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Physical Review Applied

Surrogate-constructed scalable-circuits adaptive variational quantum eigensolver in the Schwinger model

Erik Gustafson, Kyle Sherbert, Adrien Florio, Karunya Shirali, Yanzhu Chen, Henry Lamm, S. N. Valgushev, Andreas Weichselbaum, Sophia E. Economou, Robert D. Pisarski, Norm M. Tubman

Published Jun 2, 2025• 10 citations
Publisher

Abstract

Inspired by recent advancements in simulating periodic systems on quantum computers, we develop an approach to further advance the simulation of these systems, named (SC)${}^{2}$-ADAPT-VQE. Our approach extends the scalable-circuits ADAPT-VQE framework, which builds an ansatz from a pool of coordinate-invariant operators defined for arbitrarily large, though not arbitrarily small, volumes. Our method uses a classically tractable ``surrogate constructed'' method to remove irrelevant operators from the pool, reducing the minimum size for which the scalable circuits are defined. Bringing together the scalable circuits and the surrogate constructed approaches forms the core of the (SC)${}^{2}$ methodology. Our approach allows for a wider set of classical computations on small volumes, which can be used for a more robust extrapolation protocol. While developed in the context of lattice models, the surrogate construction portion is applicable to a wide variety of problems where information about the relative importance of operators in the pool is available. As an example, we use it to compute the properties of the Schwinger model---quantum electrodynamics for a single, massive fermion in $1+1$ dimensions---and show that our method can be used to accurately extrapolate to the continuum limit.

