Quantum Physics
Formally Verifying Quantum Phase Estimation Circuits with 1,000+ Qubits
Arun Govindankutty and Sudarshan K. Srinivasan
We present a scalable formal verification methodology for
Quantum Phase Estimation (QPE)
circuits. Our approach uses a symbolic
qubit abstraction based on quantifier-free bit-vector logic, capturing key
quantum phenomena, including superposition, rotation, and measurement. The proposed methodology maps
quantum circuit functional behaviour from
Hilbert space to a bit-vector domain. We develop formal properties aligned with this abstraction to ensure functional correctness of QPE
circuits. The method scales efficiently, verifying QPE
circuits with up to 6 precision
qubits and 1,024 phase
qubits using under 7.5~GB of
memory.
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Quantum Physics
Coupled-Layer Construction of Quantum Product Codes
Shuyu Zhang, Tzu-Chieh Wei and Nathanan Tantivasadakarn
Product codes are a class of
quantum error correcting codes built from two or more constituent codes. They have recently gained prominence for a breakthrough yielding
quantum low-density parity-check (qLDPC) codes with favorable scaling of both code distance and encoding rate. However, despite its powerful algebraic formulation, the physical mechanism for assembling a general product code from its constituents remains unclear. In this letter, we show that the tensor and balanced product codes admit an intuitive coupled-layer construction by taking a stack of one code and condensing a set of excitations in the pattern given by the checks of the other code. We also make a connection to concatenated codes by showing that the tensor product code can be obtained by gauging large-weight logicals in concatenated codes, making them qLDPC. Our framework accommodates both classical or
quantum CSS input codes, unifies known physical mechanisms for constructing higher dimensional topological phases via anyon condensation, and naturally extends to non-topological codes.
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Quantum Physics
Approximate QCAs in one dimension using approximate algebras
Daniel Ranard, Michael Walter and Freek Witteveen
Quantum cellular automata (QCAs) are
automorphisms of tensor product
algebras that preserve locality, with local
quantum circuits as a simple example. We study approximate QCAs, where the locality condition is only satisfied up to a small error, as occurs for local
quantum dynamics on the
lattice. A priori, approximate QCAs could exhibit genuinely new behavior, failing to be well-approximated by any exact QCA. We show this does not occur in one dimension: every approximate QCA on a finite circle can be rounded to a strict QCA with approximately the same action on local operators, so these systems are classified by the same index as in the exact case. Previous work considered the case of the infinite line, by using global methods not amenable to finite systems. Our new approach proceeds locally and now applies to finite systems, including circles or homomorphisms from sub-intervals. We extract exact local boundary
algebras from the approximate QCA restricted to local patches, then glue these to form a strict QCA. The key technical ingredient is a robust notion of the intersection of two subalgebras: when the projections onto two subalgebras approximately commute, we construct an exact subalgebra that serves as a stable proxy for their intersection. This construction uses a recent
theorem of Kitaev on the
rigidity of approximate $C^*$-
algebras.
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Quantum Physics · Cross-listed from math.LO
Four negations and the spectral presheaf
Benjamin Engel and Ryshard-Pavel Kostecki
Using Vakarelov's theory of
lattice logics with negation, we introduce the (co)quasiintuitionistic logic, and prove its soundness and completeness with respect to the class of (co)quasiintuitionistic
algebras. Combining these
algebras together, we obtain biquasiintuitionistic
algebras and the biquasiintuitionistic logic. Their further extension with the Skolem
algebra structure defines Akchurin
algebras and the respective logic, which is a product of biquasiintuitionistic and biintuitionistic logics, featuring four distinct negations. Next we generalise the framework of spectral presheaves (which is a main object in the Butterfield–Isham–Döring topos theoretic approach to
quantum mechanics) to arbitrary complete orthocomplemented
lattices, and show that the orthocomplementation determines two negation operators on the spectral presheaf (one paraconsistent, another paracomplete), equipping the set of all closed-and-open subpresheaves of a spectral presheaf with the structure of a biquasiintuitionistic
algebra. Combined with the generic Skolem (i.e. Heyting and Brouwer)
algebra structure of this set, this gives a particular instance of an Akchurin
algebra. We also show that the underlying orthocomplemented
lattice can be reconstructed as an internal object of the spectral presheaf, resulting as the image of a double coquasiintuitionistic (resp., quasiintuitionistic) negation monad (resp., comonad). Finally, we prove a no-go
theorem for the claim that the spectral presheaf is a model of a dialectical (or any other) relevance logic.
