Papers and preprints from Perimeter Institute and the Institute for Quantum Computing, updated daily from arXiv. https://perimeterqi.ca/papers/feed.xml 2026-10-02T00:00:00.000Z https://arxiv.org/abs/2610.02097 2026-10-02T00:00:00.000Z Shunta Takahashi Zhi Li Beni Yoshida

Electromagnetic duality in the toric code has order two at the level of anyon types and acts as a Hadamard-type logical transformation on the encoded quantum information. Here, we ask whether it can likewise be realized microscopically as an order-two Clifford operation. For the $\mathbb{Z}_2$ toric code, we prove that any locality-preserving Clifford realization of electric-magnetic exchange cannot have order two. Our proof is fully general and requires neither translation symmetry with restricted families of system sizes nor a fixed pairing between vertex and plaquette stabilizers. Geometrically, the proof locally emulates the unavoidable crossing between electric and magnetic strings, similar to a cross-cap in a non-orientable manifold. Extending the problem to the $\mathbb{Z}_N$ toric code, we find that an order-two Clifford realization exists for odd $N$, whereas it is impossible for even $N$. Our results show that the group law of an emergent electromagnetic duality need not lift faithfully to its microscopic Clifford realization.

https://arxiv.org/abs/2610.02099 2026-10-02T00:00:00.000Z Ryan Anselm Srijita Kundu Olivier Lalonde Ashwin Nayak

A longstanding question in quantum communication complexity is whether some task can be accomplished with a small amount of communication in the presence of entanglement, yet require much more quantum communication in the absence of entanglement. Separations of this nature were previously known for relational problems and, in the simultaneous message passing model, for partial functions. But it has remained unresolved whether any such separation exists for a total Boolean function. We resolve this question with an exponential separation in the one-way setting: we exhibit a family of total Boolean functions $f_n\colon \{0,1\}^n \times \{0,1\}^n \to \{0,1\}$ that can be computed with $O(\log n)$ bits of one-way classical communication given prior entanglement, but that require $\Omega(n^{1/3})$ qubits of one-way quantum communication without entanglement. Our function is a special case of the subgroup membership problem, first studied in the communication setting by Aaronson, Le Gall, Russell, and Tani.

https://arxiv.org/abs/2610.01860 2026-10-02T00:00:00.000Z Amir-Reza Negari Farzin Salek Zoltán Zimborás Aram Harrow Patrick Hayden Jens Eisert

A recurring principle in many-body physics is that sufficiently distributed interactions or correlations lead to an effectively mean-field description. For fermionic Gaussian states, we establish a quantitative version of this principle directly at the level of Majorana covariance matrices. The main observation is that the admissibility condition for fermionic covariance matrices imposes a quantitative monogamy constraint on two-point correlations: a fixed region has only a bounded covariance budget to distribute among many disjoint regions. We use this principle in three directions. First, for quadratic fermionic Hamiltonians on finite simple graphs of high degree, we obtain product-state approximations to both the ground-state energy and the finite-temperature free energy, with error of order \(D^{-1/2}\) for \(D\)-regular graphs. Second, we prove a finite fermionic Gaussian de Finetti theorem: a \(k\)-copy Gaussian state that is \(n\)-exchangeable under graded fermionic copy permutations is \(O(k/n)\)-close in trace norm to the product of its one-copy marginal. In particular, infinite exchangeability within the Gaussian class implies exact product structure. Third, for spatial fermionic Gaussian states with exponentially clustering mutual information, we prove that the conditional mutual information across a separating buffer decays as \(O(r^{-1})\), and hence, by recoverability, the state admits an \(O(r^{-1/2})\) trace-norm approximation by a recovered state. These results show that product and de Finetti approximations and recoverability estimates for fermionic Gaussian systems can all be derived directly from covariance-level structure.

https://arxiv.org/abs/2610.02037 2026-10-02T00:00:00.000Z Daniel Grier Hakop Pashayan Luke Schaeffer

Consider the following optimization problem over stabilizer product states: given an $n$-qubit stabilizer state $\left|\psi\right\rangle$ and a set of single-qubit stabilizer states $S$, maximize $\left|\langle \psi | \phi_1, \ldots, \phi_n \rangle\right|^2$ over single-qubit stabilizer states $\left|\phi_i\right\rangle \in S$. By varying the set $S$, we show that solutions to this problem can be useful in a variety of settings: tighter runtime bounds for certain classical simulation algorithms; measures of entanglement; and the complexity of low-rank matrix completion. Moreover, we give a complete complexity classification of this nearest stabilizer product state problem. After accounting for the symmetries in the Clifford group, there are $9$ distinct possible sets $S$, and we show that all but the two simplest of these are $\NP$-complete.

https://arxiv.org/abs/2610.00444 2026-10-02T00:00:00.000Z Amir Arqand Srijita Kundu Ernest Y.-Z. Tan

We give a generic compiler for turning a wide class of device-dependent protocols with trusted state preparation into sequential device-independent protocols. In order for our compiler to apply, the trusted-preparation protocol needs to satisfy certain minimal conditions: having an entanglement-based realization in the first place, and the entanglement-based realization corresponding to the optimal strategy of any non-local game that satisfies a fairly weak rigidity condition. We apply our generic compiler to give sequential device-independent protocols for uncloneable encryption, copy-protection of point functions, and blind randomness expansion. Our technical contribution is a new class of rigidity theorems based on Rényi divergences, with flexible cryptographic applications. They allow our compiler to achieve a constant rate (i.e., the ratio of trusted states prepared to device uses), while tolerating a constant level of noise per device usage. This overcomes a fundamental scaling obstacle faced by previous rigidity theorems for trace distance or fidelity. For the generic sequential case, our proof is based on the sharp-divergence chain rule by Fawzi and Fawzi (2021), which suffices for a constant but fairly low rate. In the special case when the devices retain no memory, we improve the rates by deriving a novel subadditivity property for a modified channel sandwiched divergence, which may be of independent interest. Finally, as a prospect for future improvements, we also prove a chain rule for the iterated-mean divergences from Brown, Fawzi and Fawzi (2021).

https://arxiv.org/abs/2610.02176 2026-10-02T00:00:00.000Z Zahra Baghali Khanian Debbie Leung Graeme Smith

