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Quantum simulations of realistic systems by auxiliary fields

Shiwei Zhang, Henry Krakauer, Wissam A. Al-Saidi +1 more

Computer Physics CommunicationsApr 13, 200520 citations

Auxiliary field methods for the Simulation of Quantum circuits

正道石川, Masamichi Ishikawa

Jan 1, 20020 citations

Stochastic simulation of quantum computation

L. R. U. MANSSUR, Renato Portugal

We discuss a stochastic method to simulate quantum computing algorithms in a classical computer using the Hubbard-Stratonovich decomposition of n -qubit gates into one-qubit gates integrated over auxiliary fields. The problem reduces to finding the fixed points of the associated system of Langevin differential equations. We show that the method can be applied to Grover's algorithm.

Europhysics Letters (EPL)Aug 1, 20030 citations

Simulation of Quantum Computation

Tzvetan S. Metodi, Frederic T. Chong

Synthesis lectures on computer architectureJan 1, 20060 citations

Efficient Ab Initio Auxiliary-Field Quantum Monte Carlo Calculations in Gaussian Bases via Low-Rank Tensor Decomposition

Mário Motta, James Shee, Shiwei Zhang +1 more

We describe an algorithm to reduce the cost of auxiliary-field quantum Monte Carlo (AFQMC) calculations for the electronic structure problem. The technique uses a nested low-rank factorization of the electron repulsion integral (ERI). While the cost of conventional AFQMC calculations in Gaussian bases scales as, where N is the size of the basis, we show that ground-state energies can be computed through tensor decomposition with reduced memory requirements and subquartic scaling. The algorithm is applied to hydrogen chains and square grids, water clusters, and hexagonal BN. In all cases, we observe significant memory savings and, for larger systems, reduced, subquartic simulation time.We describe an algorithm to reduce the cost of auxiliary-field quantum Monte Carlo (AFQMC) calculations for the electronic structure problem. The technique uses a nested low-rank factorization of the electron repulsion integral (ERI). While the cost of conventional AFQMC calculations in Gaussian bases scales as, where N is the size of the basis, we show that ground-state energies can be computed through tensor decomposition with reduced memory requirements and subquartic scaling. The algorithm is applied to hydrogen chains and square grids, water clusters, and hexagonal BN. In all cases, we observe significant memory savings and, for larger systems, reduced, subquartic simulation time.

arXiv:1810.01549Journal of Chemical Theory and ComputationMay 15, 201963 citations

Contextual Subspace Auxiliary-Field Quantum Monte Carlo: Improved Bias with Reduced Quantum Resources

Matthew Kiser, Matthias Beuerle, Fedor Šimkovic

Using trial wave functions prepared on quantum devices to reduce the bias of auxiliary-field quantum Monte Carlo (QC-AFQMC) has established itself as a promising hybrid approach to the simulation of strongly correlated many body systems. Here, we further reduce the required quantum resources by decomposing the trial wave function into classical and quantum parts, respectively treated by classical and quantum devices, within the contextual subspace projection formalism. Importantly, we show that our algorithm is compatible with the recently developed matchgate shadow protocol for efficient overlap calculation in QC-AFQMC. Investigating the nitrogen dimer and the reductive decomposition of ethylene carbonate in lithium-based batteries, we observe that our method outperforms a number of established algorithm for ground state energy computations, while reaching chemical precision with less than half of the original number of qubits.Using trial wave functions prepared on quantum devices to reduce the bias of auxiliary-field quantum Monte Carlo (QC-AFQMC) has established itself as a promising hybrid approach to the simulation of strongly correlated many body systems. Here, we further reduce the required quantum resources by decomposing the trial wave function into classical and quantum parts, respectively treated by classical and quantum devices, within the contextual subspace projection formalism. Importantly, we show that our algorithm is compatible with the recently developed matchgate shadow protocol for efficient overlap calculation in QC-AFQMC. Investigating the nitrogen dimer and the reductive decomposition of ethylene carbonate in lithium-based batteries, we observe that our method outperforms a number of established algorithm for ground state energy computations, while reaching chemical precision with less than half of the original number of qubits.

arXiv:2408.06160Journal of Chemical Theory and ComputationFeb 20, 20258 citations

Quantum Computing Simulation using the Auxiliary Field Decomposition

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