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Quantum Physics
Scalable Postselection of Quantum Resources
J. Wilson Staples, Winston Fu and Jeff D. Thompson
The large overhead imposed by
quantum error correction is a critical challenge to the realization of
quantum computers, and motivates searching for alternative error correcting codes and fault-tolerant
circuit constructions. Postselection is a powerful tool that builds large programs out of probabilistically generated sub-
circuits, and has been shown to increase the threshold of
quantum error correction based on fusing fixed-size resource states or concatenated codes. In this work, we present an approach to lower the overhead of
quantum computing using scalable postselection, based on directly postselecting sub-
circuits with a size extensive in the code distance using decoder soft information. We introduce a metric, the partial gap, that estimates what the logical gap of a resource state will be after it is consumed, and show that postselection based on the partial gap leads to scalable improvements in the logical error rate. In the specific context of implementing logical gates via teleportation through a cluster state, we demonstrate that scalable postselection provides a $4\times$ reduction in the overhead per logical gate, at the same logical error probability.
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Quantum Physics
Exploring pathways towards quantum advantage in quantum chemistry: the case of a molecule with half-Möbius topology
Samuele Piccinelli, Stefano Barison, Alberto Baiardi et al. (+8 more)
We report
quantum chemistry calculations performed on superconducting
quantum processors for a molecule exhibiting the half-Möbius electronic
topology originally introduced by Rončević et al. Using SqDRIFT, a randomized sample-based Krylov
quantum diagonalization
algorithm, we achieve reliable
quantum simulations on active spaces corresponding to 36 orbitals (72
qubits) and extend previous studies up to 50 orbitals (100
qubits). We demonstrate that a systematic increase of active space sizes, which has a concrete impact on the accuracy of the electronic structure description, is achievable with state-of-the-art
quantum processors, thus offering a promising path towards practically relevant
quantum-assisted electronic-structure calculations.
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All authors Samuele Piccinelli, Stefano Barison, Alberto Baiardi, Francesco Tacchino, Jascha Repp, Igor Rončević, Florian Albrecht, Harry L. Anderson, Leo Gross, Alessandro Curioni, Ivano Tavernelli
Quantum Physics · Cross-listed from cond-mat.quant-gas
Fermi-pressure-assisted superradiant transition with a mesoscopic Fermi gas in a cavity
Francesca Orsi, Ekaterina Fedotova, Rohit Prasad Bhatt et al. (+3 more)
We study the superradiant phase transition of a mesoscopic
Fermi gas comprising between a few tens and a few thousand $^6$Li atoms in a high-finesse cavity across a wide range of densities. We observe a non-monotonic variation of the superradiant threshold as a function of density, with a minimum reached when the
Fermi and
recoil wavevectors are comparable. The minimum corresponds to a crossover between
Fermi pressure-assisted ordering and Pauli blocking of
photon scattering, in good agreement with theory. This interpretation is confirmed by a study of the atom-number dependence of the ordering threshold and
photon number scaling. Our system opens the perspective of studying few-
fermion systems with strong and coherent light-matter coupling.
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All authors Francesca Orsi, Ekaterina Fedotova, Rohit Prasad Bhatt, Mae Eichenberger, Léa Dubois, Jean-Philippe Brantut
Quantum Physics
Metriq: A Collaborative Platform for Benchmarking Quantum Computers
Alessandro Cosentino, Changhao Li, Vincent Russo et al. (+6 more)
The fragmented landscape of
quantum computer
benchmarks, characterized by system-specific tools and inconsistent evaluation methodologies, hinders reliable cross-platform performance assessment. We introduce Metriq, an open-source collaborative platform for reproducible cross-platform
quantum benchmarking that integrates
benchmark definition and execution, data collection, and public presentation into a unified workflow. The Metriq
benchmark suite spans both system-level metrics that characterize fundamental device properties such as
entanglement quality, gate performance, and
circuit speed, as well as application-inspired protocols that assess performance on
quantum machine learning, optimization, and
quantum simulation tasks.