Correlations across channel uses can improve quantum communication rates, making optimization over arbitrarily large blocks a central difficulty in determining quantum capacity. We show how full permutation invariance limits this advantage for every finite-dimensional memoryless channel. The optimized coherent information per use converges to the single-use maximum and consequently attains its supremum at a finite block length. Thus finite-block superadditivity remains possible, while the asymptotic optimization reduces to a single channel use. We also establish a strong converse for pure-source entanglement generation with permutation-invariant inputs: at any fixed rate above the single-use coherent-information maximum, the fidelity tends to zero. Beyond these communication bounds, we identify a common structure underlying completely bounded norms and the sandwiched Rényi channel quantities governing discrimination against a replacer and entanglement-assisted communication. De Finetti reduction and permutation covariance yield systematic alternative proofs of their known multiplicativity and additivity results within a shared variational framework. We further show that, for permutation-invariant inputs, correlations cannot sustain an asymptotic reduction in output entropy per use below the single-use minimum. This entropy limit holds for Rényi orders greater than one and for the von Neumann entropy, extending the role of symmetry from communication bounds to the control of output entropy.

https://arxiv.org/abs/2610.01992 2026-10-02T00:00:00.000Z Baisong Sun Ningping Cao Yiu Tung Poon Bei Zeng

Knill-Laflamme coefficients characterize exact quantum error detection through scalar compressions of error operators to the code space. For prescribed Pauli observables and a fixed code dimension, attainable coefficient vectors form a joint higher-rank numerical range, whose Euclidean norm image is the signature spectrum. We study how operator representation, code dimension, and detection constraints govern this geometry. Our main theorem identifies representation multiplicity as sufficient to lift active expectation data to exact scalar compressions: a lift exists whenever each occupied block has multiplicity at least the code dimension times the rank of the corresponding active state. When multiplicity suffices to realize all active states, the coefficient range is the full active expectation body and is therefore convex and connected, with a closed interval as its signature spectrum. This framework unifies commuting Pauli families, where sufficient common-eigenspace degeneracy yields polytopes, and subsystem stabilizer codes, where protected logical subsystems supply multiplicity spaces for noncommuting gauge observables. Explicit examples show how increasing the code dimension can make a range shrink, collapse, or become empty, while increasing multiplicity can turn a Bloch sphere into a filled ball. In the subsystem setting, parent-Hamiltonian constructions realize exact detecting codes as degenerate ground spaces, selecting distinguished vectors and continuous paths within these ranges. A final three-qubit example shows additional noncommuting detection constraints reduce a tetrahedral range to its barycenter and four vertices, producing a disconnected signature spectrum. The results provide a structural framework for Knill-Laflamme coefficient geometry and motivate sharper criteria for connected coefficient ranges and interval signature spectra under structured error models.

https://arxiv.org/abs/2610.00595 2026-10-02T00:00:00.000Z Daniel Centeno Roberto D. Baldijão Maria Ciudad Alañón Yujie Zhang Pedro Lauand Elie Wolfe

Bell nonlocality allows secret key to be certified without trusting the internal operation of the devices, and even against eavesdroppers constrained only by the no-signaling principle. We ask whether generalized contextuality, a notion of nonclassicality available in prepare-and-measure experiments on a single system, can play an analogous role. In our approach, Alice and Bob first establish operational equivalences among their local preparation and measurement procedures, which are then treated as theory-independent constraints that any physical intervention on the communication channel, including that of an adversary, must respect. Eve is otherwise unrestricted, that is, her intervention on the transmitted system is not assumed to be described by quantum theory. Within this adversarial model, we show that Eve's optimal guessing probability against individual attacks is the solution of a finite linear program, and hence that a worst-case asymptotic key rate follows from the observed statistics and the operational equivalences alone. We prove that contextuality is necessary for a positive key rate. However, we also show that it is not sufficient. Concretely, the (3,2)-parity-oblivious random access code, known to yield secret key against a quantum eavesdropper, yields none certifiable key rate against a post-quantum one. Conversely, operational equivalences with no analogue among no-signaling constraints can strictly increase the asymptotic key rate. We illustrate this with the prepare-and-measure version of the standard CHSH protocol with an aligned key-generating setting.

https://arxiv.org/abs/2609.18671 2026-09-17T00:00:00.000Z Vinicius P. Rossi Emanuele Polino Beatrice Polacchi Valeria Cimini David Schmid John H. Selby Giacomo Corrielli Andrea Crespi Roberto Osellame Fabio Sciarrino Ana Belén Sainz

Certifying nonclassicality without assuming any particular underlying physical theory constitutes both a foundational challenge and a requirement for device-independent protocols. Realizing such theory-independent certification in scalable architectures is essential for connecting fundamental tests with emerging quantum technologies. Integrated photonic circuits are a leading platform for scalable quantum information processing, motivating the development of rigorous methods to certify the nonclassical resources underpinning quantum advantage. In this paper, we report a theory-independent certification of generalized contextuality on a three-mode integrated photonic circuit. Our approach combines theory-agnostic tomography with simplex-embeddability certification---a framework that requires no assumptions about the underlying physical theory---and applies it to experimental data from a three-mode photonic circuit seeded by single photons. An independently constructed quantum model of the experiment provides a consistency check on the observed nonclassicality, without entering the certification as a theoretical assumption. The method rules out simplex-embeddability for our experimental data, providing robust, theory-independent evidence that our photonic circuit exhibits nonclassicality.

https://arxiv.org/abs/2609.10514 2026-09-10T00:00:00.000Z Ashwin Nayak Xingyu Zhou

We determine the optimal sample complexity of low-rank quantum state tomography when each measurement may act jointly on at most $t$ samples. For sufficiently small $\varepsilon$, estimating an unknown state on $\mathbb{C}^d$ of rank at most $r$ to trace norm error $\varepsilon$ with constant success probability requires, and is achievable with, $$ \Theta\left( \frac{dr}{\varepsilon^2} \max\left\{1,\frac r{\sqrt t}\right\} \right)$$ samples. The lower bound allows the protocol to choose each joint measurement adaptively using all previous classical outcomes; the matching upper bound is nonadaptive. Thus joint measurements on at most $t$ samples improve the complexity of algorithms making single-sample measurements by at most a factor $\sqrt t$. Further, measuring order $r^2$ samples jointly is necessary and sufficient to attain the unrestricted collective rate. For the lower bound, we vary the support of a state with fixed uniform spectrum and bound the Fisher information trace of every joint measurement on $t$ samples. The adaptive Fisher chain rule and the van Trees inequality then give the trace norm lower bound. For the upper bound, we construct and analyze a nonadaptive tomography protocol based on a Gaussian joint measurement. An explicit second moment identity and a conditional Gaussian law outside the state's support give a rank-dependent error analysis, yielding the matching rate.

