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Bulletin of the American Physical Society

High accuracy many-body calculations on quantum computers

James K. Freericks, Jeffrey Cohn, Khadijeh Najafi, Forest Yang

Published Jun 1, 2018• 0 citations
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Determining the dynamics of the expectation values for operators acting on a quantum many-body (QMB) system is a challenging task. Matrix product states (MPS) have traditionally been the "go-to" models for these systems because calculating expectation values in this representation can be done with relative simplicity and high accuracy. However, such calculations can become computationally costly when extended to long times. Here, we present a solution for efficiently extending the computation of expectation values to long time intervals. We utilize a multi-layer perceptron (MLP) model as a tool for regression on MPS expectation values calculated within the regime of short time intervals. With this model, the computational cost of generating long-time dynamics is significantly reduced, while maintaining a high accuracy. These results are demonstrated with operators relevant to quantum spin models in one spatial dimension.

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Abstract Accurate quantum many-body calculations often depend on reliable reference states or good human-designed ansätze, yet such knowledge can become unreliable in hard problems like strongly correlated systems. Here we show that high-accuracy many-body ground states can be discovered directly from random Slater determinants. We introduce the Trimmed Configuration Interaction (TrimCI) method, which self-refines by iteratively expanding and trimming configurations in the variational space. TrimCI matches state-of-the-art accuracy using orders of magnitude fewer determinants and computer time: 10 6 -fold fewer than a recent quantum computing calculation on an iron-sulfur cluster, 10 5 -fold fewer than a leading classical method on a larger iron-sulfur cluster in nitrogenase, and over 99% of the ground-state energy of a strongly correlated lattice system from 10 −28 of its Hilbert space, exceeding quantum Monte Carlo accuracy by orders of magnitude in some regimes. TrimCI thus provides an auto-initializing, accurate and highly efficient framework for quantum many-body systems, whose compact explicit wavefunctions enable direct and rapid evaluation of observables.

Nature Communications•Sep 29, 2026•0 citations
Quantum many-body calculation methods, including exact diagonalization, quantum Monte Carlo, density matrix and tensor renormalization, and dynamic mean field theory, as well as emerging methods harnessing the power of artificial intelligence and quantum computing, can be used to accurately and efficiently calculate the physical properties of correlated quantum many-body systems. The quantum particles in the interacting, non-perturbative many-body system are highly entangled, and the mean field theory often lacks sufficient accuracy or may even break down for certain problems. It is thus very necessary to develop new methods for studying the exotic states and emergent phenomena in correlated systems, such as high-temperature superconductivity and frustrated quantum magnetism. Recently, the rapid progress in the field of many-body calculation has shown the characteristics of interdisciplinary cross, and there is increasingly significant interplay and integration with machine learning, materials science, quantum simulation and computation, among other fields. This paper outlines the brief history of many-body calculations, major approaches and their current status, as well as main challenges in this field.
Determining the dynamics of the expectation values for operators acting on a quantum many-body (QMB) system is a challenging task. Matrix product states (MPS) have traditionally been the "go-to" models for these systems because calculating expectation values in this representation can be done with relative simplicity and high accuracy. However, such calculations can become computationally costly when extended to long times. Here, we present a solution for efficiently extending the computation of expectation values to long time intervals. We utilize a multi-layer perceptron (MLP) model as a tool for regression on MPS expectation values calculated within the regime of short time intervals. With this model, the computational cost of generating long-time dynamics is significantly reduced, while maintaining a high accuracy. These results are demonstrated with operators relevant to quantum spin models in one spatial dimension.
Abstract Accurate quantum many-body calculations often depend on reliable reference states or good human-designed ansätze, yet such knowledge can become unreliable in hard problems like strongly correlated systems. Here we show that high-accuracy many-body ground states can be discovered directly from random Slater determinants. We introduce the Trimmed Configuration Interaction (TrimCI) method, which self-refines by iteratively expanding and trimming configurations in the variational space. TrimCI matches state-of-the-art accuracy using orders of magnitude fewer determinants and computer time: 10 6 -fold fewer than a recent quantum computing calculation on an iron-sulfur cluster, 10 5 -fold fewer than a leading classical method on a larger iron-sulfur cluster in nitrogenase, and over 99% of the ground-state energy of a strongly correlated lattice system from 10 −28 of its Hilbert space, exceeding quantum Monte Carlo accuracy by orders of magnitude in some regimes. TrimCI thus provides an auto-initializing, accurate and highly efficient framework for quantum many-body systems, whose compact explicit wavefunctions enable direct and rapid evaluation of observables.