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Saturday 11 October

Quantum Physics

On the Noisy Road to Open Quantum Dynamics: The Place of Stochastic Hamiltonians

Pietro De Checchi, Federico Gallina, Barbara Fresch et al. (+1 more)

Stochastic evolution underpins several approaches to the dynamics of open quantum systems, such as random modulation of Hamiltonian parameters, the stochastic Schrodinger equation (SSE), and the stochastic Liouville equation (SLE). These approaches replace the explicit system-environment coupling with an effective system-only dynamics, where dissipative behavior emerges from ensemble averaging. Stochastic Hamiltonians, in particular, have long served as phenomenological tools in physical chemistry to include environmental effects without recourse to an explicit microscopic derivation. In this work, we aim at a self-contained and accessible presentation of these approaches to further elaborate on their common roots in essential concepts of stochastic calculus and to delineate the conditions under which they are equivalent. We also discuss how different formulations naturally lead to different numerical time-integration schemes, better suited for either classical simulation platforms, based on finite-difference approximations, or quantum algorithms, that employ random unitary maps. Our analysis aims at providing a unified perspective and actionable recipes for classical and quantum implementations of stochastic evolution in the simulation of open quantum systems.
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All authors Pietro De Checchi, Federico Gallina, Barbara Fresch, Giulio G. Giusteri

Quantum Physics · Cross-listed from nucl-th

Quasiparticle pairing encoding of atomic nuclei for quantum annealing

Emanuele Costa, Axel Pérez-Obiol, Javier Menéndez et al. (+3 more)

Quantum computing is emerging as a promising tool in nuclear physics. However, the cost of encoding fermionic operators hampers the application of algorithms in current noisy quantum devices. In this work, we analyze an encoding scheme based on pairing nucleon modes. This approach significantly reduces the complexity of the encoding, while maintaining a high accuracy for the ground states of semimagic nuclei across the $sd$ and $pf$ shells and for tin isotopes. In addition, we also explore the encoding ability to describe open-shell nuclei within the above configuration spaces. When this scheme is applied to a trotterized quantum adiabatic evolution, our results demonstrate a computational advantage of up to three orders of magnitude in CNOT gate count compared to the standard Jordan-Wigner encoding. Our approach paves the way for efficient quantum simulations of nuclear structure using quantum annealing, with applications to both digital and hybrid quantum computing platforms.
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All authors Emanuele Costa, Axel Pérez-Obiol, Javier Menéndez, Arnau Rios, Artur García-Sáez, Bruno Juliá-Díaz

Quantum Physics · Cross-listed from cond-mat.mes-hall

Hybrid Quantum Systems: Coupling Single-Molecule Magnet Qudits with Industrial Silicon Spin Qubits

Daniel Schroller, Daniel Sitter, Thomas Koch et al. (+12 more)

Molecular spin qudits offer an attractive platform for quantum memory, combining long coherence times with rich multi-level spin structures. Terbium bis(phthalocyaninato) (TbPc$_2$) exemplifies such systems, with demonstrated quantum control and chemical reproducibility. In hybrid quantum architectures, TbPc$_2$ can act as the primary memory element, with semiconductor qubits providing scalable readout and coupling. Here we present a step toward such a hybrid system: using an industrially manufactured silicon metal-oxide-semiconductor (SiMOS) spin qubit to detect electronic spin transitions of an ensemble of TbPc$_2$ molecules. The readout is based on a compact and robust protocol that applies a microwave pulse while all gate voltages defining the qubit are held at a fixed operating point. This protocol, which combines simultaneous Rapid adiabatic Passage and Spin- Selective tunneling (RPSS), enables high-contrast resonance detection and avoids repeated $\pi$-pulse recalibration common in decoupling schemes. By demonstrating ensemble detection, we establish a foundation for integrating molecular quantum memories with industrial qubit platforms and mark an important step toward single-molecule hybrid quantum technologies.
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All authors Daniel Schroller, Daniel Sitter, Thomas Koch, Viktor Adam, Noah Glaeser, Clement Godfrin, Stefan Kubicek, Julien Jussot, Roger Loo, Yosuke Shimura, Danny Wan, Yaorong Chen, Mario Ruben, Kristiaan De Greve, Wolfgang Wernsdorfer

Quantum Physics

Spin exchange of two spin-1/2 atoms

Pan Zeming, Tan Naiming, Gao Chao et al. (+2 more)