https://arxiv.org/abs/2608.24527 2026-08-26T00:00:00.000Z Enrico Olivucci Mariia Sobchuk Sehmimul Hoque Jeffrey Hnybida Kyungho W. Kim Ala Shayeghi Pooya Ronagh

We prove the first quantum--classical separation for a sampling problem over a continuous domain. For a class of Gibbs states $p\propto e^{-\beta E}$ on the torus $\mathbb{T}^d$ with smooth ($s$-Gevrey) potential and barrier amplitude $\alpha=e^{\beta\Delta}$, where $\Delta = \max E-\min E$, every classical algorithm---querying the value, gradient, or any higher-order derivatives of the log-density---requires $\Omega(\alpha)$ queries to sample at constant accuracy in total variation distance, while a quantum algorithm based on quantum singular value thresholding and temperature annealing samples with $\tilde{O}\left(\sqrt{\alpha}\right)$ queries to an oracle for the gradient. The advantage is quadratic in the barrier amplitude, which becomes exponential in the dimension, $e^{\Omega(d)}$, at low temperature. The classical bound is information-theoretic, holding for every classical algorithm with query access to the Gibbs potential and its derivatives at any order.

https://arxiv.org/abs/2608.16495 2026-08-18T00:00:00.000Z Alex May Philip Verduyn Lunel

Quantum position-verification is a cryptographic task wherein a verifier attempts to establish the location in space of a prover. Recent experiments have implemented a well-studied class of position-verification schemes, known as the $f$-BB84 scenario, but their security under realistic loss and imperfect state preparation remains incompletely understood. We give a new lower bound on any attack on this scheme, in particular proving nearly-linear quantum gate lower bounds on the attacker, even when allowing the attacker to declare a transmission loss of up to $50\%$, allowing for the challenges prepared by the referee to be imperfect, and allowing the quantum messages used in the protocol to be arbitrarily slow. Our results are applicable to recent and upcoming experimental implementations of $f$-BB84, and in particular establish their security under a bounded quantum gate assumption on the attacker. The key ingredient is a tight analytic tradeoff for a lossy BB84 monogamy-of-entanglement game, valid without requiring the attackers' outputs to agree, which replaces observations previously made numerically.

https://arxiv.org/abs/2608.13399 2026-08-14T00:00:00.000Z Ramy Tannous Stéphane Vinet Kaylee Sherk Kimia Mohammadi Thomas Jennewein

Interference of optical signals in free-space channels requires optical receivers to support many spatial modes due to atmospheric turbulence, typically necessitating adaptive optics systems. Field-widened interferometers offer a passive alternative, making them particularly attractive for time-bin encoded signals with delays on the order of one nanosecond. Here, we demonstrate a field-widened, multimode interferometer design that achieves a high interference visibility for spatially multimode beams with large time bin separations. The interference of the multimode beams is enabled using a multi-pass Herriott cell that enables a very long path separation with a small form-factor. The design is tested using both numerical ray-tracing simulations and proof-of-principle demonstrations. We create a prototype interferometer with a path length difference of 12ns and determine that it maintains a high interference visibility with a large field-of-view of $0.4^{\circ}$.

https://arxiv.org/abs/2608.12255 2026-08-12T00:00:00.000Z Yinchen Liu Max McGinley Thomas Schuster David Gosset

The output state of a 2D geometrically local shallow random quantum circuit does not have long range correlations due to its lightcone structure. But this changes if one measures a subset of the qubits: long-range entanglement can be induced by the measurement process, leading to conditional correlations between distant qubits. In this paper we investigate the structure of conditional dependence in these circuits and its consequences for quantum advantage. For a tripartition $ABC$ of the qubits, we consider the ensemble of post-measurement states on $A$ that is conditioned on a specific measurement outcome on $B$ and ranges over all possible measurement outcomes on $C$. For circuit depths exceeding a constant critical value $d^*$, we conjecture that this ensemble is well approximated by a certain generalization of the Haar ensemble, called the Scrooge ensemble~[Jozsa \textit{et al.}, \href{ this https URL }{Phys. Rev. A \textbf{49}, 668 (1994)}]; we also provide supporting numerical and analytical evidence. Our conjecture describes a precise sense in which the state retains its lightcone structure on the remaining unmeasured qubits, but also develops some globally random features arising from the measurement. A consequence is that $n$-qubit shallow random quantum circuits in two dimensions are classically efficiently simulable in the presence of a tiny depolarizing noise rate $\Omega(\log(n)/n)$.

https://arxiv.org/abs/2608.10377 2026-08-11T00:00:00.000Z Yunkai Wang Peixue Wu Graeme Smith Sisi Zhou

We show that private correlations in a bipartite quantum state constitute a metrological resource for distributed sensing assisted by a possibly noisy channel from one party to the other. We begin with an example with distillable secret key but poor locally accessible sensing performance and show that an assisting channel substantially improves its performance. We then prove a general theorem showing that positive private information in the encoding basis certifies a quantitative lower bound on the locally accessible sensing capability after assistance. We further show that classical correlations alone provide no analogous guarantee, whereas, in the absence of the assisting subsystem, the privacy-based guarantee reduces to an entanglement-based one. Finally, in a channel formulation, we show that a channel with positive private information allows nonzero locally accessible sensitivity when paired with a suitable assisting channel.

https://arxiv.org/abs/2608.10783 2026-08-11T00:00:00.000Z Lauritz van Luijk Amine Marrakchi Tobias Osborne Alexander Stottmeister Henrik Wilming

In systems with infinitely many degrees of freedom, fundamental results from quantum information theory can fail. An important example is the uniqueness of purifications: Even when two subsystems, described by commuting von Neumann algebras $A$ and $B$, are tomographically complete, purifications of a state on $A$ need not be related by unitaries in $B$. It was recently shown that this occurs precisely when Haag duality fails, i.e., when the commutant $B'$ is strictly larger than $A$. This raises the question of which fundamental entanglement properties survive in such a setting. We show that, for a pure global state, the ability to steer any ensemble decomposition of the marginal state on $A$ by measurements on $B$ is equivalent to the existence of a state-preserving conditional expectation from $B'$ onto $A$. This establishes a direct connection between quantum steering and subfactor theory. The key observation is that steering is equivalent to the existence of extensions of ensemble decompositions from $A$ to $B'$. Working with general Jordan algebras, we prove that unital positive maps have state-preserving left inverses if and only if ensemble decompositions can be lifted. For the inclusion $A\hookrightarrow B'$, a left inverse is precisely a conditional expectation, yielding the characterization above.