Benchmarks are chosen to scale with processor size, and the framework incorporates cost and resource estimation to support practical evaluation. Using Metriq, we collect and publicly release results from more than ten
quantum computers across multiple hardware vendors, enabling systematic cross-platform comparison. The resulting curated
dataset also reveals the practical strengths and limitations of individual
benchmarks, creating a feedback loop that informs the ongoing refinement of the suite. To summarize performance across the
benchmark suite, we introduce the Metriq Score, a composite index aggregating
benchmark outcomes. We further present cross-
benchmark analyses enabled by the shared
dataset and their correlations with hardware calibration metrics. Through open development and data sharing, Metriq provides a practical foundation for reproducible benchmarking of
quantum computers as hardware and benchmarking methods continue to evolve.
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All authors Alessandro Cosentino, Changhao Li, Vincent Russo, Bradley A. Chase, Tom Lubinski, Siyuan Niu, Neer Patel, Nathan Shammah, William J. Zeng
Quantum Physics
Characterization and upgrade of a quantum graph neural network for charged particle tracking
Matteo Argenton, Laura Cappelli and Concezio Bozzi
In the forthcoming years the LHC experiments are going to be upgraded to benefit from the substantial increase of the LHC instantaneous luminosity, which will lead to larger, denser events, and, consequently, greater complexity in reconstructing charged particle tracks, motivating frontier research in new technologies.
Quantum machine learning models are being investigated as potential new approaches to high energy physics (HEP) tasks. We characterize and upgrade a
quantum graph neural network (QGNN) architecture for charged particle track reconstruction on a simulated high luminosity
dataset. The model operates on a set of event graphs, each built from the hits generated in tracking detector layers by particles produced in
proton collisions, performing a classification of the possible hit connections between adjacent layers. In this approach the QGNN is designed as a hybrid architecture, interleaving classical feedforward networks with parametrized
quantum circuits. We characterize the interplay between the classical and
quantum components. We report on the principal upgrades to the original design, and present new evidence of improved training behavior, specifically in terms of convergence toward the final trained configuration.
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Quantum Physics
Symmetry-based perturbation theory for electronic structure calculations
Hiromichi Nishimura, Nam Nguyen, Tanvi Gujarati et al. (+1 more)
We develop a multi-reference perturbation theory for electronic structure calculations based on
symmetries of the
Hamiltonian. The reference
Hamiltonian in the
symmetry-based perturbation theory (SBPT) is chosen such that it possesses more
symmetries than the original
Hamiltonian, leading to a larger reduction of computational resources in terms of both the number of configurations in the configuration interaction expansion and the number of required
qubits in
quantum computing applications. We provide approximate, scalable solutions for the second-order correction, as well as an application to selected configuration interaction. We show that SBPT is an extension of other existing multi-reference perturbation theories and that it can give better results for some molecular systems in a robust way.
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All authors Hiromichi Nishimura, Nam Nguyen, Tanvi Gujarati, Mario Motta
Quantum Physics
Bias in Local Spin Measurements from Deformed Symmetries
Michele Arzano, Goffredo Chirco and Jerzy Kowalski-Glikman
We study local
spin measurements on bipartite singlet states when rotational
symmetry is described by a
quantum group rather than an ordinary Lie group. Although the fundamental
spin-1/2 representation has the usual one-particle action on states, the non-trivial coproduct selects a deformed analogue of the Bell singlet state. We show that conventional tensor-factor measurements on this invariant singlet lead to deformation-dependent one-site outcome statistics. We then compare this standard-local prescription with a braided-local one, obtained by dressing local observables with the R-
matrix and using the corresponding braided inner product. The braided observables are covariant under the
Hopf adjoint action, but define a distinct measurement structure and lead to the reciprocal bias on the deformed singlet state.