The quantum Cheshire cat effect is an important phenomenon in quantum mechanics that reveals the separability of physical properties from their carriers. This effect transcends the classical framework whose attributes must be inherently attached to objects, providing new perspectives for quantum information and precision measurement. According to the quantum Cheshire cat effect, we prepare a pre-selected state of a spin1/2 atomic system composed of two particles through a pre-selection process. We conduct quantum weak measurements on the spins and positions of these two atoms and extract weak values by using the method of imaginary time evolution(ITE). Subsequently, we perform post-selection on these two atoms and design two distinct post-selected states. Initially, we calculate analytical solutions when both atoms encounter these two different post-selected states separately. We also compare the analytical and numerical solutions. Our research theoretically confirms the feasibility of fermionic systems within bipartite quantum Cheshire cat effects and illustrates how delayed-choice influences quantum Cheshire cat effects in spin-1/2 atomic systems.
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All authors Pan Zeming, Tan Naiming, Gao Chao, Yao Zhihai, Wang Xiaoqian

Quantum Physics

Broad nonlocal spectrum in the Pb-InSb hybrid three terminals for potential realization of Kitaev chains

Guoan Li, Xiaofan Shi, Ruixuan Zhang et al. (+21 more)

Hybrid superconductor-semiconductor(SC-SM) nanowires remain one of the foremost platforms for engineering topological superconductivity and Majorana zero modes(MZMs) towards fault-tolerant topological qubits, especially with the rapid development of artificial Kitaev chains. In contrast to the widely used aluminum(Al)-based hybrids, lead(Pb) offers a bulk superconducting gap of ~1.4meV and a critical temperature of ~7.2K, giving rise to a proximity-induced gap that is roughly five times larger than that obtained with Al. Here we present the first three-terminal Pb-hybrid devices and perform nonlocal differential-conductance spectroscopy on this platform. The nonlocal measurement simultaneously resolves a dual-gap feature of the parent Pb gap and the large, hard, gate-tunable induced superconducting gap, distinguished by a switch between electron- and hole-like dissipation processes. Within the induced gap we observe several types of Andreev bound states(ABSs) that undergo singlet-doublet transitions. Moreover, by tuning gate voltages we achieve gate-controlled resonating sign reversals of the nonlocal conductance, identifying three distinct regimes that correspond to different configurations of quantum-dot(QD) resonances(single-resonance, double-resonance, and series-resonance). Finally, the coupling between ABSs and QDs also present and can be modulated from the weak- to strong-coupling limit, indicating the feasibility of realizing the artificial Kitaev chains. Crucially, the robust nonlocal signatures persist up to temperatures(~1K) far above the operating temperature of Al-based devices thanks to the unusually large induced gap, thereby widening the accessible parameter space greatly and underscoring the suitability of Pb-based hybrids for implementing warm temperature artificial Kitaev chains and the topological quantum devices protected by a substantially larger topological gap.
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All authors Guoan Li, Xiaofan Shi, Ruixuan Zhang, Yuxiao Song, Marco Rossi, Ghada Badawy, Zhiyuan Zhang, Anqi Wang, Xingchen Guo, Xiao Deng, Xiao Chen, Liangqian Xu, Bingbing Tong, Peiling Li, Xiaohui Song, Zhaozheng Lyu, Guangtong Liu, Fanming Qu, Michał P. Nowak, Paweł Wójcik, Ziwei Dou, Erik P. A. M. Bakkers, Li Lu, Jie Shen

Quantum Physics

Observational entropy of quantum correlations and entanglement

Leonardo Rossetti, Stefano Mancini, Andreas Winter et al. (+1 more)

The use of coarse graining to connect physical and information theoretic entropies has recently been given a precise formulation in terms of “observational entropy”, describing entropy for observers with respect to a measurement. Here we consider observers with various locality restrictions, including local measurements (LO), measurements based on local operations with classical communication (LOCC), and separable measurements (SEP), with the idea that the “entropy gap” between the minimum locally measured observational entropy and the von Neumann entropy quantifies quantum correlations in a given state. After introducing entropy gaps for general classes of measurements and deriving their general properties, we specialize to LO, LOCC, SEP and other measurement classes related to the locality of subsystems. For those, we show that the entropy gap can be related to well-known measures of entanglement or non-classicality of the state (even though we point out that they are not entanglement monotones themselves). In particular, for bipartite pure states, all of the “local” entropy gaps reproduce the entanglement entropy, and for general multipartite states they are lower-bounded by the relative entropy of entanglement. The entropy gaps of the different measurement classes are ordered, and we show that in general (mixed and multipartite states) they are all different.
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All authors Leonardo Rossetti, Stefano Mancini, Andreas Winter, Joseph Schindler