https://arxiv.org/abs/2608.05274 2026-08-05T00:00:00.000Z Takato Mori Beni Yoshida

We determine the relative entropy of entanglement of a bipartite mixed state $\rho_{AB}$ obtained by tracing out one subsystem of a tripartite Haar-random pure state $|\psi\rangle_{ABC}$, finding $E_R(\rho_{AB})=\log\frac{d_Ad_B}{\max(d_A,d_B,d_C)}+O(1)$. Equivalently, the relative entropy of entanglement nearly saturates the smaller of the entanglement of formation $E_F(\rho_{AB})$ and the mutual information $I(A:B)$. The upper bound is achieved by an explicit separable state obtained through one-sided Schmidt dephasing, which is therefore approximately closest.

https://arxiv.org/abs/2608.01617 2026-08-03T00:00:00.000Z Liang Mao Senrui Chen Hsin-Yuan Huang John Preskill Sisi Zhou

Quantum metrology, which addresses parameter estimation in quantum systems, has broad applications across science and technology. Conventional metrology protocols for multi-qubit states in the multi-parameter regime typically require highly complex quantum measurements, leading to substantial quantum-resource costs. In this work, we introduce a family of metrology protocols that use only few-qubit measurements, thereby significantly reducing the required resources. For arbitrary pure states, one of our protocols approaches the quantum Cramér-Rao bound up to an overhead in sample complexity that scales linearly with the number of qubits, irrespective of the number of parameters to be estimated. For typical Haar-random states, this overhead can be reduced to a constant. Our results build on recent advances in quantum state certification protocols with few-qubit measurements: we establish a universal connection between certification and metrology in which the precision of the certification protocol determines the metrological overhead. We also illustrate our approach through an example of Hamiltonian estimation from ground states.

https://arxiv.org/abs/2607.15210 2026-07-16T00:00:00.000Z Debbie Leung Benjamin Lovitz Peixue Wu

Additivity of minimum output entropies is a central problem in quantum information theory. Nonadditivity is known for every Rényi order $p>1$, at the von Neumann point $p=1$, and near $p=0$, while most of the interval $0<p<1$ has remained open. We prove that for every Rényi order $p$ satisfying either $p>3/4$ or $0\leq p<1/4$, there exist finite-dimensional projection-induced quantum channels such that additivity of the minimum output $p$-Rényi entropy fails. The proof combines two correlated random-projection constructions: a product-conjugate Bell-state witness for $p>3/4$, and a transpose-complement rank-defect witness for $p<1/4$. Thus the unresolved part of $0<p<1$ is reduced to $[1/4,3/4]$. Our estimates also improve the output dimension threshold for additivity violation of minimum output von Neumann entropy, first established in Belinschi, Collins and Nechida.

https://arxiv.org/abs/2607.14401 2026-07-15T00:00:00.000Z Sergey Bravyi David Gosset Yinchen Liu Benjamin Wong

We consider a broad family of Heisenberg-type quantum spin systems that were studied by Suzuki and Fisher in 1971. This family includes, for example, the Heisenberg antiferromagnet on any bipartite graph. The ground and Gibbs states of these models are Lee-Yang tensors with radius 1: they are associated with multilinear polynomials that possess an extraordinary zero-freeness property inside the unit polydisk in the complex plane. For each Hamiltonian in this family we show that the spectral gap between the first-excited and ground-state energies is lower bounded by $2\mu$, where $\mu$ is the magnetic field along the $Z$ direction. Using this result we obtain an efficient quantum adiabatic algorithm for the ground energy of any model in this family. The proof is based on a new inequality that relates the spectral gap of a positive semidefinite operator to its Lee-Yang radius -- a quantitative strengthening of prior work of the authors that may find applications elsewhere.

https://arxiv.org/abs/2606.27276 2026-06-25T00:00:00.000Z Yujie Zhang Yunkai Wang Wilson Wu Thomas Jennewein

Conventional stellar interferometry reconstructs incoherent sources from pairwise mutual coherences between telescopes. Are such pairwise measurements sufficient for quantum-limited subdiffraction imaging with a telescope array? We show that for generic image-moment estimation, they are not. We consider weak incoherent light from a generic extended source observed by an array of telescopes, each supporting a single optical mode. For an N-telescope array, we derive the quantum Fisher information (QFI) scaling of image moments up to the cutoff 2N-2 and prove that arbitrary measurements restricted to telescope pairs attain the full-array QFI scaling only up to second order. Thus, estimating higher-order moments at the quantum limit requires genuinely multi-telescope interference. Inspired by spatial-mode demultiplexing (SPADE) from single-aperture subdiffraction imaging, we construct array-SPADE measurements that attain the optimal QFI scaling up to the finite-array cutoff. Finally, we show that these measurements can, in principle, be embedded in ancilla- and memory-assisted quantum-network architectures for long-baseline telescopy.

https://arxiv.org/abs/2606.26354 2026-06-24T00:00:00.000Z Andreas Bluhm Simon Höfer Alex May Florian Speelman Philip Verduyn Lunel

Non-local quantum computation (NLQC) studies how two collaborating players can implement channels on distributed systems using a single simultaneous round of quantum communication and shared entanglement. NLQC has applications in diverse areas, ranging from quantum position-verification to quantum gravity. Recently, it has been realized that the relationships among families of NLQC tasks are highly structured: many seemingly distinct tasks are related by reductions, wherein implementations of one task can be used to efficiently implement a second task. This is analogous to the notion of reduction in complexity theory, and reveals the relative hardness of NLQC tasks. In this work we continue the study of reductions among NLQC tasks. We focus on NLQC examples of the greatest interest in quantum position-verification; in particular examples involving large classical inputs and fixed-size quantum inputs, since these constitute the most feasible protocols for position-verification schemes. Within this setting, we find many new relationships among NLQC tasks. For instance, protocols for the simplest example of redirecting a quantum system based on a classical control imply protocols for controlled single qubit measurements in arbitrary bases, the controlled application of any Clifford unitary, and even the controlled application of any unitary of the form $U=C_1DC_0$ with $D$ an arbitrary diagonal unitary and $C_0, C_1$ Clifford circuits. This implies that many feasible position-verification schemes have the same asymptotic scaling for their entanglement cost, and hence a similar level of security. Our techniques rely on ideas from gate teleportation and measurement based quantum computation, among other areas, bringing several new strategies into NLQC which may be of independent interest.

