be computationally forbidden from happening inside the black hole.

• Enhancing Quantum Computation via Superposition of Quantum Gates

  Jorge Miguel-Ramiro, Zheng Shi, Luca Dellantonio, Albie Chan, Christine A. Muschik, Wolfgang Dür

  arXiv:2304.08529 · April 17, 2023 · quant-ph · Phys. Rev. A 108, 062604 (2023) · doi

  Abstract

  Overcoming the influence of noise and imperfections in quantum devices is one of the main challenges for viable quantum applications. In this article, we present different protocols, which we denote as "superposed quantum error mitigation", that enhance the fidelity of single gates or entire computations by performing them in coherent superposition. Our results demonstrate that via our methods, significant noise suppression can be achieved for most kinds of decoherence and standard experimental parameter regimes. Our protocols can be either deterministic, such that the outcome is never post-selected, or probabilistic, in which case the resulting state must be discarded unless a well-specified condition is met. By using sufficiently many resources and working under broad assumptions, our methods can yield the desired output state with unit fidelity. Finally, we analyze our approach for gate-based, measurement-based and interferometric-based models, demonstrating the applicability in all cases and investigating the fundamental mechanisms they rely upon.

• Superposed Quantum Error Mitigation

  Jorge Miguel-Ramiro, Zheng Shi, Luca Dellantonio, Albie Chan, Christine A. Muschik, Wolfgang Dür

  arXiv:2304.08528 · April 17, 2023 · quant-ph · Phys. Rev. Lett. 131, 230601 (2023) · doi

  Abstract

  Overcoming the influence of noise and imperfections is a major challenge in quantum computing. Here, we present an approach based on applying a desired unitary computation in superposition between the system of interest and some auxiliary states. We demonstrate, numerically and on the IBM Quantum Platform, that parallel applications of the same operation lead to significant noise mitigation when arbitrary noise processes are considered. We first design probabilistic implementations of our scheme that are plug and play, independent of the noise characteristic and require no postprocessing. We then enhance the success probability (up to deterministic) using adaptive corrections. We provide an analysis of our protocol performance and demonstrate that unit fidelity can be achieved asymptotically. Our approaches are suitable to both standard gate-based and measurement-based computational models.

• A simple criterion for essential self-adjointness of Weyl pseudodifferential operators

  Robert Fulsche, Lauritz van Luijk

  arXiv:2304.07153 · April 14, 2023 · math-ph · Journal of Pseudo-Differential Operators and Applications 16, 38 (2025) · doi

  Abstract

  We prove a new criterion for the essential self-adjointness of pseudodifferential operators that does not involve ellipticity-type assumptions. For example, we show that self-adjointness holds in case the symbol is $C^{2d+3}$ with derivatives of order two and higher being uniformly bounded. These results also apply to hermitian operator-valued symbols on infinite-dimensional Hilbert spaces, which are important to applications in physics. Our method relies on a phase space differential calculus for quadratic forms on $L^2(\mathbb{R}^d)$, Calderón-Vaillancourt type theorems, and a recent self-adjointness result for Toeplitz operators on the Segal-Bargmann space.

• Exact and lower bounds for the quantum speed limit in finite dimensional systems

  Mattias T. Johnsson, Lauritz van Luijk, Daniel Burgarth

  arXiv:2304.06617 · April 13, 2023 · quant-ph · Phys. Rev. A 108, 052403 (2023) · doi

  Abstract

  A fundamental problem in quantum engineering is determining the lowest time required to ensure that all possible unitaries can be generated with the tools available, which is one of a number of possible quantum speed limits. We examine this problem from the perspective of quantum control, where the system of interest is described by a drift Hamiltonian and set of control Hamiltonians. Our approach uses a combination of Lie algebra theory, Lie groups and differential geometry, and formulates the problem in terms of geodesics on a differentiable manifold. We provide explicit lower bounds on the quantum speed limit for the case of an arbitrary drift, requiring only that the control Hamiltonians generate a topologically closed subgroup of the full unitary group, and formulate criteria as to when our expression for the speed limit is exact and not merely a lower bound. These analytic results are then tested and confirmed using a numerical optimization scheme. Finally we extend the analysis to find a lower bound on the quantum speed limit in the common case where the system is described by a drift Hamiltonian and a single control Hamiltonian.