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Quantum Physics
Communication-constrained nonlocal correlations
Lucas Pollyceno, Denis Freudenheim, José Nogueira et al. (+3 more)
Identifying the physical grounds distinguishing
quantum theory from broader probabilistic frameworks remains an open challenge. Communication-based proposals – most notably the principles of impossibility of superluminal signaling and information causality (IC) – highlight the role of communication in ruling out unphysical theories and offer an operational rationale on why
quantum predictions prevail over these alternative models. Nevertheless, most such developments rely on communicating parts optimizing over specific tasks, such as communication complexity problems and random access codes (RAC). In this work, we systematically extend this communication-based approach. We characterize the class of communication tasks relevant for this context, and employ the general information-theoretic framework to derive new operational constraints preventing such unphysical behaviors. Remarkably, our results reveal a broad family of previously undetected implausible behaviors, independent of any particular encoding or decoding strategy, reinforcing the role of communication as a fundamental lens through which physically meaningful theories can be identified.
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All authors Lucas Pollyceno, Denis Freudenheim, José Nogueira, Anubhav Chaturvedi, Rafael Rabelo, Marcin Pawłowski
Quantum Physics · Cross-listed from physics.optics
Heterogeneously Integrated Diamond-on-Lithium Niobate Quantum Photonic Platform
Sophie W. Ding, Chang Jin, Zixi Li et al. (+9 more)
Diamond photonics has enabled efficient interfaces for
quantum memories and is predicted to be a critical component of
quantum networks. However, scalable network architectures require spatial, temporal, and spectral control of
photons, which relies on nonlinear and electro-optic functionalities that diamond alone cannot provide. Here, we demonstrate heterogeneous integration of a thin-film lithium niobate (TFLN) platform, which has strong chi-2 nonlinearity and electro-optic effects, with thin diamond films. We demonstrate high-Q diamond photonic
crystal cavities (Q factors exceeding 5x10^4 at 735 nm) that are lithographically aligned with TFLN photonic backbone and critically coupled to it. This allows us to realize low-loss diamond-TFLN "escalators" (loss ~1 dB/coupler) that support efficient light transfer between them. At cryogenic temperatures (5K), we can collect
photons emitted from silicon vacancies (SiVs) embedded within the diamond structure via the TFLN photonic
circuit. This approach establishes a scalable route toward integrated photonic
circuits for practical
quantum networking and other technologies.
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All authors Sophie W. Ding, Chang Jin, Zixi Li, Nicholas Achuthan, Kazuhiro Kuruma, Xinghan Guo, Brandon Grinkemeyer, David D. Awschalom, Nazar Delegan, F. Joseph Heremans, Alexander A. High, Marko Loncar
Quantum Physics
Quantum-limited estimation of the difference between photonic momenta via spatially resolved two-photon interference
Luca Maggio and Vincenzo Tamma
We present a
quantum sensing protocol for three-dimensional estimation of the difference between the momenta of two
photons based on spatially resolved interferometric sampling measurements. The protocol attains ultimate
quantum precision in the simultaneous estimation of the components of the relative momentum for any values of the parameters already with $\sim 2000$ sampling measurements and a bias below $1\%$. These results identify 3D spatially resolved two-
photon interference as an efficient tool for multi-parameter
quantum sensing, with potential applications in high-precision 3D localization, refractometry, and near-field calibration in free-space
quantum technologies.
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Quantum Physics · Cross-listed from hep-th
Parity-dependent Casimir forces and Hall currents for a confined Dirac field
Aitor Fernández and César D. Fosco
We study a massless Dirac field subjected to two alternative boundary conditions on two parallel thin walls, in d + 1 dimensions. The two configurations correspond to the system being even or odd under reflection about the midplane between the two walls, and lead to qualitatively different behaviors. The even (symmetric) configuration produces an attractive Casimir force, whereas the odd (antisymmetric) one yields repulsion, in agreement with a general
theorem linking parity to the sign of the fermionic Casimir effect. We complement this result by studying two phenomena associated with the
vacuum fluctuations responsible for the Casimir interaction, both of which are also sensitive to parity: the correlation between currents concentrated on the walls, and the induced bulk current under the influence of an external electric field. For the latter we show that, in 2 + 1 dimensions, an induced transverse (
Hall-like) current arises, whose spatial profile inherits the
symmetry of the confining potential.
