Papers 2022

• Quantum Car-Parrinello Molecular Dynamics: A Cost-Efficient Molecular Simulation Method on Near-Term Quantum Computers

  Kohdai Kuroiwa, Takahiro Ohkuma, Hirokazu Sato, Ryosuke Imai

  arXiv:2212.11921 · December 22, 2022 · quant-ph

  Abstract

  In this paper, we propose a cost-reduced method for finite-temperature molecular dynamics on a near-term quantum computer, Quantum Car-Parrinello molecular dynamics (QCPMD). One of the most promising applications of near-term quantum computers is quantum chemistry. It has been expected that simulations of molecules via molecular dynamics can be also efficiently performed on near-term quantum computers by applying a promising near-term quantum algorithm of the variational quantum eigensolver (VQE). However, this method may demand considerable computational costs to achieve a sufficient accuracy, and otherwise, statistical noise can significantly affect the results. To resolve these problems, we invent an efficient method for molecular time evolution inspired by Car-Parrinello method. In our method, parameters characterizing the quantum state evolve based on equations of motion instead of being optimized. Furthermore, by considering Langevin dynamics, we can make use of the intrinsic statistical noise. As an application of QCPMD, we propose an efficient method for vibrational frequency analysis of molecules in which we can use the results of the molecular dynamics calculated by QCPMD. Numerical experiments show that our method can precisely simulate the Langevin dynamics at the equilibrium state, and we can successfully predict a given molecule's eigen frequencies. Furthermore, in the numerical simulation, our method achieves a substantial cost reduction compared with molecular dynamics using the VQE. Our method achieves an efficient computation without using widely employed method of the VQE. In this sense, we open up a new possibility of molecular dynamics on near-term quantum computers. We expect our results inspire further invention of efficient near-term quantum algorithms for simulation of molecules.

• Area law for steady states of detailed-balance local Lindbladians

  Raz Firanko, Moshe Goldstein, Itai Arad

  arXiv:2212.10061 · December 20, 2022 · quant-ph · doi

  Abstract

  We study steady-states of quantum Markovian processes whose evolution is described by local Lindbladians. We assume that the Lindbladian is gapped and satisfies quantum detailed balance with respect to a unique full-rank steady state $σ$. We show that under mild assumptions on the Lindbladian terms, which can be checked efficiently, the Lindbladian can be mapped to a local Hamiltonian on a doubled Hilbert space that has the same spectrum, and a ground state that is the vectorization of $σ^{1/2}$. Consequently, we can use Hamiltonian complexity tools to study the steady states of such open systems. In particular, we show an area-law in the mutual information for the steady state of such 1D systems, together with a tensor-network representation that can be found efficiently.

• Ultrafast Entanglement Dynamics in Monitored Quantum Circuits

  Shengqi Sang, Zhi Li, Timothy H. Hsieh, Beni Yoshida

  arXiv:2212.10634 · December 20, 2022 · cond-mat.stat-mech · doi

  Abstract

  Projective measurement, a basic operation in quantum mechanics, can induce seemingly nonlocal effects. In this work, we analyze such effects in many-body systems by studying the non-equilibrium dynamics of weakly monitored quantum circuits, focusing on entanglement generation and information spreading. We find that, due to measurements, the entanglement dynamics in monitored circuits is indeed "faster" than that of unitary ones in several ways. Specifically, we find that a pair of well-separated regions can become entangled in a time scale $\ell^{2/3}$, sub-linear in their distance $\ell$. For the case of Clifford monitored circuits, this originates from super-ballistically growing stabilizer generators of the evolving state. In addition, we find initially local information can spread super-ballistically as $t^{3/2}$. Furthermore, by viewing the dynamics as a dynamical encoding process, we show that the super-ballistic growing length scale relates to an encoding time that is sublinear in system size. To quantify the information dynamics, we develop a formalism generalizing operator spreading to non-unitary dynamics, which is of independent interest.