• On Krylov complexity in open systems: an approach via bi-Lanczos algorithm

  Aranya Bhattacharya, Pratik Nandy, Pingal Pratyush Nath, Himanshu Sahu

  arXiv:2303.04175 · March 7, 2023 · quant-ph · JHEP 12 (2023) 066 · doi

  Abstract

  Continuing the previous initiatives arXiv: 2207.05347 and arXiv: 2212.06180, we pursue the exploration of operator growth and Krylov complexity in dissipative open quantum systems. In this paper, we resort to the bi-Lanczos algorithm generating two bi-orthogonal Krylov spaces, which individually generate non-orthogonal subspaces. Unlike the previously studied Arnoldi iteration, this algorithm renders the Lindbladian into a purely tridiagonal form, thus opening up a possibility to study a wide class of dissipative integrable and chaotic systems by computing Krylov complexity at late times. Our study relies on two specific systems, the dissipative transverse-field Ising model (TFIM) and the dissipative interacting XXZ chain. We find that, for the weak coupling, initial Lanczos coefficients can efficiently distinguish integrable and chaotic evolution before the dissipative effect sets in, which results in more fluctuations in higher Lanczos coefficients. This results in the equal saturation of late-time complexity for both integrable and chaotic cases, making the notion of late-time chaos dubious.

• Achieving metrological limits using ancilla-free quantum error-correcting codes

  Sisi Zhou, Argyris Giannisis Manes, Liang Jiang

  arXiv:2303.00881 · March 2, 2023 · quant-ph · Physical Review A 109, 042406 (2023) · doi

  Abstract

  Quantum error correction (QEC) is theoretically capable of achieving the ultimate estimation limits in noisy quantum metrology. However, existing quantum error-correcting codes designed for noisy quantum metrology generally exploit entanglement between one probe and one noiseless ancilla of the same dimension, and the requirement of noiseless ancillas is one of the major obstacles to implementing the QEC metrological protocol in practice. Here we successfully lift this requirement by explicitly constructing two types of multi-probe quantum error-correcting codes, where the first one utilizes a negligible amount of ancillas and the second one is ancilla-free. Specifically, we consider Hamiltonian estimation under Markovian noise and show that (i)~when the Heisenberg limit (HL) is achievable, our new codes can achieve the HL and its optimal asymptotic coefficient; (ii)~when only the standard quantum limit (SQL) is achievable (even with arbitrary adaptive quantum strategies), the optimal asymptotic coefficient of the SQL is also achievable by our new codes under slight modifications.

• Quantum complexity of the Kronecker coefficients

  Sergey Bravyi, Anirban Chowdhury, David Gosset, Vojtech Havlicek, Guanyu Zhu

  arXiv:2302.11454 · February 22, 2023 · quant-ph · PRX Quantum, vol. 5, issue 1, (Feb 2024), pp 010329

  Abstract

  Whether or not the Kronecker coefficients of the symmetric group count some set of combinatorial objects is a longstanding open question. In this work we show that a given Kronecker coefficient is proportional to the rank of a projector that can be measured efficiently using a quantum computer. In other words a Kronecker coefficient counts the dimension of the vector space spanned by the accepting witnesses of a QMA verifier, where QMA is the quantum analogue of NP. This implies that approximating the Kronecker coefficients to within a given relative error is not harder than a certain natural class of quantum approximate counting problems that captures the complexity of estimating thermal properties of quantum many-body systems. A second consequence is that deciding positivity of Kronecker coefficients is contained in QMA, complementing a recent NP-hardness result of Ikenmeyer, Mulmuley and Walter. We obtain similar results for the related problem of approximating row sums of the character table of the symmetric group. Finally, we discuss an efficient quantum algorithm that approximates normalized Kronecker coefficients to inverse-polynomial additive error.