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Quantum Physics
Gate Optimization via Efficient Two-Qubit Benchmarking for NV Centers in Diamond
Alessandro Marcomini, Philipp J. Vetter, Tommaso Calarco et al. (+3 more)
High-fidelity gate implementation requires sophisticated control pulses that steer the
quantum system to undergo the desired transformation.
Quantum Optimal Control allows to derive these control pulses in an open-loop fashion based on numerical simulations. However, their precision can be limited by incomplete knowledge of the system. Closed-loop optimization overcomes this limitation by incorporating feedback from measurements, provided a suitable and efficient measure of the gate performance can be defined. In this article, we present an efficient method to evaluate the performance of a two-
qubit gate by preparation and measurement of only two
quantum states, enabling experimental closed-loop optimization with a metric previously believed to be limited to open-loop control. We tailor the approach to nitrogen-vacancy centers in diamond and, through numerical simulations, demonstrate how the method can optimize a two-
qubit gate while reducing the number of required measurements by two orders of magnitude compared to standard process
tomography under realistic experimental settings.
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All authors Alessandro Marcomini, Philipp J. Vetter, Tommaso Calarco, Felix Motzoi, Fedor Jelezko, Matthias M. Müller
Quantum Physics
The Grasshopper Problem on the Sphere
David Llamas, Dmitry Chistikov, Adrian Kent et al. (+2 more)
The spherical grasshopper problem is a
geometric optimization problem that arises in the context of Bell inequalities and can be interpreted as identifying the best local hidden variable approximation to
quantum singlet correlations for measurements along random axes separated by a fixed angle. In a parallel publication [arXiv:2504.20953], we presented numerical solutions for this problem and explained their significance for singlet simulation and testing. In this companion paper, we describe in detail the
geometric and computational framework underlying these results. We examine the role of spherical discretization and compare three natural variants of the problem: antipodal complementary lawns, antipodal independent lawns, and non-antipodal complementary lawns. We analyze the
geometric structure of the corresponding optimal lawn configurations and interpret it in terms of a spherical harmonics expansion. We also discuss connections to other physical models and to classical problems in
geometric probability.
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All authors David Llamas, Dmitry Chistikov, Adrian Kent, Mike Paterson, Olga Goulko
Quantum Physics · Cross-listed from cond-mat.mes-hall
Microwave response of electrically driven spins in a three-qubit quantum processor
Tanner M. Janda, Heun Mo Yoo, Connor Nasseraddin et al. (+3 more)
In electric dipole
spin resonance (EDSR), a single
spin is electrically driven in the field gradient produced by a micromagnet. While EDSR has enabled high fidelity gate operations in many devices, there are reports of unexpected non-linearities in the Rabi frequency as a function of microwave drive amplitude. We carefully measure the response of Loss-DiVincenzo (LD) single
spin qubits to resonant drives as well as simultaneous resonant and off-resonant drives, as would be encountered in a realistic
quantum processor. With the microwave amplitude carefully calibrated, we find that the Rabi frequency scales linearly with drive amplitude, even when all three
spins are driven simultaneously. We also determine that heating-induced resonance frequency shifts from off-resonant drives are comparable to typical temporal drifts. Our results indicate that the previously observed nonlinear response is not a general feature of LD
spin qubits.
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All authors Tanner M. Janda, Heun Mo Yoo, Connor Nasseraddin, Adam R. Mills, Zhaoyi Joy Zheng, Jason R. Petta
Quantum Physics
Space-sharing and Singleton Bounds for Entanglement-assisted Classical Coding
Yuhang Yao, Tushita Prasad, Markus Grassl et al. (+2 more)
Recent work has noted that a space-sharing argument proves the tightness of the entropic
quantum Singleton bounds, which was left open in the literature for various settings involving only-
quantum messages, only-classical messages, or both classical and
quantum messages. Focusing on the setting of
entanglement-assisted classical coding (EACC), in this letter we first elaborate upon the space-sharing argument and the tight Singleton bound for this setting, and then establish a new tight entropic Singleton bound for EACC codes with
entanglement assistance distributed across a subset of encoders when only local
quantum operations are allowed at each encoder.