Quantum Physics · Cross-listed from math.OC

Quantum Alternating Direction Method of Multipliers for Semidefinite Programming

Hantao Nie, Dong An and Zaiwen Wen

Semidefinite programming (SDP) is a fundamental convex optimization problem with wide-ranging applications. However, solving large-scale instances remains computationally challenging due to the high cost of solving linear systems and performing eigenvalue decompositions. In this paper, we present a quantum alternating direction method of multipliers (QADMM) for SDPs, building on recent advances in quantum computing. An inexact ADMM framework is developed, which tolerates errors in the iterates arising from block-encoding approximation and quantum measurement. Within this robust scheme, we design a polynomial proximal operator to address the semidefinite conic constraints and apply the quantum singular value transformation to accelerate the most costly projection updates. We prove that the scheme converges to an $\epsilon$-optimal solution of the SDP problem under the strong duality assumption. A detailed complexity analysis shows that the QADMM algorithm achieves favorable scaling with respect to dimension compared to the classical ADMM algorithm and quantum interior point methods, highlighting its potential for solving large-scale SDPs.
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Quantum Physics · Cross-listed from physics.comp-ph

Random State Approach to Quantum Computation of Electronic-Structure Properties

Yiran Bai, Feng Xiong and Xueheng Kuang

Classical computation of electronic properties in large-scale materials remains challenging. Quantum computation has the potential to offer advantages in memory footprint and computational scaling. However, general and practical quantum algorithms for simulating large-scale materials are still lacking. We propose and implement random-state quantum algorithms to calculate electronic-structure properties of real materials. Using a random state circuit with only a few qubits, we employ real-time evolution with first-order Trotter decomposition and Hadamard test to obtain electronic density of states, and we develop a modified quantum phase estimation algorithm to calculate real-space local density of states via direct quantum measurements. Furthermore, we validate these algorithms by numerically computing the density of states and spatial distributions of electronic states in graphene, twisted bilayer graphene quasicrystals, and fractal lattices, covering system sizes from hundreds to thousands of atoms. Our results manifest that the random-state quantum algorithms provide a general and qubit-efficient route to simulating electronic properties of large-scale periodic and aperiodic materials on quantum computers.
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Quantum Physics

Bounds on Eventually Universal Quantum Gate Sets

Chaitanya Karamchedu, Matthew Fox and Daniel Gottesman

Say a collection of $n$-qu$d$it gates $\Gamma$ is eventually universal if and only if there exists $N_0 \geq n$ such that for all $N \geq N_0$, one can approximate any $N$-qu$d$it unitary to arbitrary precision by a circuit over $\Gamma$. In this work, we improve the best known upper bound on the smallest $N_0$ with the above property. Our new bound is roughly $d^4n$, where $d$ is the local dimension (the `$d$' in qu$d$it), whereas the previous bound was roughly $d^8n$. For qubits ($d = 2$), our result implies that if an $n$-qubit gate set is eventually universal, then it will exhibit universality when acting on a $16n$ qubit system, as opposed to the previous bound of a $256n$ qubit system. In other words, if adding just $15n$ ancillary qubits to a quantum system (as opposed to the previous bound of $255 n$ ancillary qubits) does not boost a gate set to universality, then no number of ancillary qubits ever will. Our proof relies on the invariants of finite linear groups as well as a classification result for all finite groups that are unitary $2$-designs.
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Friday 10 October

Quantum Physics · Cross-listed from cs.AI

A Quantum-Inspired Algorithm for Solving Sudoku Puzzles and the MaxCut Problem

Max B. Zhao and Fei Li

We propose and evaluate a quantum-inspired algorithm for solving Quadratic Unconstrained Binary Optimization (QUBO) problems, which are mathematically equivalent to finding ground states of Ising spin-glass Hamiltonians. The algorithm employs Matrix Product States (MPS) to compactly represent large superpositions of spin configurations and utilizes a discrete driving schedule to guide the MPS toward the ground state. At each step, a driver Hamiltonian – incorporating a transverse magnetic field – is combined with the problem Hamiltonian to enable spin flips and facilitate quantum tunneling. The MPS is updated using the standard Density Matrix Renormalization Group (DMRG) method, which iteratively minimizes the system's energy via multiple sweeps across the spin chain. Despite its heuristic nature, the algorithm reliably identifies global minima, not merely near-optimal solutions, across diverse QUBO instances. We first demonstrate its effectiveness on intermediate-level Sudoku puzzles from publicly available sources, involving over $200$ Ising spins with long-range couplings dictated by constraint satisfaction. We then apply the algorithm to MaxCut problems from the Biq Mac library, successfully solving instances with up to $251$ nodes and $3,265$ edges. We discuss the advantages of this quantum-inspired approach, including its scalability, generalizability, and suitability for industrial-scale QUBO applications.
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Quantum Physics · Cross-listed from cond-mat.quant-gas