• Quantum Computing Toolkit From Nuts and Bolts to Sack of Tools

  Himanshu Sahu, Hari Prabhat Gupta

  arXiv:2302.08884 · February 17, 2023 · quant-ph

  Abstract

  Quantum computing has the potential to provide exponential performance benefits in processing over classical computing. It utilizes quantum mechanics phenomena (such as superposition, entanglement, and interference) to solve a computational problem. It can explore atypical patterns over data that classical computers can't perform efficiently. Quantum computers are in the nascent stage of development and are noisy due to decoherence, i.e., quantum bits deteriorate with environmental interactions. It will take a long time for quantum computers to achieve fault tolerance although quantum algorithms can be developed in advance. Heavy investment in developing quantum hardware, software development kits, and simulators has led to multiplicity of quantum development tools. Selection of a suitable development platform requires a proper understanding of the capabilities and limitations of these tools. Although a comprehensive comparison of the different quantum development tools would be of great value, to the best of our knowledge, no such extensive study is currently available.

• Covariant catalysis requires correlations and good quantum reference frames degrade little

  Lauritz van Luijk, Reinhard F. Werner, Henrik Wilming

  arXiv:2301.09877 · January 24, 2023 · quant-ph · Quantum 7, 1166 (2023) · doi

  Abstract

  Catalysts are quantum systems that open up dynamical pathways between quantum states which are otherwise inaccessible under a given set of operational restrictions while, at the same time, they do not change their quantum state. We here consider the restrictions imposed by symmetries and conservation laws, where any quantum channel has to be covariant with respect to the unitary representation of a symmetry group, and present two results. First, for an exact catalyst to be useful, it has to build up correlations to either the system of interest or the degrees of freedom dilating the given process to covariant unitary dynamics. This explains why catalysts in pure states are useless. Second, if a quantum system ("reference frame") is used to simulate to high precision unitary dynamics (which possibly violates the conservation law) on another system via a global, covariant quantum channel, then this channel can be chosen so that the reference frame is approximately catalytic. In other words, a reference frame that simulates unitary dynamics to high precision degrades only very little.

• Averaging gate approximation error and performance of Unitary Coupled Cluster ansatz in Pre-FTQC Era

  Kohdai Kuroiwa, Yuya O. Nakagawa

  arXiv:2301.04150 · January 10, 2023 · quant-ph · Quantum 9, 1800 (2025) · doi

  Abstract

  Fault-tolerant quantum computation (FTQC) is essential to implement quantum algorithms in a noise-resilient way, and thus to enjoy advantages of quantum computers even with presence of noise. In FTQC, a quantum circuit is decomposed into universal gates that can be fault-tolerantly implemented, for example, Clifford+T gates. Here, T gate is usually regarded as an essential resource for quantum computation because its action cannot be simulated efficiently on classical computers and it is experimentally difficult to implement fault-tolerantly. Practically, it is highly likely that only a limited number of T gates are available in the near future. Pre-FTQC era, due to the constraint on available resources, it is vital to precisely estimate the decomposition error of a whole circuit. In this paper, we propose that the Clifford+T decomposition error for a given quantum circuit containing a large number of quantum gates can be modeled as the depolarizing noise by averaging the decomposition error for each quantum gate in the circuit, and our model provides more accurate error estimation than the naive estimation. We exemplify this by taking unitary coupled-cluster (UCC) ansatz used in the applications of quantum computers to quantum chemistry as an example. We theoretically evaluate the approximation error of UCC ansatz when decomposed into Clifford+T gates, and the numerical simulation for a wide variety of molecules verified that our model well explains the total decomposition error of the ansatz. Our results enable the precise and efficient usage of quantum resources in the early-stage applications of quantum computers and fuel further research towards what quantum computation can achieve in the upcoming future.