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All authors Yuhang Yao, Tushita Prasad, Markus Grassl, Syed Jafar, Hua Sun
Quantum Physics
Extrapolative Quantum Error Mitigation in Continuous-Variable Systems beyond the Training Horizon
Jingpeng Zhang, Shengyong Li, Jie Han et al. (+3 more)
Continuous-variable (CV)
quantum systems provide a versatile platform for
quantum information processing, in which
quantum states can be represented in the quadrature phase space. In realistic implementations, environmental noise, primarily
photon loss and dephasing, progressively degrades these states. Machine-learning-based
quantum error mitigation (QEM) has recently emerged as a promising approach to suppress such noise; however, existing methods are typically limited to the training horizon and require training data that cover the entire
evolution, which is experimentally demanding. Here we introduce a framework for extrapolative
quantum error mitigation based on a time-conditioned Swin
Transformer. By explicitly
embedding the
evolution time via adaptive layer normalization, the model learns a correction map that accounts for the continuous accumulation of noise while capturing nonlocal phase-space correlations. Numerical simulations under both Markovian and non-Markovian noise demonstrate accurate state recovery in the long-time regime, where existing approaches deteriorate. Our results establish extrapolative QEM as a practical route to mitigating noise in CV
quantum systems without exhaustive training data.
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All authors Jingpeng Zhang, Shengyong Li, Jie Han, Qianchuan Zhao, Jing Zhang, Zeliang Xiang
Quantum Physics · Cross-listed from physics.atom-ph
The robustness of composite pulses elucidated by classical mechanics. II. The role of initial state imperfection
Jonathan Berkheim and David J. Tannor
In
nuclear magnetic resonance (NMR), Composite Pulses (CPs) are widely used to correct for pulse imperfections, e.g., RF field inhomogeneity and resonance offset. Although robust pulse sequences have been developed throughout the years, the imperfection of the initial state has not been widely discussed in the literature as an additional systematic error. In previous work, we developed a classical canonical framework to perform stability analysis and used this as a measure of CP robustness. In that work, a single initial condition was allowed to evolve under various pulse imperfections. The current work extends this approach to $2D$ distributions of initial conditions on the Bloch Sphere; the objective is to minimize the area in order to preserve coherence, while maximizing population inversion of the entire distribution. As a case study, we investigate Levitt's $90(x)180(y)90(x)$ pulse sequence, when there is a spread in initial conditions. The canonical framework enables us to assess the robustness of Levitt's pulse sequence, and we find that it is maintained to a great extent even when considering a spread of initial conditions. Nevertheless, by conducting a numerical optimization, we have identified several variants of Levitt's pulse sequence that produce a larger coherent population inversion when there is a spread in initial conditions.
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Quantum Physics · Cross-listed from physics.optics
Mid-Infrared Modulation of Quantum Emitters in Hexagonal Boron Nitride
Karin Yamamura, Xinyang Yu, Chaohao Chen et al. (+3 more)
Single
photon emitters (SPEs) are promising building blocks for practical devices in
quantum technologies. Traditionally, these systems are excited using off-resonant visible light through their
phonon transitions, yet this process remains poorly understood. Here, we explore the interaction of mid-infrared (MIR) excitation on the properties of SPEs in hexagonal boron nitride. Notably, we present a reversible, non-destructive method to enhance emission from blue SPEs using MIR co-excitation. By resonantly driving defect-localized in-plane infrared-active optical
phonon modes near 7.3 um, the MIR field modulates carrier dynamics through a
phonon-assisted recombination. This unique feature, not observed previously for defects in solids, is a promising reservoir in a growing toolkit to modulate
quantum emitters at room temperature for their use in practical
quantum technologies.