• Accelerating cosmology from $Λ<0$ gravitational effective field theory

  Stefano Antonini, Petar Simidzija, Brian Swingle, Mark Van Raamsdonk, Chris Waddell

  arXiv:2212.00050 · November 30, 2022 · hep-th · doi

  Abstract

  A large class of $Λ< 0$ cosmologies have big-bang / big crunch spacetimes with time-symmetric backgrounds and asymptotically AdS Euclidean continuations suggesting a possible holographic realization. We argue that these models generically have time-dependent scalar fields, and these can lead to realistic cosmologies at the level of the homogeneous background geometry, with an accelerating phase prior to the turnaround and crunch. We first demonstrate via explicit effective field theory examples that models with an asymptotically AdS Euclidean continuation can also exhibit a period of accelerated expansion without fine tuning. We then show that certain significantly more tuned examples can give predictions arbitrarily close to a $Λ$CDM model. Finally, we demonstrate via an explicit construction that the potentials of interest can arise from a superpotential, thus suggesting that these solutions may be compatible with an underlying supersymmetric theory.

• Optimizing sparse fermionic Hamiltonians

  Yaroslav Herasymenko, Maarten Stroeks, Jonas Helsen, Barbara Terhal

  arXiv:2211.16518 · November 29, 2022 · quant-ph · Quantum 7, 1081 (2023) · doi

  Abstract

  We consider the problem of approximating the ground state energy of a fermionic Hamiltonian using a Gaussian state. In sharp contrast to the dense case, we prove that strictly $q$-local $\rm {\textit {sparse}}$ fermionic Hamiltonians have a constant Gaussian approximation ratio; the result holds for any connectivity and interaction strengths. Sparsity means that each fermion participates in a bounded number of interactions, and strictly $q$-local means that each term involves exactly $q$ fermionic (Majorana) operators. We extend our proof to give a constant Gaussian approximation ratio for sparse fermionic Hamiltonians with both quartic and quadratic terms. With additional work, we also prove a constant Gaussian approximation ratio for the so-called sparse SYK model with strictly $4$-local interactions (sparse SYK-$4$ model). In each setting we show that the Gaussian state can be efficiently determined. Finally, we prove that the $O(n^{-1/2})$ Gaussian approximation ratio for the normal (dense) SYK-$4$ model extends to SYK-$q$ for even $q>4$, with an approximation ratio of $O(n^{1/2 - q/4})$. Our results identify non-sparseness as the prime reason that the SYK-$4$ model can fail to have a constant approximation ratio.

• Error bounds for Lie Group representations in quantum mechanics

  Lauritz van Luijk, Niklas Galke, Alexander Hahn, Daniel Burgarth

  arXiv:2211.08582 · November 15, 2022 · quant-ph · Journal of Physics A: Mathematical and Theoretical 57, 105301 (2024) · doi

  Abstract

  We provide state-dependent error bounds for strongly continuous unitary representations of connected Lie groups. That is, we bound the difference of two unitaries applied to a state in terms of the energy with respect to a reference Hamiltonian associated to the representation and a left-invariant metric distance on the group. Our method works for any connected Lie group and the metric is independent of the chosen representation. The approach also applies to projective representations and allows us to provide bounds on the energy constrained diamond norm distance of any suitably continuous channel representation of the group.

• Deep-Circuit QAOA

  Gereon Koßmann, Lennart Binkowski, Lauritz van Luijk, Timo Ziegler, René Schwonnek

