Quantum algorithms for quantum dynamics

Miessen, Alexander; Ollitrault, Pauline J.; Tacchino, Francesco; Tavernelli, Ivano

doi:10.1038/s43588-022-00374-2

Cited by 30 publications

(20 citation statements)

References 190 publications

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“…The rapid evolution of quantum hardware has opened a venue for addressing challenging problems in quantum chemistry with quantum computation. − However, quantum computing is currently not a practical tool for electronic structure theory. The heart of the problem is that existing implementations of digital quantum computers are noisy, intermediate-scale quantum (NISQ) devices ,, with a limited number of qubits and short coherence times and are subject to several sources of error.…”

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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“…One of the most important applications of quantum computers is the simulation of large quantum systems that are intractable using conventional classical computers [1][2][3]. A vast number of quantum techniques has been developed to simulate quantum dynamics with this purpose in mind [4,5]. Specially, many body systems give rise to extremely large Hamiltonians [6] that are classically impossible to tackle even for a small number of particles.…”

Section: Introductionmentioning

confidence: 99%

“…First the time evolution operator of a given Hamiltonian is expressed as a series of unitary quantum gates through the Jordan-Wigner isomorphism [9]. Second, the time evolution operator is used to propagate an initial state [3,5], typically by shifting locally the wave function forward in time over discrete and sufficiently small time slices [3][4][5] as long as the interval Δt is small enough [16]. Through the Trotter-Suzuki formula [17][18][19], that takes into account the non-commutativity of the H i ʼs, the accuracy of U(t) can then be improved but at the cost of increasing the circuit depth.…”

Section: Introductionmentioning

confidence: 99%

Vectorization of the density matrix and quantum simulation of the von Neumann equation of time-dependent Hamiltonians

Kunold

2024

Phys. Scr.

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Based oh the properties of Lie algebras,in this work we develop a general frameworkto linearize the von Neumann equationrendering it in a suitable formfor quantum simulations.Departing from the conventionalmethod of expanding the densitymatrix in the Liouville space formed by matricesunit we express the von Neumannequation in terms of Pauli strings.This provides several advantagesrelated to the quantum tomography of the densitymatrix and the formulation ofthe unitary gates that generatethe time evolution.The use of Pauli strings facilitates thequantum tomography of the density matrixwhose elements are purely real.As for any other basis of Hermitian matrices,this eliminates the need to calculatethe phase of the complex entries of thedensity matrix.This approach also enables to expressthe evolution operator as a sequenceof commuting Hamiltonian gatesof Pauli strings that can readilybe synthetized using Clifford gates.Additionally, the fact that these gates commutewith each other alongwith the unique properties of the algebra formed by Paulistrings allows to avoid the use of Trotterizationhence considerably reducing the circuit depth.The algorithm is demonstrated for threeHamiltonians using the IBMnoisy quantum circuitsimulator.

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“…Since performing quantum time evolution generally requires representing the exponentially large wave function of a quantum system, quantum computers are a promising platform for developing efficient algorithms [12]. In fact, in 1996, the Trotter algorithm for real-time evolution was among the first proposed use cases for a quantum computer [13].…”

Section: Introductionmentioning

confidence: 99%