Superresolution of Green's functions on noisy quantum computers

Cruz, Diogo; Duarte, Magano,

doi:10.1103/physreva.108.012618

Cited by 5 publications

(2 citation statements)

References 38 publications

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“…Quantum devices have been used for ground-state methods including quantum Monte Carlo, quantum phase estimation, perturbation theory, , and the Hermitian and anti-Hermitian contracted Schrödinger equations. − Quantum annealing techniques have been used for ground states and other problems. − Reduced density matrices from non-VQE methods may be passed into other, larger algorithms. , Hardware experiments with variants of quantum imaginary time evolution (QITE) have been used to query zero-temperature and finite-temperature properties on hardware. − Hardware has also been used to study the dynamics of both closed − and open − quantum systems. Other algorithms without VQE have also been applied to hardware to study vibrational and molecular dynamics, , response properties, eigenstates and electronic spectra, − and even problems on the frontiers of interest to computational chemistry. − …”

Section: Introductionmentioning

confidence: 99%

Implementation of the Projective Quantum Eigensolver on a Quantum Computer

Misiewicz,

Evangelista

2024

J. Phys. Chem. A

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We study the performance of our previously proposed projective quantum eigensolver (PQE) on IBM’s quantum hardware in conjunction with error mitigation techniques. For a single qubit model of H2, we find that we are able to obtain energies within 4 millihartree (2.5 kcal/mol) of the exact energy along the entire potential energy curve, with the accuracy limited by both the stochastic error and the inconsistent performance of the IBM devices. We find that an optimization algorithm using direct inversion of the iterative subspace can converge swiftly, even to excited states, but stochastic noise can prompt large parameter updates. For the 4-site transverse-field Ising model at its critical point, PQE with an appropriate application of qubit tapering can recover 99% of the correlation energy, even after discarding several parameters. The large number of CNOT gates needed for the additional parameters introduces a concomitant error that, on the IBM devices, results in a loss of accuracy despite the increased expressivity of the trial state. Error extrapolation techniques and tapering or postselection are recommended to mitigate errors in PQE hardware experiments.

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Section: Introductionmentioning

confidence: 99%

Implementation of the Projective Quantum Eigensolver on a Quantum Computer

Misiewicz,

Evangelista

2024

J. Phys. Chem. A

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“…Most of the recent work on noisy intermediate-scale quantum (NISQ) simulation of the many-body GF is in the time domain via Hamiltonian simulation. 27 − 30 Efficient Hamiltonian simulation can be done by doing Trotter decomposition of the time evolution operator. However, Trotter-based methods suffer from accumulating circuit depth with time and thus quickly become impractical for NISQ devices.…”

Section: Introductionmentioning

confidence: 99%

Computing the Many-Body Green’s Function with Adaptive Variational Quantum Dynamics

Gomes

Williams‐Young

Jong

2023

J. Chem. Theory Comput.

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We present a method to compute the many-body real-time Green’s function using an adaptive variational quantum dynamics simulation approach. The real-time Green’s function involves the time evolution of a quantum state with one additional electron with respect to the ground state wave function that is first expressed as a linear–linear combination of state vectors. The real-time evolution and the Green’s function are obtained by combining the dynamics of the individual state vectors in a linear combination. The use of the adaptive protocol enables us to generate compact ansatzes on-the-fly while running the simulation. In order to improve the convergence of spectral features, Padé approximants are applied to obtain the Fourier transform of the Green’s function. We demonstrate the evaluation of the Green’s function on an IBM Q quantum computer. As a part of our error mitigation strategy, we develop a resolution-enhancing method that we successfully apply on the noisy data from the real-quantum hardware.

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