  arXiv:2210.12406 · October 22, 2022 · quant-ph · Quantum 9, 1882 (2025) · doi

  Abstract

  Despite its popularity, several empirical and theoretical studies suggest that the quantum approximate optimization algorithm (QAOA) has persistent issues in providing a substantial practical advantage. Numerical results for few qubits and shallow circuits are, at best, ambiguous, and the well-studied barren plateau phenomenon draws a rather sobering picture for deeper circuits. However, as more and more sophisticated strategies are proposed to circumvent barren plateaus, it stands to reason which issues are actually fundamental and which merely constitute - admittedly difficult - engineering tasks. By shifting the scope from the usually considered parameter landscape to the quantum state space's geometry we can distinguish between problems that are fundamentally difficult to solve, independently of the parameterization, and those for which there could at least exist a favorable parameterization. Here, we find clear evidence for a 'no free lunch'-behavior of QAOA on a general optimization task with no further structure; individual cases have, however, to be analyzed more carefully. Based on our analysis, we propose and justify a performance indicator for the deep-circuit QAOA that can be accessed by solely evaluating statistical properties of the classical objective function. We further discuss the various favorable properties a generic QAOA instance has in the asymptotic regime of infinitely many gates, and elaborate on the immanent drawbacks of finite circuits. We provide several numerical examples of a deep-circuit QAOA method based on local search strategies and find that - in alignment with our performance indicator - some special function classes, like QUBOs, indeed admit a favorable optimization landscape.

• Optimal protocols for quantum metrology with noisy measurements

  Sisi Zhou, Spyridon Michalakis, Tuvia Gefen

  arXiv:2210.11393 · October 20, 2022 · quant-ph · PRX Quantum 4, 040305 (2023) · doi

  Abstract

  Measurement noise is a major source of noise in quantum metrology. Here, we explore preprocessing protocols that apply quantum controls to the quantum sensor state prior to the final noisy measurement (but after the unknown parameter has been imparted), aiming to maximize the estimation precision. We define the quantum preprocessing-optimized Fisher information, which determines the ultimate precision limit for quantum sensors under measurement noise, and conduct a thorough investigation into optimal preprocessing protocols. First, we formulate the preprocessing optimization problem as a biconvex optimization using the error observable formalism, based on which we prove that unitary controls are optimal for pure states and derive analytical solutions of the optimal controls in several practically relevant cases. Then we prove that for classically mixed states (whose eigenvalues encode the unknown parameter) under commuting-operator measurements, coarse-graining controls are optimal, while unitary controls are suboptimal in certain cases. Finally, we demonstrate that in multi-probe systems where noisy measurements act independently on each probe, the noiseless precision limit can be asymptotically recovered using global controls for a wide range of quantum states and measurements. Applications to noisy Ramsey interferometry and thermometry are presented, as well as explicit circuit constructions of optimal controls.

• TF1 Snowmass Report: Quantum gravity, string theory, and black holes

  Daniel Harlow, Shamit Kachru, Juan Maldacena, Ibrahima Bah, Mike Blake, Raphael Bousso, Mirjam Cvetic, Xi Dong, Netta Engelhardt, Tom Faulkner … Beni Yoshida

  arXiv:2210.01737 · October 4, 2022 · hep-th

  Abstract

  We give an overview of the field of quantum gravity, string theory and black holes summarizing various white papers in this subject that were submitted as part of the Snowmass process.

• The connected wedge theorem and its consequences

  Alex May, Jonathan Sorce, Beni Yoshida

  arXiv:2210.00018 · September 30, 2022 · hep-th · doi

  Abstract

  In the AdS/CFT correspondence, bulk causal structure has consequences for boundary entanglement. In quantum information science, causal structures can be replaced by distributed entanglement for the purposes of information processing. In this work, we deepen the understanding of both of these statements, and their relationship, with a number of new results. Centrally, we present and prove a new theorem, the $n$-to-$n$ connected wedge theorem, which considers $n$ input and $n$ output locations at the boundary of an asymptotically AdS$_{2+1}$ spacetime described by AdS/CFT. When a sufficiently strong set of causal connections exists among these points in the bulk, a set of $n$ associated regions in the boundary will have extensive-in-N mutual information across any bipartition of the regions. The proof holds in three bulk dimensions for classical spacetimes satisfying the null curvature condition and for semiclassical spacetimes satisfying standard conjectures. The $n$-to-$n$ connected wedge theorem gives a precise example of how causal connections in a bulk state can emerge from large-N entanglement features of its boundary dual. It also has consequences for quantum information theory: it reveals one pattern of entanglement which is sufficient for information processing in a particular class of causal networks. We argue this pattern is also necessary, and give an AdS/CFT inspired protocol for information processing in this setting. Our theorem generalizes the $2$-to-$2$ connected wedge theorem proven in arXiv:1912.05649. We also correct some errors in the proof presented there, in particular a false claim that existing proof techniques work above three bulk dimensions.