Vacuum tunneling of vortices in two-dimensional $^4$He superfluid films

Michael J. Desrochers, Dominic Marchand and P.C.E. Stamp

At low temperature T we expect vacuum tunneling processes to occur in superfluid $^{4}$ He films. We distinguish between extrinsic processes, in which single vortices nucleate by tunneling off boundaries in the system, and intrinsic processes, in which vortex/anti-vortex pairs nucleate far from boundaries. It is crucial to incorporate the varying effective mass of the vortex in tunneling calculations. The intrinsic processes are the superfluid analogue of the Schwinger mechanism in quantum field theory; here they appear as a quantum phase transition at T = 0, driven by an external supercurrent. We calculate the tunneling rate for these processes, and describe a means of testing the predictions using a specific vortex counting experiment.
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Quantum Physics · Cross-listed from cond-mat.stat-mech

Algorithmic Temperature Induced by Adopted Regular Universal Turing Machine

Kentaro Imafuku

We prove that an effective temperature naturally emerges from the algorithmic structure of a regular universal Turing machine (UTM), without introducing any external physical parameter. In particular, the redundancy growth of the machine's wrapper language induces a Boltzmann–like exponential weighting over program lengths, yielding a canonical ensemble interpretation of algorithmic probability. This establishes a formal bridge between algorithmic information theory and statistical mechanics, in which the adopted UTM determines the intrinsic “algorithmic temperature.” We further show that this temperature approaches its maximal limit under the universal mixture (Solomonoff distribution), and discuss its epistemic meaning as the resolution level of an observer.
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Quantum Physics

Mathematical aspects of the decomposition of diagonal U(N) operators

M. M. Fedin and A. A. Morozov

We prove the decomposition of arbitrary diagonal operators into tensor and matrix products of smaller matrices, focusing on the analytic structure of the resulting formulas and their inherent symmetries. Diagrammatic representations are introduced, providing clear visualizations of the structure of these decompositions. We also discuss symmetries of the suggested decomposition. Methods and representations developed in this paper can be applied in different areas, including optimization of quantum computing algorithms, complex biological analysis, crystallography, optimization of AI models, and others.
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Quantum Physics

How much can we learn from quantum random circuit sampling?

Tudor Manole, Daniel K. Mark, Wenjie Gong et al. (+3 more)

Benchmarking quantum devices is a foundational task for the sustained development of quantum technologies. However, accurate in situ characterization of large-scale quantum devices remains a formidable challenge: such systems experience many different sources of errors, and cannot be simulated on classical computers. Here, we introduce new benchmarking methods based on random circuit sampling (RCS), that substantially extend the scope of conventional approaches. Unlike existing benchmarks that report only a single quantity–the circuit fidelity–our framework extracts rich diagnostic information, including spatiotemporal error profiles, correlated and contextual errors, and biased readout errors, without requiring any modifications of the experiment. Furthermore, we develop techniques that achieve this task without classically intractable simulations of the quantum circuit, by leveraging side information, in the form of bitstring samples obtained from reference quantum devices. Our approach is based on advanced high-dimensional statistical modeling of RCS data. We sharply characterize the information-theoretic limits of error estimation, deriving matching upper and lower bounds on the sample complexity across all regimes of side information. We identify surprising phase transitions in learnability as the amount of side information varies. We demonstrate our methods using publicly available RCS data from a state-of-the-art superconducting processor, obtaining in situ characterizations that are qualitatively consistent yet quantitatively distinct from component-level calibrations. Our results establish both practical benchmarking protocols for current and future quantum computers and fundamental information-theoretic limits on how much can be learned from RCS data.
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All authors Tudor Manole, Daniel K. Mark, Wenjie Gong, Bingtian Ye, Yury Polyanskiy, Soonwon Choi

Quantum Physics

Quantum Algorithms for the Minimum Steiner Tree problem with application to Binary Near-Perfect Phylogenies

Lingfa Meng, David Salvador Novo, Albert H. Werner et al. (+1 more)