https://arxiv.org/abs/2606.20472 2026-06-18T00:00:00.000Z Tyler D. Ellison Dongjin Lee Zhi Li Amin Moharramipour Yasamin Panahi Beni Yoshida

A defining feature of chirality is the distinction between a system and its mirror image. Despite extensive experimental observations of chiral phases and theoretical advances, a quantum-information theoretic characterization of chirality based solely on the entanglement structure of many-body quantum states remains elusive. Here, we introduce the notion of many-body chirality by formulating it as an obstruction to transforming a quantum state into its complex conjugate through finite-depth local operations. We rigorously establish many-body chirality for stabilizer realizations of $\mathbb{Z}_d^{(k)}$ anyon theories, proving that complex conjugation can be implemented by local quantum channels if and only if the underlying anyon data are mirror invariant. This reveals forms of chirality that evade conventional diagnostics, including examples with vanishing modular commutator, vanishing chiral central charge, and commuting-projector realizations. We further show that this obstruction is intrinsically four-partite, while invisible to tripartite entanglement structure. Finally, we prove that $\mathbb{Z}_d^{(k)}$ states with $d>2$ possess intrinsic many-body imaginarity: their complex phase structure cannot be removed by finite-depth local unitaries. Remarkably, this includes states that are not many-body chiral.

https://arxiv.org/abs/2606.19628 2026-06-17T00:00:00.000Z Qiushi Liu Sisi Zhou

Quantum error correction has been successfully applied to enhance the precision of parameter estimation in the presence of noise. Nonetheless, existing methods require a number of noiseless, controllable ancillae and lack efficient encoding and decoding procedures. In this Letter, we demonstrate that subsystem error correction provides a new direction that can substantially simplify the metrological protocol. We derive general conditions under which subsystem stabilizer codes achieve the Heisenberg limit and show that, for broad classes of noise, this can be realized by syndrome-free protocols using at most a single ancilla qubit. Furthermore, we extend this framework to dynamical error correction and show that Floquet codes can protect time-dependent metrological signals in reaching the Heisenberg limit.

https://arxiv.org/abs/2606.13638 2026-06-11T00:00:00.000Z Entong He Zihao Li Noam Scully Sisi Zhou Yuxiang Yang

Full tomography of an unknown quantum evolution is resource-intensive and often unnecessary when the goal is only to predict selected properties. This motivates the study of classical shadow estimation of unitary channels (CSEU), a task in which one queries an unknown $d$-dimensional unitary $U$ and stores classical data that can later be used to predict expectation values $\mathrm{tr}[O \cdot U\rho U^\dagger]$ up to additive error $\varepsilon$ for arbitrary input states $\rho$ and observables $O$. We propose a parallel, non-adaptive CSEU protocol using $\mathcal{O}(d\varepsilon^{-1})$ queries when the input states or observables have constant rank. This achieves Heisenberg scaling with respect to $\varepsilon$ and is query-optimal, as we prove a matching $\Omega(d\varepsilon^{-1})$ lower bound that remains valid even with stronger access to the unknown unitary. Our query-optimal CSEU protocol provides a versatile and powerful tool for quantum learning theory, pushing the performance limits of several fundamental learning tasks, including unitary channel tomography, Hamiltonian learning, boundary-regime quantum channel tomography, Pauli transfer matrix learning, inverse-free amplitude estimation, pure-state property estimation, and shallow-circuit learning. Remarkably, we show that optimal unitary channel tomography can be achieved using only parallel queries, closing the gap between the best achievable efficiency of parallel and sequential tomography protocols. Together, these applications establish our framework as a fundamental tool for learning properties of quantum processes, particularly for certain key tasks that require high precision.

https://arxiv.org/abs/2606.12557 2026-06-10T00:00:00.000Z Uma Girish Alex May Natalie Parham Henry Yuen

In the private simultaneous message (PSM) setting, $k$ players obtain inputs $x_i\in\{0,1\}^n$ and then each send messages to a referee, who should learn $f(x_1,...,x_k)$ but no other information about $(x_1,...,x_k)$. The PSM setting was introduced as a minimal model for secure multiparty computation and has connections to Boolean function complexity. In the quantum setting, PSM has been related to non-local quantum computation (NLQC). The communication and correlation cost of implementing PSM remains poorly understood. Here, we give new upper and lower bounds on the (quantum) PSM model. For lower bounds, we show: 1) Nečiporuk's measure lower bounds the entanglement required for $k$-player quantum PSM with perfect correctness. This leads to quadratic lower bounds for explicit functions. 2) The rank of the communication matrix of $f(x_1,x_2)$ lower bounds 2-player quantum PSM with perfect privacy but imperfect correctness. This implies a previously unknown lower bound on classical PSM with imperfect correctness. When allowing quantum communication and shared entanglement, these are the first lower bounds on quantum PSM that make use of the privacy condition. For upper bounds, we show: 1) Letting $s$ be the size of a quantum circuit computing $f$, $d_f$ be the circuit depth, $k$ the number of players, $n$ the number of bits received by each player, and $\epsilon$ a correctness parameter, we obtain $\mathsf{PSM}_k^*(f) \leq (kn +s) \cdot \log^{O(d_f)}(s/\epsilon)$. 2) The square of the Fourier 1 norm of $f$, $\Vert \hat{f}\Vert_1^2$, upper bounds the classical PSM complexity, $\mathsf{PSM}(f)\leq O(\Vert \hat{f} \Vert^2_1)$. In proving the first upper bound, we generalize existing $T$-depth based techniques for NLQC from $2$ to $k\geq 2$ parties, and consider cases where the Clifford layers are restricted to having small light cones.

https://arxiv.org/abs/2605.15439 2026-05-14T00:00:00.000Z Shokoufe Faraji Zahra Baghali Khanian

