Gauss law codes identify the full gauge-invariant sector as the code space while vacuum codes restrict to the matter vacuum, with the two shown to be unitarily equivalent for finite gauge groups.
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Quantum simulation
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abstract
Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficulty may be overcome by using some controllable quantum system to study another less controllable or accessible quantum system, i.e., quantum simulation. Quantum simulation promises to have applications in the study of many problems in, e.g., condensed-matter physics, high-energy physics, atomic physics, quantum chemistry and cosmology. Quantum simulation could be implemented using quantum computers, but also with simpler, analog devices that would require less control, and therefore, would be easier to construct. A number of quantum systems such as neutral atoms, ions, polar molecules, electrons in semiconductors, superconducting circuits, nuclear spins and photons have been proposed as quantum simulators. This review outlines the main theoretical and experimental aspects of quantum simulation and emphasizes some of the challenges and promises of this fast-growing field.
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A structure-aware transformer trained on 3-14 qubit systems predicts Trotter orderings for 16-20 qubit 1D Heisenberg Hamiltonians with a mean fidelity gap of 0.00115 to the best of 24 candidates.
Hybrid Path-Sums offer a new symbolic framework with rewriting rules and assertions to represent, simplify, and verify properties of hybrid quantum-classical programs.
Sudden quenches in a pair of coupled oscillators produce exact or approximate thermalization of a quantum harmonic oscillator to arbitrary temperatures via solvable equations on the Gaussian covariance matrix.
CBMD decomposes non-Hermitian operators via contour residues to enable optimal-query quantum simulation of first-order dynamics and special functions such as Bessel and Airy evolutions without requiring diagonalizability.
A state discrimination game on energy-restricted quantum states creates a hierarchy of optimal success probabilities that certifies multipartite entanglement structure.
VarQEC uses a distinguishability loss as a machine-learning objective to variationally discover resource-efficient encoding circuits optimized for given noise models.
Hybrid simulation of the 2-qubit quantum kicked top on IBMQ shows periodic evolution and chaos signatures in time-averaged entanglement, with gate count independent of kick number.
A scalable Trotterization and Localized Diagonal Operator Approximation enable real-time quantum simulation of the multi-flavor Gross-Neveu model on utility-scale superconducting hardware.
SD-FSNN combines stochastic dimension sampling, frozen random weights, Gaussian ansatz, and structure-preserving layers to solve high-dimensional GPEs on unbounded domains with dimension-independent cost and improved accuracy over prior solvers.
SQD needs an exponentially increasing number of computational-basis configurations to approximate ground-state energies of Heisenberg and Hubbard models within fixed accuracy, even when configurations are chosen optimally by probability.
Higher entanglement entropy reduces variance of Trotter errors and higher magic reduces kurtosis, making error distributions more robust in quantum simulation.
Empirical scaling study reports VQS requires shallower circuits than Trotterization for time evolution as system size and simulation time grow.
A synthesis of expert insights from the ADAC Quantum Computing Working Group and member survey on the complementary roles of quantum and classical high-performance computing in future hybrid infrastructures.
citing papers explorer
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Gauss law codes and vacuum codes from lattice gauge theories
Gauss law codes identify the full gauge-invariant sector as the code space while vacuum codes restrict to the matter vacuum, with the two shown to be unitarily equivalent for finite gauge groups.
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Structure-Aware Transformers for Learning Near-Optimal Trotter Orderings with System-Size Generalization in 1D Heisenberg Hamiltonians
A structure-aware transformer trained on 3-14 qubit systems predicts Trotter orderings for 16-20 qubit 1D Heisenberg Hamiltonians with a mean fidelity gap of 0.00115 to the best of 24 candidates.
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Hybrid Path-Sums for Hybrid Quantum Programs
Hybrid Path-Sums offer a new symbolic framework with rewriting rules and assertions to represent, simplify, and verify properties of hybrid quantum-classical programs.
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Thermalization from quenching in coupled oscillators
Sudden quenches in a pair of coupled oscillators produce exact or approximate thermalization of a quantum harmonic oscillator to arbitrary temperatures via solvable equations on the Gaussian covariance matrix.
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Quantum Simulation of Non-Hermitian Special Functions and Dynamics via Contour-based Matrix Decomposition
CBMD decomposes non-Hermitian operators via contour residues to enable optimal-query quantum simulation of first-order dynamics and special functions such as Bessel and Airy evolutions without requiring diagonalizability.
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Entanglement Structure Certification Based on Energy-Restricted State Discrimination
A state discrimination game on energy-restricted quantum states creates a hierarchy of optimal success probabilities that certifies multipartite entanglement structure.
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Learning Encodings by Maximizing State Distinguishability: Variational Quantum Error Correction
VarQEC uses a distinguishability loss as a machine-learning objective to variationally discover resource-efficient encoding circuits optimized for given noise models.
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Simulating quantum chaos on a quantum computer
Hybrid simulation of the 2-qubit quantum kicked top on IBMQ shows periodic evolution and chaos signatures in time-averaged entanglement, with gate count independent of kick number.
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Quantum Simulation of the Real-time Dynamics in the multi-flavor Gross-Neveu Model at the utility scale using Superconducting Quantum Computers
A scalable Trotterization and Localized Diagonal Operator Approximation enable real-time quantum simulation of the multi-flavor Gross-Neveu model on utility-scale superconducting hardware.
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Stochastic-Dimension Frozen Sampled Neural Network for High-Dimensional Gross-Pitaevskii Equations on Unbounded Domains
SD-FSNN combines stochastic dimension sampling, frozen random weights, Gaussian ansatz, and structure-preserving layers to solve high-dimensional GPEs on unbounded domains with dimension-independent cost and improved accuracy over prior solvers.
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A Critical Assessment of the Sample-Based Quantum Diagonalization for Heisenberg and Hubbard Models
SQD needs an exponentially increasing number of computational-basis configurations to approximate ground-state energies of Heisenberg and Hubbard models within fixed accuracy, even when configurations are chosen optimally by probability.
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Taming Trotter Errors with Quantum Resources
Higher entanglement entropy reduces variance of Trotter errors and higher magic reduces kurtosis, making error distributions more robust in quantum simulation.
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Performance and scaling analysis of variational quantum simulation
Empirical scaling study reports VQS requires shallower circuits than Trotterization for time evolution as system size and simulation time grow.
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The Role of Quantum Computing in Advancing Scientific High-Performance Computing: A perspective from the ADAC Institute
A synthesis of expert insights from the ADAC Quantum Computing Working Group and member survey on the complementary roles of quantum and classical high-performance computing in future hybrid infrastructures.