We present a quantum algorithm in bioinformatics for solving the Binary Near-Perfect Phylogeny Problem (BNPP) with a complexity bound of $O(8.926^q + 8^q nm2)$, where n is the number of input taxa and m is the sequence length for each taxon with each character in the sequence being a binary bit using the QRAM model. We give another polynomial space exact algorithm for the Minimum Steiner Tree (MST) problem with complexity $O^*(e^{(1+g(k,l))k})$ in the circuit model.
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All authors Lingfa Meng, David Salvador Novo, Albert H. Werner, Samir Bhatt

Quantum Physics

Quantum Action-Dependent Channels

Michael Korenberg and Uzi Pereg

We study communication over a quantum action-dependent channel, where the transmitter first performs an action that "shocks" the channel environment, and subsequently encodes a message into a transmission sent through the channel. This two-stage interaction arises in various settings, including rewriting over defective memory and quantum effects such as measurement-induced state collapse. Our model can be viewed as a quantum generalization of Weissman's classical action-dependent channel (2010). Here, however, Alice cannot have a copy of the environment state due to the no-cloning theorem. Instead, she may share entanglement with this environment. We derive achievable rates for reliable message transmission via the quantum action-dependent channel, with either causal or non-causal channel side information (CSI). As a case study, we analyze memory storage with depolarization and selective rewriting, demonstrating how action-dependent control influences performance.
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Quantum Physics

Quantum Circuit for Quantum Fourier Transform for Arbitrary Qubit Connectivity Graphs

Kamil Khadiev, Aliya Khadieva, Vadim Sagitov et al. (+1 more)

In the paper, we consider quantum circuits for the Quantum Fourier Transform (QFT) algorithm. The QFT algorithm is a very popular technique used in many quantum algorithms. We present a generic method for constructing quantum circuits for this algorithm implementing on quantum devices with restrictions. Many quantum devices (for example, based on superconductors) have restrictions on applying two-qubit gates. These restrictions are presented by a qubit connectivity graph. Typically, researchers consider only the linear nearest neighbor (LNN) architecture of the qubit connection, but current devices have more complex graphs. We present a method for arbitrary connected graphs that minimizes the number of CNOT gates in the circuit for implementing on such architecture. We compare quantum circuits built by our algorithm with existing quantum circuits optimized for specific graphs that are Linear-nearest-neighbor (LNN) architecture, “sun” (a cycle with tails, presented by the 16-qubit IBMQ device) and “two joint suns” (two joint cycles with tails, presented by the 27-qubit IBMQ device). Our generic method gives similar results with existing optimized circuits for “sun” and “two joint suns” architectures, and a circuit with slightly more CNOT gates for the LNN architecture. At the same time, our method allows us to construct a circuit for arbitrary connected graphs.
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All authors Kamil Khadiev, Aliya Khadieva, Vadim Sagitov, Kamil Khasanov

Quantum Physics

Efficient Emulation of Neutral Atom Quantum Hardware

Kemal Bidzhiev, Stefano Grava, Pablo le Henaff et al. (+3 more)

Simulating the dynamics of neutral atom arrays is a challenging problem. To address this, we introduce two emulators, emu-sv and emu-mps, as computational backends for Pasqal's pulser package. Emu-sv is designed for high-precision state-vector simulations, giving the possibility to emulate systems of up to $\thicksim 27$ qubits on an A100 40GB GPU, making it perfect for cases where numerically exact results are needed. In contrast, emu-mps uses a Matrix Product State representation and other controlled approximations to efficiently simulate much larger arrays of atoms with manageable errors. We show through benchmark comparisons that both emulators provide significant speed-ups over generic solvers such as QuTiP. In addition, we provide practical guidance on choosing between the two emulators. These quantum software tools are designed to support researchers and developers aiming to simulate quantum systems either as a precursor to full hardware implementation or as a means of benchmarking hardware performance.
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All authors Kemal Bidzhiev, Stefano Grava, Pablo le Henaff, Mauro Mendizabal, Elie Merhej, Anton Quelle

Quantum Physics

Bounds in the Projective Unitary Group with Respect to Global Phase Invariant Metric