• State-dependent Trotter Limits and their approximations

  Daniel Burgarth, Niklas Galke, Alexander Hahn, Lauritz van Luijk

  arXiv:2209.14787 · September 29, 2022 · quant-ph · Phys. Rev. A 107, L040201 (2023) · doi

  Abstract

  The Trotter product formula is a key instrument in numerical simulations of quantum systems. However, computers cannot deal with continuous degrees of freedom, such as the position of particles in molecules, or the amplitude of electromagnetic fields. It is therefore necessary to discretize these variables to make them amenable to digital simulations. Here, we give sufficient conditions to conclude the validity of this approximate discretized physics. Essentially, it depends on the state-dependent Trotter error, for which we establish explicit bounds that are also of independent interest.

• Few-photon transport via a multimode nonlinear cavity: theory and applications

  Yunkai Wang, Kejie Fang

  arXiv:2209.03877 · September 8, 2022 · quant-ph · doi

  Abstract

  Few-photon transport via waveguide-coupled local quantum systems has attracted extensive theoretical and experimental studies. Most of the study has focused on atomic or atomic-like local quantum systems due to their strong light-matter interaction useful for quantum applications. Here, we study few-photon transport via a waveguide-coupled multimode optical cavity with second-order bulk nonlinearity. We develop a Feynman diagram approach and compute the scattering matrix of the one- and two-photon transport. Based on the calculated scattering matrix, we show highly nonclassical photonic effects, including photon blockade and $π-$conditional phase shift, are achievable in the waveguide-coupled multimode optical cavity system via quantum interference and linear response engineering. Our results might lead to significant applications of quantum photonic circuits in all-optical quantum information processing and quantum network protocols.

• Rate-Distortion Theory for Mixed States

  Zahra Baghali Khanian, Kohdai Kuroiwa, Debbie Leung

  arXiv:2208.11698 · August 24, 2022 · quant-ph

  Abstract

  This paper is concerned with quantum data compression of asymptotically many independent and identically distributed copies of ensembles of mixed quantum states. The encoder has access to a side information system. The figure of merit is per-copy or local error criterion. Rate-distortion theory studies the trade-off between the compression rate and the per-copy error. The optimal trade-off can be characterized by the rate-distortion function, which is the best rate given a certain distortion. In this paper, we derive the rate-distortion function of mixed-state compression. The rate-distortion functions in the entanglement-assisted and unassisted scenarios are in terms of a single-letter mutual information quantity and the regularized entanglement of purification, respectively. For the general setting where the consumption of both communication and entanglement are considered, we present the full qubit-entanglement rate region. Our compression scheme covers both blind and visible compression models (and other models in between) depending on the structure of the side information system.

• Entanglement entropy and non-local duality: quantum channels and quantum algebras

  Oliver DeWolfe, Kenneth Higginbotham

  arXiv:2207.12436 · July 25, 2022 · hep-th · doi

  Abstract

  We investigate the transformation of entanglement entropy under dualities, using the Kramers-Wannier duality present in the transverse field Ising model as our example. Entanglement entropy between local spin degrees of freedom is not generically preserved by the duality; instead, entangled states may be mapped to states with no local entanglement. To understand the fate of this entanglement, we consider two quantitative descriptions of degrees of freedom and their transformation under duality. The first involves Kraus operators implementing the partial trace as a quantum channel, while the second utilizes the algebraic approach to quantum mechanics, where degrees of freedom are encoded in subalgebras. Using both approaches, we show that entanglement of local degrees of freedom is not lost; instead it is transferred to non-local degrees of freedom by the duality transformation.