DOI
10.1103/physrevapplied.23.064002

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Inspired by recent advancements in simulating periodic systems on quantum computers, we develop an approach to further advance the simulation of these systems, named (SC)2{}^{2}2-ADAPT-VQE. Our approach extends the scalable-circuits ADAPT-VQE framework, which builds an ansatz from a pool of coordinate-invariant operators defined for arbitrarily large, though not arbitrarily small, volumes. Our method uses a classically tractable ``surrogate constructed'' method to remove irrelevant operators from the pool, reducing the minimum size for which the scalable circuits are defined. Bringing together the scalable circuits and the surrogate constructed approaches forms the core of the (SC)2{}^{2}2 methodology. Our approach allows for a wider set of classical computations on small volumes, which can be used for a more robust extrapolation protocol. While developed in the context of lattice models, the surrogate construction portion is applicable to a wide variety of problems where information about the relative importance of operators in the pool is available. As an example, we use it to compute the properties of the Schwinger model---quantum electrodynamics for a single, massive fermion in 1+11+11+1 dimensions---and show that our method can be used to accurately extrapolate to the continuum limit.
Inspired by recent advancements of simulating periodic systems on quantum computers, we develop a new approach, (SC)2^22-ADAPT-VQE, to further advance the simulation of these systems. Our approach extends the scalable circuits ADAPT-VQE framework, which builds an ansatz from a pool of coordinate-invariant operators defined for arbitrarily large, though not arbitrarily small, volumes. Our method uses a classically tractable ``Surrogate Constructed'' method to remove irrelevant operators from the pool, reducing the minimum size for which the scalable circuits are defined. Bringing together the scalable circuits and the surrogate constructed approaches forms the core of the (SC)2^22 methodology. Our approach allows for a wider set of classical computations, on small volumes, which can be used for a more robust extrapolation protocol. While developed in the context of lattice models, the surrogate construction portion is applicable to a wide variety of problems where information about the relative importance of operators in the pool is available. As an example, we use it to compute properties of the Schwinger model - quantum electrodynamics for a single, massive fermion in 1+11+11+1 dimensions - and show that our method can be used to accurately extrapolate to the continuum limit.
The vacuum of the lattice Schwinger model is prepared on up to 100 qubits of IBM’s Eagle-processor quantum computers. A new algorithm to prepare the ground state of a gapped translationally invariant system on a quantum computer is presented, which we call “scalable circuits ADAPT-VQE” (SC-ADAPT-VQE). This algorithm uses the exponential decay of correlations between distant regions of the ground state, together with ADAPT-VQE, to construct quantum circuits for state preparation that can be scaled to arbitrarily large systems. These scalable circuits can be determined with use of classical computers, avoiding the challenging task of optimizing parameterized circuits on a quantum computer. SC-ADAPT-VQE is applied to the Schwinger model, and is shown to be systematically improvable, with an accuracy that converges exponentially with circuit depth. Both the structure of the circuits and the deviations of prepared wave functions are found to become independent of the number of spatial sites, L . This allows a controlled extrapolation of the circuits, determined with use of small or modest-sized systems, to arbitrarily large L . The circuits for the Schwinger model are determined on lattices up to L=14 (28 qubits) with the Qiskit classical simulator, and are subsequently scaled up to prepare the L=50 (100 qubits) vacuum on IBM’s 127-superconducting-qubit quantum computers ibm_brisbane and ibm_cusco. After introduction of an improved error-mitigation technique, which we call “operator decoherence renormalization”, the chiral condensate and charge-charge correlators obtained from the quantum computers are found to be in good agreement with classical matrix product state simulations. Published by the American Physical Society 2024
Adaptive variational quantum simulation algorithms use information from a quantum computer to dynamically create optimal trial wave functions for a given problem Hamiltonian. A key ingredient in these algorithms is a predefined operator pool from which trial wave functions are constructed. Finding suitable pools is critical for the efficiency of the algorithm as the problem size increases. Here, we present a technique called operator pool tiling that facilitates the construction of problem-tailored pools for arbitrarily large problem instances. By first performing an Adaptive Derivative-Assembled Problem-Tailored Ansatz Variational Quantum Eigensolver (ADAPT-VQE) calculation on a smaller instance of the problem using a large, but computationally inefficient, operator pool, we extract the most relevant operators and use them to design more efficient pools for larger instances. We demonstrate the method here on strongly correlated quantum spin models in one and two dimensions, finding that ADAPT automatically finds a highly effective ansatz for these systems. Given that many problems, such as those arising in condensed matter physics, have a naturally repeating lattice structure, we expect the pool tiling method to be a widely applicable technique apt for such systems. Published by the American Physical Society 2024
We study variational preparation of ground states and sector-resolved excited states in the (1+1)(1+1)(1+1)-dimensional lattice Gross-Neveu model. We construct fixed circuits preserving either total fermion number or every flavor number, and a problem-specific scalable-circuit adaptive variational quantum eigensolver (SC-ADAPT-VQE). Classical circuit benchmarks cover massless and massive systems through 30 qubits, using exact-diagonalization and tensor-network reference results. Imposing flavor-number conservation improves the achieved energies in the completed two-flavor comparisons. Selected massive fixed-ansatz benchmarks with one to four flavors have relative energy errors of approximately 1×10−51 \times 10^{-5}1×10−5 - 2×10−42 \times 10^{-4}2×10−4, smaller than the quoted literature errors where available, although discretizations and computational resources differ. The adaptive pool combines translated bulk and boundary-sensitive generators with an interaction-sensitive cross-flavor family. Selected massive SC-ADAPT benchmarks with one to three flavors have relative energy errors below 2.1×10−32.1 \times 10^{-3}2.1×10−3. For one flavor, matrix-product-state evaluations extend the transferred circuits to 60-400 qubits without target-side operator selection or parameter optimization, giving energy deviations of approximately 0.35%0.35\%0.35% - 1.76%1.76\%1.76% from density-matrix renormalization-group reference values at maximum bond dimension 256. At fixed flavor number, range caps, and append count, the adaptive construction has a precompilation local-factor count linear in volume and a volume-independent shared-parameter count; fixed-accuracy performance at arbitrary volumes remains unestablished. Sequential deflation also prepares low-lying states within a fixed flavor-number sector, with projector fidelities providing a basis-independent assessment of degenerate target eigenspaces.
Materials design stands to be one of the most promising applications of quantum computing. However, the presence of noise in near-term quantum devices restricts quantum simulations of materials to shallow circuits. In this work, we present circuit-efficient variational quantum eigensolver (VQE) simulations of periodic materials using qubit-encoded wave functions based on Adaptive Derivative-Assembled Pseudo-Trotter (ADAPT) VQE. To iteratively construct accurate wave functions for periodic systems, we introduce operator pools comprising a complete set of anti-Hermitian one- and two-body qubit excitation/flipping operators. Numerical results demonstrate that these qubit-encoded algorithms can accurately predict the ground-state energy of periodic systems while significantly reducing circuit depth compared to Fermion-encoded algorithms. Additionally, we integrate the variance extrapolation technique with ADAPT-VQE algorithms to enhance the accuracy of ground-state energy estimations. This strategy further reduces the required circuit depth, enabling scalable and precise simulations of periodic systems.
Abstract Adaptive construction of ansatz circuits offers a promising route towards applicable variational quantum eigensolvers on near-term quantum hardware. Those algorithms aim to build up optimal circuits for a certain problem and ansatz circuits are adaptively constructed by selecting and adding entanglers from a predefined pool. In this work, we propose a way to construct entangler pools with reduced size by leveraging classical algorithms. Our method uses mutual information between the qubits in classically approximated ground state to rank and screen the entanglers. The density matrix renormalization group method is employed for classical precomputation in this work. We corroborate our method numerically on small molecules. Our numerical experiments show that a reduced entangler pool with a small portion of the original entangler pool can achieve same numerical accuracy. We believe that our method paves a new way for adaptive construction of ansatz circuits for variational quantum algorithms.