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All authors Karin Yamamura, Xinyang Yu, Chaohao Chen, Mehran Kianinia, Christophe Galland, Igor Aharonovich
Quantum Physics
The Transfer Tensor Method: an Analytical Study Case
Marcel Morillas-Rozas, Alberto López-García, Gonzalo Reina Rivero et al. (+2 more)
The transfer tensor method is a versatile tool for analyzing and propagating general open
quantum systems. It captures in a compact manner all
memory effects in a non-Markovian system through a straightforward transformation of a set of dynamical maps. Transfer tensors provide the exact convolutional propagator associated with a given time discretization over the past
evolution of an open
quantum system. Here we show that, for any finite time discretization, the
memory kernel of the Nakajima Zwanzig equation deviates from the exact transfer tensors, although both converge in the continuous-time limit, as expected. We examine this behaviour in the context of an analytically solvable model: a two level atom resonant with a lossy cavity in the Jaynes Cummings limit. The atomic dynamics separate into two decoupled degrees of freedom – the coherence and the population inversion. We derive exact expressions for the dynamical map, the transfer tensors and the
memory kernel governing the coherence, and we relate them to their counterparts for the population inversion. As a function of the ratio between the cavity loss rate and the atom-cavity coupling strength, we identify regions of enhanced non-Markovianity in which the system can be described as fully Markovian for certain time-step choices.
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All authors Marcel Morillas-Rozas, Alberto López-García, Gonzalo Reina Rivero, Jianshu Cao, Javier Cerrillo
Quantum Physics · Cross-listed from cond-mat.str-el
Stochastic Loop Corrections to Belief Propagation for Tensor Network Contraction
Gi Beom Sim, Tae Hyeon Park, Kwang S. Kim et al. (+6 more)
Tensor network contraction is a fundamental computational challenge underlying
quantum many-body physics, statistical mechanics, and machine learning. Belief propagation (BP) provides an efficient approximate solution, but introduces systematic errors on graphs with loops. Here, we introduce a hybrid method that achieves accurate results by stochastically sampling loop corrections to BP and showcase our method by applying it to the two-dimensional
ferromagnetic Ising model. For any pairwise Markov random field with symmetric edge potentials, our approach exploits an exact factorization of the partition function into the BP contribution and a loop correction factor summing over all valid loop configurations, weighted by edge weights derived directly from the potentials. We sample this sum using Markov chain Monte Carlo with moves that preserve the loop constraint, combined with umbrella sampling to ensure efficient exploration across all correlation strengths. Our
stochastic approach provides unbiased estimates with controllable statistical error in any parameter regime.
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All authors Gi Beom Sim, Tae Hyeon Park, Kwang S. Kim, Yanmei Zang, Xiaorong Zou, Hye Jung Kim, D. ChangMo Yang, Soohaeng Yoo Willow, Chang Woo Myung
Quantum Physics
Experimental Realization of the Markov Chain Monte Carlo Algorithm on a Quantum Computer
Baptiste Claudon, Sergi Ramos-Calderer and Jean-Philip Piquemal
Quantum algorithms present a quadratically improved complexity over classical ones for certain sampling tasks. For instance, the
Quantum Amplitude Estimation (QAE)
algorithm promises to speed up the estimation of the mean of certain functions, given access to the
quantum state corresponding to the probability distribution to be sampled from. Classically, samples are often obtained by simulating a Markov chain. In this work, we experimentally use encodings of Markov chains to prepare
quantum states and run a
quantum Markov Chain Monte Carlo (qMCMC)
algorithm on Quantinuum System Model H2 and Quantinuum Helios
quantum computers. We first demonstrate that it is possible to obtain accurate results by operating directly on the physical
qubits. Crucially, to pave the way toward fault-tolerant execution, we also implement these
algorithms using logical
qubits protected by the Iceberg
Quantum Error Detection (QED) code. By applying multiple rounds of mid-
circuit QED during a random walk, we successfully catch and filter out hardware errors. These experiments demonstrate the feasibility of qMCMC on
quantum hardware, bringing us closer to realizing quadratic
quantum speedups with broad applications ranging from molecular modeling to machine learning and finance.
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Quantum Physics
Bound states in a semi-infinite square potential well
Nivaldo A. Lemos
The finite square potential well is a staple problem in introductory
quantum mechanics. There is an extensive literature on the determination of the allowed energies, which requires the solution of a transcendental equation by numerical, graphical or approximate analytic methods. Here we investigate the less explored problem of a particle in a semi-infinite potential well. The energy
eigenvalues, which are also determined by a transcendental equation, are found by a standard graphical method, and a simple rule that yields the number of stationary states is provided. Next a simplification of the aforementioned transcendental equation is attempted. During the process pitfalls are encountered and a purportedly simpler graphical treatment of the problem given in the solutions manual to a fine textbook is shown to be flawed. A more careful analysis brings forth the correct simplification, which is shown to be particularly suitable for finding highly accurate approximations to the energy levels. Finally, a class of exact solutions is produced, the associated normalized eigenfunctions are constructed and the probability of finding the particle inside the well is computed.