• A rapidly mixing Markov chain from any gapped quantum many-body system

  Sergey Bravyi, Giuseppe Carleo, David Gosset, Yinchen Liu

  arXiv:2207.07044 · July 14, 2022 · quant-ph · Quantum 7, 1173 (2023) · doi

  Abstract

  We consider the computational task of sampling a bit string $x$ from a distribution $π(x)=|\langle x|ψ\rangle|^2$, where $ψ$ is the unique ground state of a local Hamiltonian $H$. Our main result describes a direct link between the inverse spectral gap of $H$ and the mixing time of an associated continuous-time Markov Chain with steady state $π$. The Markov Chain can be implemented efficiently whenever ratios of ground state amplitudes $\langle y|ψ\rangle/\langle x|ψ\rangle$ are efficiently computable, the spectral gap of $H$ is at least inverse polynomial in the system size, and the starting state of the chain satisfies a mild technical condition that can be efficiently checked. This extends a previously known relationship between sign-problem free Hamiltonians and Markov chains. The tool which enables this generalization is the so-called fixed-node Hamiltonian construction, previously used in Quantum Monte Carlo simulations to address the fermionic sign problem. We implement the proposed sampling algorithm numerically and use it to sample from the ground state of Haldane-Shastry Hamiltonian with up to 56 qubits. We observe empirically that our Markov chain based on the fixed-node Hamiltonian mixes more rapidly than the standard Metropolis-Hastings Markov chain.

• Operator growth and Krylov construction in dissipative open quantum systems

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

  arXiv:2207.05347 · July 12, 2022 · quant-ph · JHEP 12 (2022) 081 · doi

  Abstract

  Inspired by the universal operator growth hypothesis, we extend the formalism of Krylov construction in dissipative open quantum systems connected to a Markovian bath. Our construction is based upon the modification of the Liouvillian superoperator by the appropriate Lindbladian, thereby following the vectorized Lanczos algorithm and the Arnoldi iteration. This is well justified due to the incorporation of non-Hermitian effects due to the environment. We study the growth of Lanczos coefficients in the transverse field Ising model (integrable and chaotic limits) for boundary amplitude damping and bulk dephasing. Although the direct implementation of the Lanczos algorithm fails to give physically meaningful results, the Arnoldi iteration retains the generic nature of the integrability and chaos as well as the signature of non-Hermiticity through separate sets of coefficients (Arnoldi coefficients) even after including the dissipative environment. Our results suggest that the Arnoldi iteration is meaningful and more appropriate in dealing with open systems.

• Simulating one-dimensional quantum chromodynamics on a quantum computer: Real-time evolutions of tetra- and pentaquarks

  Yasar Y. Atas, Jan F. Haase, Jinglei Zhang, Victor Wei, Sieglinde M. -L. Pfaendler, Randy Lewis, Christine A. Muschik

  arXiv:2207.03473 · July 7, 2022 · quant-ph

  Abstract

  Quantum chromodynamics - the theory of quarks and gluons - has been known for decades, but it is yet to be fully understood. A recent example is the prediction and experimental discovery of tetraquarks, that opened a new research field. Crucially, numerous unsolved questions of the standard model can exclusively be addressed by nonperturbative calculations. Quantum computers can solve problems for which well established QCD methods are inapplicable, such as real-time evolution. We take a key step in exploring this possibility by performing a real-time evolution of tetraquark and pentaquark physics in one-dimensional SU(3) gauge theory on a superconducting quantum computer. Our experiment represents a first quantum computation involving quarks with three colour degrees of freedom, i.e. with the gauge group of QCD.