Bhanu Pratap Yadav, Mahdi Bayanifar and Olav Tirkkonen

We consider a global phase-invariant metric in the projective unitary group PUn, relevant for universal quantum computing. We obtain the volume and measure of small metric ball in PUn and derive the Gilbert-Varshamov and Hamming bounds in PUn. In addition, we provide upper and lower bounds for the kissing radius of the codebooks in PUn as a function of the minimum distance. Using the lower bound of the kissing radius, we find a tight Hamming bound. Also, we establish bounds on the distortion-rate function for quantizing a source uniformly distributed over PUn. As example codebooks in PUn, we consider the projective Pauli and Clifford groups, as well as the projective group of diagonal gates in the Clifford hierarchy, and find their minimum distances. For any code in PUn with given cardinality we provide a lower bound of covering radius. Also, we provide expected value of the covering radius of randomly distributed points on PUn, when cardinality of code is sufficiently large. We discuss codebooks at various stages of the projective Clifford + T and projective Clifford + S constructions in PU2, and obtain their minimum distance, distortion, and covering radius. Finally, we verify the analytical results by simulation.
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Quantum Physics

Vari-Cool: a non-unitary quantum variational protocol for simulated cooling

Jeffrey Z. Song, Gilad Kishony, Erez Berg et al. (+1 more)

We introduce a variational approach for preparing low energy states of arbitrary target Hamiltonians. The protocol is defined in terms of a repeated cycle consisting of p layers of unitary gates applied to the system and ancilla "bath" qubits, followed by reset of the bath qubits. The gate parameters within each cycle are optimized such that the steady state achieved after many cycles has a low energy expectation value with respect to the target Hamiltonian, and that the energy converges toward the steady state value in as few cycles as possible. We illustrate the protocol for the transverse field Ising model, and study its systematic behaviors with respect to system size, model parameters, and noise using tensor network based classical simulations. We then experimentally demonstrate its operation on IBM's ibm_kingston quantum processor for up to 28 system qubits coupled to 14 bath sites. Classical training on small system sizes and with few unitary layers per cycle gives robust results that transfer well to larger system sizes and to noisy hardware.
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All authors Jeffrey Z. Song, Gilad Kishony, Erez Berg, Mark S. Rudner

Quantum Physics

Spin coherence scale: operator-ordering sensitivity beyond the Heisenberg-Weyl group

Aaron Z. Goldberg, Andre J. Rodrigues, Y. Batuhan Yilmaz et al. (+2 more)

We introduce the spin coherence scale as a measure of quantum coherence for spin systems, generalizing the quadrature coherence scale (QCS) previously defined for quadrature observables. This SU($2$)-invariant measure quantifies the off-diagonal coherences of a quantum state in angular momentum bases, weighted by the classical distinguishability of the superposed states. It serves as a witness of nonclassicality, provides both upper and lower bounds on the Hilbert-Schmidt distance to the set of classical (spin coherent) states, and bounds the Wigner negativity of a spin state. We demonstrate that many hallmark properties of the QCS carry over to the spin setting, including its links to noise susceptibility of a state and moments of quasiprobability distributions and its experimental realizability with a two-copy scheme. The spin coherence scale has direct implications for quantum metrology in the guise of rotation sensing. We also generalize the framework to SU($n$) systems, identifying the unique SU($n$)-invariant depolarization channel and outlining a broad, Lie-algebraic approach to defining and characterizing the properties of coherence scale beyond harmonic oscillators.
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All authors Aaron Z. Goldberg, Andre J. Rodrigues, Y. Batuhan Yilmaz, Aephraim M. Steinberg, Anaelle Hertz

Quantum Physics

Simplified Quantum Weight Reduction with Optimal Bounds

Min-Hsiu Hsieh, Xingjian Li and Ting-Chun Lin

Quantum weight reduction is the task of transforming a quantum code with large check weight into one with small check weight. This problem is important in practice, since low-weight measurements are necessary for reliable implementations of quantum error correction on physical hardware. It is also important theoretically, as it can be used to construct constant-locality versions of quantum locally testable codes, which may be relevant to the quantum PCP conjecture. We give a streamlined geometric procedure for quantum weight reduction based entirely on coning and treating X and Z checks symmetrically, which simplifies Hastings' previous approach. In particular, given an arbitrary $[[n,k,d]]$ quantum code with weight $w$, our method produces a code with parameters $[[O(n w^2 \log w), k, \Omega(d w)]]$, check weight $5$, and qubit weight $6$; these bounds are optimal or close to optimal within the current geometric framework. Applied to random dense CSS codes, our procedure yields explicit quantum codes surpassing the square-root distance barrier, with parameters $[[n, \tilde \Omega(n^{1/3}), \tilde \Omega(n^{2/3})]]$. These codes also admit a three-dimensional embedding that saturates the Bravyi-Poulin-Terhal (BPT) bound, recovering the layer-code result. Our weight reduction technique also improves fault-tolerant logical-operator measurements by reducing the required number of ancilla qubits.
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Quantum Physics