We reformulate the Rényi entanglement of purification as a constrained minimum output Rényi entropy problem. Equivalently, for $p>1$, this formulation can be expressed in terms of a constrained maximal output Schatten $p$-norm. More precisely, for a completely positive map $\Omega:L(B')\to L(A)$, we consider the quantity $\upsilon_p(\Omega)$ defined by optimizing $\|(\Omega\otimes \mathrm{id}_E)(\sigma^{B'E})\|_p$ over all bipartite states $\sigma^{B'E}$ whose $B'$-marginal is maximally mixed. We focus on the case $p=2$. First, we compute $\upsilon_2$ for the transpose-depolarizing channel and prove that it is multiplicative under tensor powers. We then establish a general multiplicativity criterion: whenever a completely positive map $N:L(B')\to L(A)$ satisfies $N^{\dagger} \mathbin{\circ} N=a\,\mathrm{id}_A+b\,\mathrm{Tr}[\cdot]\,I_d$ for some constants $a,b\ge 0$, where $N^{\dagger}$ denotes the Hilbert-Schmidt adjoint of $N$, the quantity $\upsilon_2(N)$ is multiplicative under tensor powers. Examples of channels satisfying this criterion include the transpose-depolarizing channel, the depolarizing channel, and their respective complementary channels. Furthermore, we show that, for every completely positive map $\Omega$, multiplicativity of $\upsilon_p(\Omega)$ implies multiplicativity for its complementary map. This yields the corresponding additivity statements for the associated Rényi-2 entanglement of purification.

https://arxiv.org/abs/2605.11092 2026-05-11T00:00:00.000Z Linmu Qiao Zhichun Ouyang Sisi Zhou

We study how a punctured surface code can turn many local $Z$-type couplings into one protected logical signal for distributed quantum metrology, where the goal is to estimate a weighted sum of the coupling strengths. We consider an ordinary planar patch with two $X$-cut holes and develop a distributed sensing protocol in which all $Z$-type couplings correspond to the same nontrivial logical $\bar{Z}$ of the punctured surface code. When the couplings have prescribed placements on the lattice, we show that the relevant global condition is equivalent to the existence of a simple closed dual loop, called a witness, that has an odd number of intersections with every signal path. Together with a local clean-opening condition, this witness criterion gives a concrete punctured-code construction in which all signal paths realize the same nontrivial logical $\bar Z$. When only the abstract support structure is specified, disjoint supports are straightforward to realize, while overlapping supports are constrained by a stabilizer-difference condition, which we illustrate for three-body interactions. Overall, our results provide a novel, noise-robust distributed sensing protocol for many-body interactions, with corresponding topological design criteria.

https://arxiv.org/abs/2605.11076 2026-05-11T00:00:00.000Z Chandana Rao Himanshu Sahu Aranya Bhattacharya Suhail Ahmad Rather Mario Flory Zahra Raissi

Random circuit models often describe local dynamics using generic two-qubit gates, which have proven successful in capturing entanglement growth and operator spreading in many contexts. This approach naturally leads to the expectation that detailed gate structure plays only a limited role in coarse-grained entanglement and scrambling diagnostics. We show that the internal structure of multipartite circuit primitives can significantly influence these dynamical rates, even within a fixed random-circuit architecture. To investigate this, we study an exactly simulable family of Clifford quantum circuits built from fixed $n$-qubit graph-state preparation unitaries, which we treat as elementary building blocks. Specifically, we consider a one-dimensional chain of $N$ qubits initialized in a product state and evolved by layers in which nonoverlapping length-$n$ blocks are placed at uniformly random positions with sparsity $\alpha$. We find that different choices of graph-state building blocks lead to strongly varying dynamical rates. Graph states that are inequivalent under local Clifford (LC) transformations generate sharply different entanglement velocities $v_E$ and butterfly velocities $v_B$, even though the circuits are drawn from the same ensemble with identical architecture and randomness parameters. We further show that this hierarchy is captured by two complementary block-level characteristics: the distribution of entanglement across internal bipartitions of the graph state, which correlates with $v_E$, and a graph-theoretic connectivity profile across bipartitions, which correlates with $v_B$. Neither descriptor alone fully determines the dynamics; rather, entanglement growth and operator spreading are controlled by distinct structural features of the local circuit blocks. Notably, AME states appear among the fastest scrambling building blocks within the ensembles studied here.

https://arxiv.org/abs/2605.09138 2026-05-09T00:00:00.000Z Avantika Agarwal Amolak Ratan Kalra Sungjai Lee Debbie Leung Luke Schaeffer Pulkit Sinha Graeme Smith

The quantum capacity captures the value of a quantum channel for transmitting quantum information, establishing the fundamental limits on quantum communication. In spite of its central role in quantum information theory, the quantum capacity of most channels is unknown, with wide gaps between the best upper and lower bounds. Even deciding whether a channel has nonzero capacity -- finding its capacity threshold -- is difficult. In this paper we report significant increases in the capacity thresholds of two prototypical noise models: the depolarizing channel and Pauli channels. In the case of the depolarizing channel, this is the first improvement in 18 years, giving a bigger increase beyond the hashing bound than all previous improvements combined. Our starting point is the representation theoretic framework recently proposed by Bhalerao and Leditzky (2025) to compute coherent information for special permutation invariant states. We generalize their framework to the full symmetric subspace, which allow us to optimize coherent information over rank two states in that space. A representation theoretic calculation shows that exponentially many Kraus operators of the channel annihilate the symmetric space, corresponding to a massive decrease in environment entropy for states on the symmetric space compared to the maximally mixed state. This explains the enhanced coherent information as a manifestation of degeneracy for the resulting codes.

https://arxiv.org/abs/2605.08341 2026-05-08T00:00:00.000Z Yinan Chen Zongyuan Wang Sisi Zhou

We introduce a method for error-corrected quantum metrology where only partial quantum error correction (QEC) is needed to suppress local noise and maintain the probe states' super-standard-quantum-limit (super-SQL) sensing performance. This stands in contrast to the existing QEC-assisted sensing schemes in Phys. Rev. Lett. 112, 080801 (2014) and Phys. Rev. Lett. 112, 150802 (2014), where a probe state is encoded into the logical subspace of a quantum code and error correction involves measurements on all checks of the code. Here, we encode the probe states into superpositions of energetically different states of the underlying quantum code. For our probe states, error correction using a subset of checks is enough to suppress noise both before and after phase imprinting. We analyze the tradeoff in noise suppression. For noise parallel to our phase imprinter of weight $l$, we achieve a suppression of $p^\delta$ where $p$ is the noise strength and $\delta = \lfloor (l+1)/2 \rfloor$. We propose an adaptive imprinter weight increasing strategy to maintain super-SQL performance as we scale up the system. In all our examples, checks and phase imprinters are chosen to be local operators avoiding non-local connectivity.