• Strong Converse Bounds for Compression of Mixed States

  Zahra Baghali Khanian

  arXiv:2206.09415 · June 19, 2022 · quant-ph

  Abstract

  In this paper, we study strong converse properties for both visible and blind compression of mixed states. The optimal rate of a visible compression scheme is obtained in terms of the entanglement of purification, whose additivity remains unknown so far. For a variation of extendible states, we prove that the entanglement of purification is additive and apply this to obtain a "pretty strong" converse bound for the blind and visible compression of such states. Namely, when the rate decreases below the optimal rate, the error exhibits a discontinuous jump from 0 to at least $\frac{1}{3\sqrt{2}}$. To deal with the visible case for general states, we define a new quantity $E_{α,p}(A:R)_ρ$ for a bipartite state $ρ^{AR}$ and $α\in (0,1)\cup (1,\infty)$ as the $α$-Rényi generalization of the entanglement of purification $E_{p}(A:R)_ρ$. For $α=1$, we define $E_{1,p}(A:R)_ρ:=E_{p}(A:R)_ρ$. We show that for any rate below the regularization $\lim_{α\to 1^+}E_{α,p}^{\infty}(A:R)_ρ:=\lim_{α\to 1^+} \lim_{n \to \infty} \frac{E_{α,p}(A^n:R^n)_{ρ^{\otimes n}}}{n}$ the fidelity for the visible compression exponentially converges to zero. Moreover, we consider blind compression of a general mixed-state source $ρ^{AR}$ shared between an encoder and an inaccessible reference system $R$. We obtain a strong converse bound for the compression of this source by assuming that the decoder is a super-unital channel. This immediately implies a strong converse for the blind compression of ensembles of mixed states, by assuming a super-unital decoder, as this is a special case of the general mixed-state source $ρ^{AR}$ where the reference system $R$ has a classical structure.

• Rate Reduction of Blind Quantum Data Compression with Local Approximations Based on Unstable Structure of Quantum States

  Kohdai Kuroiwa, Debbie Leung

  arXiv:2206.03501 · June 7, 2022 · quant-ph · doi

  Abstract

  In this paper, we propose a new protocol for a data compression task, blind quantum data compression, with finite local approximations. The rate of blind data compression is susceptible to approximations even when the approximations are diminutive. This instability originates from the sensitivity of a structure of quantum states against approximations, which makes the analysis of blind compression in the presence of approximations intractable. In this paper, we constructed a protocol that takes advantage of the instability to reduce the compression rate substantially. Our protocol shows a significant reduction in rate for specific examples we examined. Moreover, we apply our methods to diagonal states, and propose two types of approximation methods in this special case. We perform numerical experiments and observe that one of these two approximation methods performs significantly better than the other. Thus, our analysis makes a first step toward general investigation of blind quantum data compression with the allowance of approximations towards further investigation of approximation-rate trade-off of blind quantum data compression.

• Complexity and entanglement in non-local computation and holography

  Alex May

  arXiv:2204.00908 · April 2, 2022 · quant-ph · Quantum 6, 864 (2022) · doi

  Abstract

  Does gravity constrain computation? We study this question using the AdS/CFT correspondence, where computation in the presence of gravity can be related to non-gravitational physics in the boundary theory. In AdS/CFT, computations which happen locally in the bulk are implemented in a particular non-local form in the boundary, which in general requires distributed entanglement. In more detail, we recall that for a large class of bulk subregions the area of a surface called the ridge is equal to the mutual information available in the boundary to perform the computation non-locally. We then argue the complexity of the local operation controls the amount of entanglement needed to implement it non-locally, and in particular complexity and entanglement cost are related by a polynomial. If this relationship holds, gravity constrains the complexity of operations within these regions to be polynomial in the area of the ridge.

• Shadow Distillation: Quantum Error Mitigation with Classical Shadows for Near-Term Quantum Processors

  Alireza Seif, Ze-Pei Cian, Sisi Zhou, Senrui Chen, Liang Jiang

  arXiv:2203.07309 · March 14, 2022 · quant-ph · PRX Quantum 4, 010303 (2023) · doi

  Abstract

  Mitigating errors in quantum information processing devices is especially important in the absence of fault tolerance. An effective method in suppressing state-preparation errors is using multiple copies to distill the ideal component from a noisy quantum state. Here, we use classical shadows and randomized measurements to circumvent the need for coherent access to multiple copies at an exponential cost. We study the scaling of resources using numerical simulations and find that the overhead is still favorable compared to full state tomography. We optimize measurement resources under realistic experimental constraints and apply our method to an experiment preparing Greenberger-Horne-Zeilinger (GHZ) state with trapped ions. In addition to improving stabilizer measurements, the analysis of the improved results reveals the nature of errors affecting the experiment. Hence, our results provide a directly applicable method for mitigating errors in near-term quantum computers.