Three Birds with One Stone: Improving Performance, Convergence, and System Throughput with Nest

Yuqian Huo, David Quiroga, Anastasios Kyrillidis et al. (+1 more)

Variational quantum algorithms (VQAs) have the potential to demonstrate quantum utility on near-term quantum computers. However, these algorithms often get executed on the highest-fidelity qubits and computers to achieve the best performance, causing low system throughput. Recent efforts have shown that VQAs can be run on low-fidelity qubits initially and high-fidelity qubits later on to still achieve good performance. We take this effort forward and show that carefully varying the qubit fidelity map of the VQA over its execution using our technique, Nest, does not just (1) improve performance (i.e., help achieve close to optimal results), but also (2) lead to faster convergence. We also use Nest to co-locate multiple VQAs concurrently on the same computer, thus (3) increasing the system throughput, and therefore, balancing and optimizing three conflicting metrics simultaneously.
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All authors Yuqian Huo, David Quiroga, Anastasios Kyrillidis, Tirthak Patel

Quantum Physics

Certifying Quantum Gates via Automata Advantage

Anna Schroeder, Lucas B. Vieira, Jan Nöller et al. (+2 more)

There is growing interest in developing rigorous tests of quantumness that are feasible even before practical quantum advantages become a reality. Such tests not only aim to certify the quantum nature of a system but also serve as benchmarks for precise quantum control. In this work, we argue that promise problems, studied in the theory of finite automata, provide a natural framework for designing sound tests of quantum gate quality. Soundness, the property that only implementations of sufficiently high quality can pass the test, is a central requirement for meaningful certification. We study several promise problems relevant to quantum gate testing and establish separations between the memory resources required by quantum and classical finite automata to solve them. These separations form the theoretical basis for using promise problems as tests of quantumness. Finally, we show how results from automata theory, in particular the minimality of automata, can be used to derive soundness guarantees.
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All authors Anna Schroeder, Lucas B. Vieira, Jan Nöller, Nikolai Miklin, Mariami Gachechiladze

Quantum Physics · Cross-listed from hep-th

Unveiling dynamical quantum error correcting codes via non-invertible symmetries

Rajath Radhakrishnan, Adar Sharon and Nathanan Tantivasadakarn

Dynamical stabilizer codes (DSCs) have recently emerged as a powerful generalization of static stabilizer codes for quantum error correction, replacing a fixed stabilizer group with a sequence of non-commuting measurements. This dynamical structure unlocks new possibilities for fault tolerance but also introduces new challenges, as errors must now be tracked across both space and time. In this work, we provide a physical and topological understanding of DSCs by establishing a correspondence between qudit Pauli measurements and non-invertible symmetries in 4+1-dimensional 2-form gauge theories. Sequences of measurements in a DSC are mapped to a fusion of the operators implementing these non-invertible symmetries. We show that the error detectors of a DSC correspond to endable surface operators in the gauge theory, whose endpoints define line operators, and that detectable errors are precisely those surface operators that braid non-trivially with these lines. Finally, we demonstrate how this framework naturally recovers the spacetime stabilizer code associated with a DSC.
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Quantum Physics · Cross-listed from cond-mat.dis-nn

Disorder-Induced Anomalous Diffusion in a 3D Spin Network

Andrew Stasiuk, Garrett Heller, Lance Berkey et al. (+2 more)

Emergent hydrodynamics (EHD) bridges short-time unitarity with late-time thermodynamics, universal transport phenomena characterize the manner and speed of transport and thermalization. Typical non-integrable systems with few conserved local quantities are expected to be diffusive. In contrast, strongly disordered systems which admit phases such as many-body localization, are predicted to inhibit thermalization and thus slow dynamical transport. Disordered systems represent a uniquely poised platform to probe the quantum-to-classical transition and the emergence of irreversible thermodynamics from the underlying unitary structure. Here, we study a strongly disordered nuclear spin ensemble, using local measurements enabled by the disordered-state technique. We observe an apparent phase transition into a sub-diffusive regime, which we model as a random walk on the emergent fractal structure of a percolating network in the dipolar spin ensemble. Our novel theoretical model provides a framework for characterizing the emergence of thermalization in closed quantum systems, even in the presence of strong disorder.
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All authors Andrew Stasiuk, Garrett Heller, Lance Berkey, Bo Xing, Paola Cappellaro