https://arxiv.org/abs/2605.03975 2026-05-05T00:00:00.000Z Sisi Zhou

Multiparameter quantum metrology is ubiquitous in physics, yet it remains fundamentally challenging. As reflected by the uncertainty principle, distinct unknown parameters generally cannot be estimated simultaneously at their individual ultimate precision limits. The quantum Cramér--Rao bound (QCRB) and the Holevo Cramér--Rao bound (HCRB) represent the ultimate precision bounds in multiparameter quantum metrology. Here we introduce new formulations of these bounds based on quantum state purification. We show that, for any mixed state, their values are directly related to those of its purification, provided that nuisance parameters are introduced on the environmental system. Leveraging this connection, we develop a remarkably simple method for asymptotically attaining either the HCRB or twice the QCRB for arbitrary mixed states, using random purification channels and individual measurements.

https://arxiv.org/abs/2605.02840 2026-05-04T00:00:00.000Z Alex May

This is a book-length treatment of the subject of non-local quantum computation (NLQC). NLQC is a method for implementing quantum operations that interact two systems without directly bringing the systems together. Instead, a single round of communication and shared entanglement is used. NLQC has appeared in the context of quantum cryptography, computational complexity, communication complexity, quantum gravity, and other applications. The understanding of entanglement cost in NLQC is closely tied to questions in all of these areas. We review upper and lower bounds on entanglement cost, as well as some of the applications of NLQC and its connections to other subjects.

https://arxiv.org/abs/2605.00088 2026-04-30T00:00:00.000Z Zhi Li Raz Firanko Timothy H. Hsieh

We propose a unifying framework for characterizing pure and mixed state phases of matter across equilibrium, non equilibrium, and metastable regimes. We introduce the concept of locally stable states, defined by the operational property that any local operation (including post selection) can be reversed by a local channel. We prove that local stability is equivalent to a state being short range correlated, defined by the decay of both correlations and conditional mutual information. We demonstrate that these properties are invariant under locally reversible channels, thus defining locally stable phases. Furthermore, we prove that local stability implies both the decay of a family of nonlinear correlators, including the fidelity correlator, and the decay of correlations in the canonical purification, thus bridging the gap between mixed and pure states. Along the way, we establish two results which may be of independent interest: we show that post-selection on locally stable (short range correlated) states can be implemented via local channels and that quantum Markov chains can be characterized by the local computability of nonlinear observables.

https://arxiv.org/abs/2604.08380 2026-04-09T00:00:00.000Z Lauritz van Luijk Henrik Wilming

We study the interconversion of families of quantum states ("statistical experiments") via positive, trace-preserving (PTP) maps and clarify its mathematical structure in terms of minimal sufficient Jordan algebras, which can be seen to generalize the Koashi-Imoto decomposition to the PTP setting. In particular, we show that Neyman-Pearson tests generate the minimal sufficient Jordan algebra, and hence also the minimal sufficient *-algebra corresponding to the Koashi-Imoto decomposition. As applications, we show that a) equality in the data-processing inequality for the relative entropy or the $\alpha$-$z$ quantum Rényi divergence implies the existence of a recovery map also in the PTP case and b) that two dichotomies can be interconverted by PTP maps if and only if they can be interconverted by decomposable, trace-preserving maps. We thoroughly review the necessary mathematical background on Jordan algebras. As a step beyond the finite-dimensional case, we prove Frenkel's formula for approximately finite-dimensional von Neumann algebras.

https://arxiv.org/abs/2603.04357 2026-03-04T00:00:00.000Z Avantika Agarwal Alan Bu Amolak Ratan Kalra Debbie Leung Luke Schaeffer Graeme Smith

This paper focuses on error thresholds for Pauli channels. We numerically compute lower bounds for the thresholds using the analytic framework of coset weight enumerators pioneered by DiVincenzo, Shor and Smolin in 1998. In particular, we study potential non-additivity of a variety of small stabilizer codes and their concatenations, and report several new concatenated stabilizer codes of small length that show significant non-additivity. We also give a closed form expression of coset weight enumerators of concatenated phase and bit flip repetition codes. Using insights from this formalism, we estimate the threshold for concatenated repetition codes of large lengths. Finally, for several concatenations of small stabilizer codes we optimize for channels which lead to maximal non-additivity at the hashing point of the corresponding channel. We supplement these results with a discussion on the performance of various stabilizer codes from the perspective of the non-additivity and threshold problem. We report both positive and negative results, and highlight some counterintuitive observations, to support subsequent work on lower bounds for error thresholds.

https://arxiv.org/abs/2602.04952 2026-02-04T00:00:00.000Z Senrui Chen Weiyuan Gong Sisi Zhou

We study the sample complexity of shadow tomography in the high-precision regime under realistic measurement constraints. Given an unknown $d$-dimensional quantum state $\rho$ and a known set of observables $\{O_i\}_{i=1}^m$, the goal is to estimate expectation values $\{\mathrm{tr}(O_i\rho)\}_{i=1}^m$ to accuracy $\epsilon$ in $L_p$-norm, using possibly adaptive measurements that act on $O(\mathrm{polylog}(d))$ number of copies of $\rho$ at a time. We focus on the regime where $\epsilon$ is below an instance-dependent threshold. Our main contribution is an instance-optimal characterization of the sample complexity as $\tilde{\Theta}(\Gamma_p/\epsilon^2)$, where $\Gamma_p$ is a function of $\{O_i\}_{i=1}^m$ defined via an optimization formula involving the inverse Fisher information matrix. Previously, tight bounds were known only in special cases, e.g. Pauli shadow tomography with $L_\infty$-norm error. Concretely, we first analyze a simpler oblivious variant where the goal is to estimate an observable of the form $\sum_{i=1}^m \alpha_i O_i$ with $\|\alpha\|_q = 1$ (where $q$ is dual to $p$) revealed after the measurement. For single-copy measurements, we obtain a sample complexity of $\Theta(\Gamma^{\mathrm{ob}}_p/\epsilon^2)$. We then show $\tilde{\Theta}(\Gamma_p/\epsilon^2)$ is necessary and sufficient for the original problem, with the lower bound applying to unbiased, bounded estimators. Our upper bounds rely on a two-step algorithm combining coarse tomography with local estimation. Notably, $\Gamma^{\mathrm{ob}}_\infty = \Gamma_\infty$. In both cases, allowing $c$-copy measurements improves the sample complexity by at most $\Omega(1/c)$. Our results establish a quantitative correspondence between quantum learning and metrology, unifying asymptotic metrological limits with finite-sample learning guarantees.

https://arxiv.org/abs/2602.03605 2026-02-03T00:00:00.000Z Benjamin Wong Sergey Bravyi David Gosset Yinchen Liu