• Projective measurement of black holes

  Beni Yoshida

  arXiv:2203.04968 · March 9, 2022 · hep-th

  Abstract

  We study the effect of projective measurements on the entanglement structure of quantum black holes. It is shown that the entanglement verification in monitored quantum circuits, recently discussed in condensed matter physics, is equivalent to the information recovery from a black hole with projective measurements. This correspondence provides useful predictions about non-perturbative effects on quantum gravity and some insights on the black hole interior as well as the final state proposal.

• Snowmass White Paper: New ideas for many-body quantum systems from string theory and black holes

  Mike Blake, Yingfei Gu, Sean A. Hartnoll, Hong Liu, Andrew Lucas, Krishna Rajagopal, Brian Swingle, Beni Yoshida

  arXiv:2203.04718 · March 9, 2022 · hep-th

  Abstract

  During the last two decades many new insights into the dynamics of strongly coupled quantum many-body systems have been obtained using gauge/gravity duality, with black holes often playing a universal role. In this white paper we summarize the results obtained and offer some outlook for future developments, including the ongoing mutually beneficial feedback loop with the study of more general, not necessarily holographic, quantum many-body systems.

• Bottom-up holographic models for cosmology

  Chris Waddell

  arXiv:2203.03096 · March 7, 2022 · hep-th · doi

  Abstract

  In this note, we investigate some simple generalizations of a bottom-up holographic approach to cosmology introduced in arXiv:1810.10601. Our models utilize the Karch/Randall/Takayanagi ansatz for the gravitational dual of a boundary conformal field theory, involving pure AdS gravity and an end-of-the-world brane. Following a suggestion made in arXiv:2102.05057, we consider models with an additional interface brane in the bulk. We find that solutions with a viable cosmological interpretation exist only if our model is further generalized, for example by including an Einstein-Hilbert term in the ETW brane action. The physical validity of such models is discussed from the perspective of the effective theory.

• Preparation of Metrological States in Dipolar-Interacting Spin Systems

  Tian-Xing Zheng, Anran Li, Jude Rosen, Sisi Zhou, Martin Koppenhöfer, Ziqi Ma, Frederic T. Chong, Aashish A. Clerk, Liang Jiang, Peter C. Maurer

  arXiv:2203.03084 · March 7, 2022 · quant-ph · npj Quantum Information (2022) 8:150 · doi

  Abstract

  Spin systems are an attractive candidate for quantum-enhanced metrology. Here we develop a variational method to generate metrological states in small dipolar-interacting ensembles with limited qubit controls and unknown spin locations. The generated states enable sensing beyond the standard quantum limit (SQL) and approaching the Heisenberg limit (HL). Depending on the circuit depth and the level of readout noise, the resulting states resemble Greenberger-Horne-Zeilinger (GHZ) states or Spin Squeezed States (SSS). Sensing beyond the SQL holds in the presence of finite spin polarization and a non-Markovian noise environment.

• Code-routing: a new attack on position verification

  Joy Cree, Alex May

  arXiv:2202.07812 · February 16, 2022 · quant-ph · Quantum 7, 1079 (2023) · doi

  Abstract

  The cryptographic task of position verification attempts to verify one party's location in spacetime by exploiting constraints on quantum information and relativistic causality. A popular verification scheme known as $f$-routing involves requiring the prover to redirect a quantum system based on the value of a Boolean function $f$. Cheating strategies for the $f$-routing scheme require the prover use pre-shared entanglement, and security of the scheme rests on assumptions about how much entanglement a prover can manipulate. Here, we give a new cheating strategy in which the quantum system is encoded into a secret-sharing scheme, and the authorization structure of the secret-sharing scheme is exploited to direct the system appropriately. This strategy completes the $f$-routing task using $O(SP_p(f))$ EPR pairs, where $SP_p(f)$ is the minimal size of a span program over the field $\mathbb{Z}_p$ computing $f$. This shows we can efficiently attack $f$-routing schemes whenever $f$ is in the complexity class $\text{Mod}_p\text{L}$, after allowing for local pre-processing. The best earlier construction achieved the class L, which is believed to be strictly inside of $\text{Mod}_p\text{L}$. We also show that the size of a quantum secret sharing scheme with indicator function $f_I$ upper bounds entanglement cost of $f$-routing on the function $f_I$.