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Quantum Physics
Dynamical Lie algebras generated by Pauli strings and quadratic spaces over $\mathbb{F}_2$
Hans Cuypers
Dynamical Lie
algebras, i.e. Lie subalgebras of $\mathfrak{su}(2^n)$, generated by Pauli strings have recently been studied intensively. They are also called Pauli Lie
algebras or
Hamiltonian Lie
algebras. In this paper we provide a uniform mathematical approach to various recent results on Pauli Lie
algebras. Moreover, we present an
algorithm that on input of a set of Pauli strings determines the isomorphism type of the dynamical Lie
algebra generated by these Pauli's in time $\mathcal{O}(\max(n,m)^3)$ where $m$ is the size of the generating set.
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Quantum Physics · Cross-listed from cond-mat.mes-hall
Bound Trions in Two-Dimensional Monolayers: A Review
Roman Ya. Kezerashvili
Trions – Coulomb-bound three-particle excitations composed of two like-charge carriers and one oppositely charged carrier – are central quasiparticles in two-dimensional
semiconductors. Reduced dielectric screening and
quantum confinement strongly enhance their binding energies, making them robust and experimentally accessible. This review surveys theoretical and experimental advances in trion physics, emphasizing rigorous few-body approaches and the role of dielectric environment, anisotropy, and external electric and
magnetic fields. We analyze computational methods for describing trions in two-dimensional configuration spaces and discuss how reduced dimensionality modifies their structure and stability. Connections to many-body phenomena, including screening, Landau-level mixing, and
exciton–polaron crossover, are also highlighted.
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Quantum Physics
Fundamental and operational limitations of Fisher-information-based quantum metrology
Zdeněk Hradil and Jaroslav Řeháček
Quantum-enhanced sensing is commonly benchmarked using the
quantum Fisher information (QFI), often interpreted as a direct indicator of achievable precision. However, such an interpreta- tion is only justified within a fully specified inference framework that consistently incorporates state preparation, measurement design, resource accounting,
estimator construction, prior information, and finite data effects. Here we develop an operational, end-to-end framework for
quantum sensing under finite resources and identify general principles required for meaningful performance assess- ment. A central conceptual point is that the relevant unit of estimation is not a single detection event, but the complete data set required to construct a consistent
estimator. Rather than relying on abstract statistical formalism, we analyze a set of paradigmatic and experimentally relevant ex- amples that expose common pitfalls in widely discussed
quantum sensing strategies. These include
quantum interferometry, sensing with squeezed states, and criticality-inspired protocols. Our results clarify when large Fisher information or nonclassical resources translate into genuine metrological advantage, and when they do not. They further provide a practical methodology for designing and evaluating
quantum sensing protocols under realistic experimental constraints.
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Quantum Physics
Construction of a Family of Quantum Codes Using Sub-exceding Functions via the Hypergraph Product and the Generalized Shor Construction
Luc Rabefihavanana, Harinaivo Andriatahiny and Randriamiarampanahy Ferdinand
In this paper, we introduce a new family of stabilizer
quantum LDPC codes derived from the classical linear codes $L_k$ and $L_k^{+}$, defined via sub-exceding functions. In previous work, these codes demonstrated strong performance in minimum distance, decoding efficiency, and structural simplicity. By combining the hypergraph product framework with a generalized Shor construction, we obtain a scalable class of
quantum codes with parameters $[[6k^2,\, k^2,\, d]]$. The resulting
quantum codes exhibit a rich combinatorial structure and promising properties, particularly in terms of locality, low-density parity-check (LDPC) structure, and asymptotic behavior. The minimum distance satisfies $d=3$ for $k=3$ and $d=4$ for $k\ge4$, establishing a new framework for structured
quantum LDPC code design and optimization.
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