For PEPS with strong injectivity above a threshold, belief propagation finds fixed points efficiently and cluster-corrected BP approximates observables to 1/poly(N) error in poly(N) time, with local perturbations affecting the fixed point only locally.
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Dynamics of disordered quantum systems with two- and three-dimensional tensor networks
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abstract
Large scale quantum annealing dynamics of Ising spin glasses were recently implemented on D-Wave's Advantage$2$ system on a range of lattices. Following extensive comparison to existing numerical methods, these experiments were claimed to be beyond the reach of classical computation. Here, we simulate these spin glass models with lattice-specific tensor networks, using belief propagation (BP) to keep up with the entanglement generated during the time evolution and then extracting expectation values with more sophisticated variants of BP. We find that state-of-the-art accuracies can be achieved with modest computational resources. Moreover, our results are scalable in both two and three dimensions, which we leverage to verify universal Kibble-Zurek physics on systems involving hundreds of qubits.
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For PEPS states with loop-decay, BP with cluster corrections approximates local observables exponentially accurately, and loop-decay necessarily implies exponential decay of connected correlations, ruling out BP at critical points.
Neural quantum states with a tailored 3D convolutional architecture simulate quench dynamics up to 1000 qubits and verify the 3D quantum Kibble-Zurek mechanism with RG-derived logarithmic corrections and data collapse.
The paper introduces the first general protocol for magnetic hysteresis on programmable quantum annealers and reports non-monotonic dependence of loop area on quantum fluctuations along with disorder-induced steps.
Presents IRD-GrAPE optimal control to generate GHZ, Dicke, and extremal states in dipolar Rydberg arrays by truncating the Hilbert space to capture leakage with linear scaling.
Deep Boltzmann Quantum States with natural-gradient optimization and annealing-like training match exact or best-known solutions for large infinite-range Ising spin glasses and solve job shop scheduling instances.
Tensor network simulations act as effective surrogate models for training QAOA on large 2D lattices, overcoming limits of parameter transfer from small instances and remaining classically feasible with moderate bond dimensions.
For unitaries from local or pairwise interactions, depolarizing noise above a critical strength makes open quantum spin chain dynamics exactly classically simulable by halting growth in the negative Markov chain representation.
SBQA adds inter-replica interactions to simulated bifurcation to mimic quantum tunneling and improves performance on sparse rugged optimization problems over standard SBM.
A parallel-in-time encoding turns quantum dynamical propagators into QUBO instances for direct benchmarking of quantum annealers against classical solvers on models from single-qubit rotations to PT-symmetric systems.
3D PEPS simulations of the SU(4) Heisenberg model on the hyperhoneycomb lattice extrapolate to a gapless spin-liquid ground state.
Generalized belief propagation approximates tensor network contractions via hierarchical region messages and fixed-point solutions, demonstrated on Ising, ice, AKLT, and random tensor networks.
Tensor networks with belief propagation fail to simulate Google's quantum echoes OTOC experiment because the circuits produce largely incompressible entanglement.
The paper identifies four key hurdles in the transition from NISQ to FASQ quantum computers and argues that targeting them will accelerate progress toward useful quantum advantage.
citing papers explorer
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Algorithmic Locality via Provable Convergence in Quantum Tensor Networks
For PEPS with strong injectivity above a threshold, belief propagation finds fixed points efficiently and cluster-corrected BP approximates observables to 1/poly(N) error in poly(N) time, with local perturbations affecting the fixed point only locally.
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Belief Propagation and Tensor Network Expansions for Many-Body Quantum Systems: Rigorous Results and Fundamental Limits
For PEPS states with loop-decay, BP with cluster corrections approximates local observables exponentially accurately, and loop-decay necessarily implies exponential decay of connected correlations, ruling out BP at critical points.
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Real-time Dynamics in 3D for up to 1000 Qubits with Neural Quantum States: Quenches and the Quantum Kibble--Zurek Mechanism
Neural quantum states with a tailored 3D convolutional architecture simulate quench dynamics up to 1000 qubits and verify the 3D quantum Kibble-Zurek mechanism with RG-derived logarithmic corrections and data collapse.
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Magnetic Hysteresis Experiments Performed on Quantum Annealers
The paper introduces the first general protocol for magnetic hysteresis on programmable quantum annealers and reports non-monotonic dependence of loop area on quantum fluctuations along with disorder-induced steps.
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Quantum optimal control of the Dicke manifold in dipolar Rydberg atom arrays
Presents IRD-GrAPE optimal control to generate GHZ, Dicke, and extremal states in dipolar Rydberg arrays by truncating the Hilbert space to capture leakage with linear scaling.
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Solving Classical and Quantum Spin Glasses with Deep Boltzmann Quantum States
Deep Boltzmann Quantum States with natural-gradient optimization and annealing-like training match exact or best-known solutions for large infinite-range Ising spin glasses and solve job shop scheduling instances.
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Tensor network surrogate models for variational quantum computation
Tensor network simulations act as effective surrogate models for training QAOA on large 2D lattices, overcoming limits of parameter transfer from small instances and remaining classically feasible with moderate bond dimensions.
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Quantum-to-Classical Computability Transition via Negative Markov Chains
For unitaries from local or pairwise interactions, depolarizing noise above a critical strength makes open quantum spin chain dynamics exactly classically simulable by halting growth in the negative Markov chain representation.
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Simulated Bifurcation Quantum Annealing
SBQA adds inter-replica interactions to simulated bifurcation to mimic quantum tunneling and improves performance on sparse rugged optimization problems over standard SBM.
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Quantum-inspired dynamical models on quantum and classical annealers
A parallel-in-time encoding turns quantum dynamical propagators into QUBO instances for direct benchmarking of quantum annealers against classical solvers on models from single-qubit rotations to PT-symmetric systems.
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SU(4) Heisenberg model on the hyperhoneycomb lattice
3D PEPS simulations of the SU(4) Heisenberg model on the hyperhoneycomb lattice extrapolate to a gapless spin-liquid ground state.
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Contracting Tensor Networks with Generalized Belief Propagation
Generalized belief propagation approximates tensor network contractions via hierarchical region messages and fixed-point solutions, demonstrated on Ising, ice, AKLT, and random tensor networks.
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Tensor Networks with Belief Propagation Cannot Feasibly Simulate Google's Quantum Echoes Experiment
Tensor networks with belief propagation fail to simulate Google's quantum echoes OTOC experiment because the circuits produce largely incompressible entanglement.
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Mind the gaps: The fraught road to quantum advantage
The paper identifies four key hurdles in the transition from NISQ to FASQ quantum computers and argues that targeting them will accelerate progress toward useful quantum advantage.