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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Native spin-changing collisions plus arbitrary quadratic Zeeman shift produce universal OAT-scalable spin squeezing in spin-1 BECs, freezable by turning the shift off.
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.
Entanglement entropy bounds the variance of Trotter error downward, and magic drives the error kurtosis downward (Kur = α + βM, β<0 for large systems).
Feynman's clock maps arbitrary circuits onto Hamiltonian dynamics whose BBGKY hierarchy enables polynomial-overhead, controllable error mitigation via informed sampling.
Linear-programming method for conjugating local fermionic unitaries with free evolution realizes arbitrary complex tunneling coefficients in fermionic lattice models constrained only by connectivity.
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 evolution operators into Hermitian LCU terms via a matrix residue theorem, matching known optimal query bounds and offering a route to polynomial matrix functions.
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.
A frozen-feature neural network with a Gaussian envelope and stochastic dimension sampling produces accurate 1D–3D GPE solutions, but the 1000-dimensional claim rests on a manufactured stationary equation, not GPE dynamics.
Lindblad dynamics admits a universal closed algebra of Hermitian operators with model dependence isolated in a single set of coefficients.
Bosonic Fock encoding in a cavity, driven by SNAP and displacement pulses, produces neutrino oscillation probabilities that match theoretical predictions for two- and three-flavor cases.
Continuous-variable photonic platform with 20,000-mode cluster state simulates advection transport equation, achieving relative errors of 0.8% and 0.92% on first- and second-order moments via homodyne readout.
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.
Exact vs. restricted particle-hole dynamics in graphene flakes after optical quench shows periodic structures captured by low-order excitations but confined ones require higher-order contributions, positioning the setup as a quantum-computing benchmark.
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.
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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.