• Generic nonadditivity of quantum capacity in simple channels

  Felix Leditzky, Debbie Leung, Vikesh Siddhu, Graeme Smith, John A. Smolin

  arXiv:2202.08377 · February 16, 2022 · quant-ph · Physical Review Letters 130, 200801 (2023) · doi

  Abstract

  Determining capacities of quantum channels is a fundamental question in quantum information theory. Despite having rigorous coding theorems quantifying the flow of information across quantum channels, their capacities are poorly understood due to super-additivity effects. Studying these phenomena is important for deepening our understanding of quantum information, yet simple and clean examples of super-additive channels are scarce. Here we study a family of channels called platypus channels. Its simplest member, a qutrit channel, is shown to display super-additivity of coherent information when used jointly with a variety of qubit channels. Higher-dimensional family members display super-additivity of quantum capacity together with an erasure channel. Subject to the "spin-alignment conjecture" introduced in the companion paper [IEEE Trans. Inf. Theory 69(6), pp. 3825-3849, 2023; arXiv:2202.08380], our results on super-additivity of quantum capacity extend to lower-dimensional channels as well as larger parameter ranges. In particular, super-additivity occurs between two weakly additive channels each with large capacity on their own, in stark contrast to previous results. Remarkably, a single, novel transmission strategy achieves super-additivity in all examples. Our results show that super-additivity is much more prevalent than previously thought. It can occur across a wide variety of channels, even when both participating channels have large quantum capacity.

• The platypus of the quantum channel zoo

  Felix Leditzky, Debbie Leung, Vikesh Siddhu, Graeme Smith, John A. Smolin

  arXiv:2202.08380 · February 16, 2022 · quant-ph · IEEE Transactions on Information Theory 69(6), pp.3825-3849, 2023 · doi

  Abstract

  Understanding quantum channels and the strange behavior of their capacities is a key objective of quantum information theory. Here we study a remarkably simple, low-dimensional, single-parameter family of quantum channels with exotic quantum information-theoretic features. As the simplest example from this family, we focus on a qutrit-to-qutrit channel that is intuitively obtained by hybridizing together a simple degradable channel and a completely useless qubit channel. Such hybridizing makes this channel's capacities behave in a variety of interesting ways. For instance, the private and classical capacity of this channel coincide and can be explicitly calculated, even though the channel does not belong to any class for which the underlying information quantities are known to be additive. Moreover, the quantum capacity of the channel can be computed explicitly, given a clear and compelling conjecture is true. This "spin alignment conjecture," which may be of independent interest, is proved in certain special cases and additional numerical evidence for its validity is provided. Finally, we generalize the qutrit channel in two ways, and the resulting channels and their capacities display similarly rich behavior. In the companion paper [Phys. Rev. Lett. 130, 200801 (2023); arXiv:2202.08377], we further show that the qutrit channel demonstrates superadditivity when transmitting quantum information jointly with a variety of assisting channels, in a manner unknown before.

• Self-Adjointness of Toeplitz Operators on the Segal-Bargmann Space

  Wolfram Bauer, Lauritz van Luijk, Alexander Stottmeister, Reinhard F. Werner

  arXiv:2202.04687 · February 9, 2022 · math-ph · Journal of Functional Analysis, Volume 284, Issue 4, 2023 · doi

  Abstract

  We prove a new criterion that guarantees self-adjointness of Toeplitz operator with unbounded operator-valued symbols. Our criterion applies, in particular, to symbols with Lipschitz continuous derivatives, which is the natural class of Hamiltonian functions for classical mechanics. For this we extend the Berger-Coburn estimate to the case of vector-valued Segal-Bargmann spaces. Finally, we apply our result to prove self-adjointness for a class of (operator-valued) quadratic forms on the space of Schwartz functions in the Schrödinger representation.