Quantum Physics

Incoherent Imaging with Spatially Structured Quantum Probes

Anthony J. Brady, Zihao Gong, Alexey V. Gorshkov et al. (+1 more)

Incoherent imaging, including fluorescence and absorption microscopy, is often limited by weak signals and resolution constraints – notoriously, Rayleigh's curse. We investigate how spatially structured quantum probes, combined with quantum detection strategies like spatial mode demultiplexing and photon counting, overcome these limitations. We propose a novel imaging protocol based on twin-beam echoes that maps the generalized incoherent-imaging model – comprising both absorption and fluorescence – onto distinct passive imaging channels that separately encode the absorption and fluorescence signatures. This enables (i) simultaneous absorption and fluorescence imaging and (ii) direct application of well-known results from passive imaging, all featuring quantum-enhanced measurement sensitivity. Remarkably, the same protocol supports displacement-field reconstruction of multiple quadratures (e.g., oscillators' positions) and works for both conventional and subdiffraction imaging, thereby functioning as a universal quantum imaging module. We also examine the utility of Fock states in a structured spatial mode basis, which offer comparable performance in principle. Though developed for optical imaging, our framework applies broadly to quantum-optical microscopy, phononic or acoustic imaging, and mapping stochastic forces, fields, or charge distributions using an array of mechanical oscillators.
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All authors Anthony J. Brady, Zihao Gong, Alexey V. Gorshkov, Saikat Guha

Quantum Physics

Big cats: entanglement in 120 qubits and beyond

Ali Javadi-Abhari, Simon Martiel, Alireza Seif et al. (+2 more)

Entanglement is the quintessential quantum phenomenon and a key enabler of quantum algorithms. The ability to faithfully entangle many distinct particles is often used as a benchmark for the quality of hardware and control in a quantum computer. Greenberger-Horne-Zeilinger (GHZ) states, also known as Schrödinger cat states, are useful for this task. They are easy to verify, but difficult to prepare due to their high sensitivity to noise. In this Letter we report on the largest GHZ state prepared to date consisting of 120 superconducting qubits. We do this via a combination of optimized compilation, low-overhead error detection and temporary uncomputation. We use an automated compiler to maximize error-detection in state preparation circuits subject to arbitrary qubit connectivity constraints and variations in error rates. We measure a GHZ fidelity of 0.56(3) with a post-selection rate of 28%. We certify the fidelity of our GHZ states using multiple methods and show that they are all equivalent, albeit with different practical considerations.
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All authors Ali Javadi-Abhari, Simon Martiel, Alireza Seif, Maika Takita, Ken X. Wei

Quantum Physics · Cross-listed from cond-mat.str-el

A microscopic approach to nonlinear theory of spin-charge separation

Oleksandr Tsyplyatyev, Yiqing Jin, María Moreno et al. (+2 more)

The fate of spin-charge separation beyond the low energy remains elusive up to now. Here we develop a microscopic theory of the correlation functions using the strong coupling expansion of the Hubbard model and demonstrate its validity down to the experimentally relevant $r_{\rm s}>1$. Evaluating the spectral function, we show the general stability of the nonlinear spin-charge modes in whole energy band and investigate all the nonlinear features systematically. We confirm the general prediction experimentally in semiconductor quantum wires. Furthermore, we observe a signal consistent with a continuum of the nonlinear excitations and with a final spectral density around the $3 k_{\rm F}$ point, indicating the robustness of the Hubbard model predictions for a finite range interaction.
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All authors Oleksandr Tsyplyatyev, Yiqing Jin, María Moreno, Wooi Kiat Tan, Christopher J.B. Ford

Quantum Physics

Subspace Leakage Error Randomized Benchmarking of Mølmer-Sørensen Gates

R. T. Sutherland, A. C. Hughes, J. P. Marceaux et al. (+3 more)

We demonstrate a new technique that adapts single-qubit randomized benchmarking to two-qubit Mølmer-Sørensen gates. We use the controllable gate phase to generate Cliffords that act on a two-state subspace, enabling benchmarking of two-qubit gates without single-qubit operations. In addition to quantifying the gate infidelity, the protocol provides valuable information about the type of error by distinguishing between those that conserve the two-state subspace and those that result in leakage out of it. We demonstrate the protocol for calibrating and validating all-electronic maximally entangling gates in a trapped-ion quantum computer, achieving a two-qubit gate error of $2.6 (2)\times10^{-4}$.
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All authors R. T. Sutherland, A. C. Hughes, J. P. Marceaux, H. M. Knaack, C. M. Löschnauer, R. Srinivas