A complex tensor with $n$ binary indices can be identified with a multilinear polynomial in $n$ complex variables. We say it is a Lee-Yang tensor with radius $r$ if the polynomial is nonzero whenever all variables lie in the open disk of radius $r$. In this work we study quantum states and observables which are Lee-Yang tensors when expressed in the computational basis. We first review their basic properties, including closure under tensor contraction and certain quantum operations. We show that quantum states with Lee-Yang radius $r > 1$ can be prepared by quasipolynomial-sized circuits. We also show that every Hermitian operator with Lee-Yang radius $r > 1$ has a unique principal eigenvector. These results suggest that $r = 1$ is a key threshold for quantum states and observables. Finally, we consider a family of two-local Hamiltonians where every interaction term energetically favors a deformed EPR state $|00\rangle + s|11\rangle$ for some $0 \leq s \leq 1$. We numerically investigate this model and find that on all graphs considered the Lee-Yang radius of the ground state is at least $r = 1/\sqrt{s}$ while the spectral gap between the two smallest eigenvalues is at least $1-s^2$. We conjecture that these lower bounds hold more generally; in particular, this would provide an efficient quantum adiabatic algorithm for the quantum Max-Cut problem on uniformly weighted bipartite graphs.

https://arxiv.org/abs/2602.00255 2026-01-30T00:00:00.000Z Richard Cleve Alex May

Understanding entanglement cost in non-local quantum computation (NLQC) is relevant to complexity, cryptography, gravity, and other areas. This entanglement cost is largely uncharacterized; previous lower bound techniques apply to narrowly defined cases, and proving lower bounds on most simple unitaries has remained open. Here, we give two new lower bound techniques that can be evaluated for any unitary, based on their controllable correlation and controllable entanglement. For Haar random two qubit unitaries, our techniques typically lead to non-trivial lower bounds. Further, we obtain lower bounds on most of the commonly studied two qubit quantum gates, including CNOT, DCNOT, $\sqrt{\text{SWAP}}$, and the XX interaction, none of which previously had known lower bounds. For the CNOT gate, one of our techniques gives a tight lower bound, fully resolving its entanglement cost. The resulting lower bounds have parallel repetition properties, and apply in the noisy setting.

https://arxiv.org/abs/2601.22286 2026-01-29T00:00:00.000Z Han Zheng Chia-Tung Chu Senrui Chen Argyris Giannisis Manes Su-un Lee Sisi Zhou Liang Jiang

Characterizing errors in quantum circuits is essential for device calibration, yet detecting rare error events requires a large number of samples. This challenge is particularly severe in calibrating fault-tolerant, error-corrected circuits, where logical error probabilities are suppressed to higher order relative to physical noise and are therefore difficult to calibrate through direct logical measurements. Recently, Wagner et al. [PRL 130, 200601 (2023)] showed that, for phenomenological Pauli noise models, the logical channel can instead be inferred from syndrome measurement data generated during error correction. Here, we extend this framework to realistic circuit-level noise models. From a unified code-theoretic perspective and spacetime code formalism, we derive necessary and sufficient conditions for learning the logical channel from syndrome data alone and explicitly characterize the learnable degrees of freedom of circuit-level Pauli faults. Using Fourier analysis and compressed sensing, we develop efficient estimators with provable guarantees on sample complexity and computational cost. We further present an end-to-end protocol and demonstrate its performance on several syndrome-extraction circuits, achieving orders-of-magnitude sample-complexity savings over direct logical benchmarking. Our results establish syndrome-based learning as a practical approach to characterizing the logical channel in fault-tolerant quantum devices.

https://arxiv.org/abs/2601.15112 2026-01-21T00:00:00.000Z Lana Bozanic Alex May Stanley Miao

In an entanglement summoning task, a set of distributed, co-operating parties attempt to fulfill requests to prepare entanglement between distant locations. The parties share limited communication resources: timing constraints may require the entangled state be prepared before some pairs of distant parties can communicate, and a restricted set of links in a quantum network may further constrain communication. Building on earlier work, we continue the characterization of entanglement summoning. We give an if and only if condition on entanglement summoning tasks with only bidirected causal connections, and provide a set of sufficient conditions addressing the most general case containing both oriented and bidirected causal connections. Our results rely on the recent development of entanglement sharing schemes.

https://arxiv.org/abs/2601.05457 2026-01-09T00:00:00.000Z Himanshu Sahu Qian Xu Sisi Zhou

Quantum effect enables enhanced estimation precision in metrology, with the Heisenberg limit (HL) representing the ultimate limit allowed by quantum mechanics. Although the HL is generally unattainable in the presence of noise, quantum error correction (QEC) can recover the HL in various scenarios. A notable example is estimating a Pauli-$Z$ signal under bit-flip noise using the repetition code, which is both optimal for metrology and robust against noise. However, previous protocols often assume noise affects only the signal accumulation step, while the QEC operations -- including state preparation and measurement -- are noiseless. To overcome this limitation, we study fault-tolerant quantum metrology where all qubit operations are subject to noise. We focus on estimating a Pauli-$Z$ signal under bit-flip noise, together with state preparation and measurement errors in all QEC operations. We propose a fault-tolerant metrological protocol where a repetition code is prepared via repeated syndrome measurements, followed by a fault-tolerant logical measurement. We demonstrate the existence of an error threshold, below which errors are effectively suppressed and the HL is attained.

https://arxiv.org/abs/2601.03123 2026-01-06T00:00:00.000Z Janani Gomathi Alex Meiburg

When the gate set has continuous parameters, synthesizing a unitary operator as a quantum circuit is, in principle, always possible using exact methods. However, efficiently finding depth- and gate-minimal circuits remains a major challenge. The landscape is very different for compiled unitaries, which arise from programming and typically have short circuits, as compared with generic unitaries, which use all parameters and typically require circuits of maximal size. Previous approaches based on random combinatorial search indicate a low success rate even when the circuit ansatz is nominally adequately parameterized, motivating the use of heavily overparameterized circuits. In this work, we present a gradient-based optimization framework that enables the synthesis of depth- and gate-optimal circuits for generic unitaries without overparameterization, even under restricted hardware connectivity. We prescribe parameter-optimal circuit skeletons and eliminate the need for random combinatorial search. We further show that the poor performance of earlier random-search approaches can be attributed to the inadvertent selection of parameter-deficient circuit topologies. By systematically avoiding such skeletons, our approach achieves reliable convergence while maintaining parameter efficiency.