Solving the Hubbard model using density matrix embedding theory and the variational quantum eigensolver

Mineh, Lana; Montanaro, Ashley

doi:10.1103/physrevb.105.125117

Cited by 16 publications

(12 citation statements)

References 39 publications

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“…To better recover the static correlations using UCCSD, more terms can be added to the UCC ansatz or one may consider combining UCC with other algorithms such as density matrix embedding theory [49,103,104].…”

Section: Hubbard Modelmentioning

confidence: 99%

TenCirChem: An Efficient Quantum Computational Chemistry Package for the NISQ Era

Li¹,

Allcock²,

Cheng³

et al. 2023

Preprint

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TenCirChem is an open-source Python library for simulating variational quantum algorithms for chemistry, biology, and material science. Its easy-to-use high-level interface enables users to optimize molecular energies or study quantum dynamics in only a few lines of code, while still allowing for a high degree of flexibility and customizability. By making use of compact representations of quantum states and excitation operators, efficient quantum circuits for fermionic excitations, and the powerful TensorCircuit software framework, TenCirChem displays high performance in simulating both noiseless and noisy quantum circuits, even when large numbers of qubits and tunable parameters are involved. As an example, we use it to compute the potential energy surface of H 2 O with 6-31G(d) basis set and (8e, 17o) active space using a quantum circuit ansatz of 34 qubits with 565 independent parameters, and achieve an equilibrium bond length error to 0.01 Å with respect to experiments.

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Section: Hubbard Modelmentioning

confidence: 99%

TenCirChem: An Efficient Quantum Computational Chemistry Package for the NISQ Era

Li¹,

Allcock²,

Cheng³

et al. 2023

Preprint

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“…where I 0 describes the 'ideal' representational ineffectiveness of a given variational circuit. It has been demonstrated in an ideal exact gradient setup that I 0 can be made arbitrarily small with a suitable choice of the Ansatz and corresponding circuit depth [24,35,36]. However, in addition to the limitations associated with the expressivity of the circuit, the measured state infidelity also stems from the finite sample size of gradient estimates per component, N s .…”

Section: B a Phenomenological Scaling Law For The Residual Infidelitymentioning

confidence: 99%

Phenomenological Theory of Variational Quantum Ground-State Preparation

Astrakhantsev¹,

Mazzola²,

Tavernelli³

et al. 2022

Preprint

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“…To take the full advantage of these quantum eigensolvers within the embedding framework, ,− two open questions immediately arise as a result of the intrinsic nature of quantum systems. First, the wave function of a quantum system collapses when measured.…”

Section: Introductionmentioning

confidence: 99%

Bootstrap Embedding on a Quantum Computer

Liu

Chin

Dutt

et al. 2023

J. Chem. Theory Comput.

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We extend molecular bootstrap embedding to make it appropriate for implementation on a quantum computer. This enables solution of the electronic structure problem of a large molecule as an optimization problem for a composite Lagrangian governing fragments of the total system, in such a way that fragment solutions can harness the capabilities of quantum computers. By employing state-of-art quantum subroutines including the quantum SWAP test and quantum amplitude amplification, we show how a quadratic speedup can be obtained over the classical algorithm, in principle. Utilization of quantum computation also allows the algorithm to match�at little additional computational cost�full density matrices at fragment boundaries, instead of being limited to 1-RDMs. Current quantum computers are small, but quantum bootstrap embedding provides a potentially generalizable strategy for harnessing such small machines through quantum fragment matching.

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Solving the Hubbard model using density matrix embedding theory and the variational quantum eigensolver

Cited by 16 publications

References 39 publications

TenCirChem: An Efficient Quantum Computational Chemistry Package for the NISQ Era

TenCirChem: An Efficient Quantum Computational Chemistry Package for the NISQ Era

Phenomenological Theory of Variational Quantum Ground-State Preparation

Bootstrap Embedding on a Quantum Computer

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