High-fidelity Trotter formulas for digital quantum simulation

Liu, Yixiang; Hines, Jordan; Zhi, Li; Ajoy, Ashok; Cappellaro, Paola

doi:10.1103/physreva.102.010601

Cited by 7 publications

(3 citation statements)

References 36 publications

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“…However, balancing the number of Trotter steps and imperfections of quantum circuits in experiments is still a fundamental challenge. In this sense, various optimization scenarios aim at quantum error mitigation [22][23][24] for achieving a good precision of the quantum simulation with limited quantum resources. Among those, the machine-learning-enhanced optimization protocol [25][26][27][28] utilizes a feedback loop between the quantum device and a classical optimizer.…”

Section: Introductionmentioning

confidence: 99%

Time-Optimal Quantum Driving by Variational Circuit Learning

Huang¹,

Ding²,

Dupays³

et al. 2022

Preprint

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Section: Introductionmentioning

confidence: 99%

Time-Optimal Quantum Driving by Variational Circuit Learning

Huang¹,

Ding²,

Dupays³

et al. 2022

Preprint

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“…Hamiltonians arising in practice often have additional features beyond sparseness, such as locality [30,71], commutativity [24,25,66], and symmetry [32,72], that can be used to improve the performance of simulation. Besides, prior knowledge of the initial state [6,26,61,65] and the norm distribution of Hamiltonian terms [17,20,31,44,53] have also been proven useful for quantum simulation.…”

Section: Introductionmentioning

confidence: 99%

Nearly tight Trotterization of interacting electrons

Huang

Campbell

2021

Quantum

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We consider simulating quantum systems on digital quantum computers. We show that the performance of quantum simulation can be improved by simultaneously exploiting commutativity of the target Hamiltonian, sparsity of interactions, and prior knowledge of the initial state. We achieve this using Trotterization for a class of interacting electrons that encompasses various physical systems, including the plane-wave-basis electronic structure and the Fermi-Hubbard model. We estimate the simulation error by taking the transition amplitude of nested commutators of the Hamiltonian terms within the η-electron manifold. We develop multiple techniques for bounding the transition amplitude and expectation of general fermionic operators, which may be of independent interest. We show that it suffices to use (n5/3η2/3+n4/3η2/3)no(1) gates to simulate electronic structure in the plane-wave basis with n spin orbitals and η electrons, improving the best previous result in second quantization up to a negligible factor while outperforming the first-quantized simulation when n=η2−o(1). We also obtain an improvement for simulating the Fermi-Hubbard model. We construct concrete examples for which our bounds are almost saturated, giving a nearly tight Trotterization of interacting electrons.

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“…It has been used to realize Hamiltonians that are not accessible in a static system, such as modifying the tunneling and coupling rates [1][2][3][4][5][6], inducing nontrivial topological structures [7][8][9][10][11][12][13][14][15][16][17], creating synthetic gauge fields [18][19][20][21][22], and spin-orbit couplings [23]. On a quantum computer, Floquet engineering also enables universal quantum simulation via the Trotter-Suzuki scheme [24][25][26][27][28][29][30]. Floquet systems also possess interesting dynamical phenomena, ranging from the discrete-time crystalline phase [31][32][33][34][35] to dynamical localization [36,37], dynamical phase transitions [38,39], and coherent destruction of tunneling [40][41][42].…”

Section: Introductionmentioning

confidence: 99%

Prethermal quasiconserved observables in Floquet quantum systems

et al. 2021

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Prethermalization, by introducing emergent quasiconserved observables, plays a crucial role in protecting periodically driven (Floquet) many-body phases over an exponentially long time, while the ultimate fate of such quasiconserved operators can signal thermalization to infinite temperature. To elucidate the properties of prethermal quasiconservation in many-body Floquet systems, here we systematically analyze infinite-temperature correlations between observables. We numerically show that the late-time behavior of the autocorrelations unambiguously distinguishes quasiconserved observables from nonconserved ones, allowing one to single out a set of linearly independent quasiconserved observables. By investigating two Floquet spin models, we identify two different mechanisms underlying the quasiconservation law. First, we numerically verify energy quasiconservation when the driving frequency is large, so that the system dynamics is approximately described by a static prethermal Hamiltonian. More interestingly, under moderate driving frequency, another quasiconserved observable can still persist if the Floquet driving contains a large global rotation. We show theoretically how to calculate this conserved observable and provide numerical verification. Having systematically identified all quasiconserved observables, we can finally investigate their behavior in the infinite-time limit and thermodynamic limit, using autocorrelations obtained from both numerical simulation and experiments in solid-state nuclear magnetic resonance systems.

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High-fidelity Trotter formulas for digital quantum simulation

Cited by 7 publications

References 36 publications

Time-Optimal Quantum Driving by Variational Circuit Learning

Time-Optimal Quantum Driving by Variational Circuit Learning

Nearly tight Trotterization of interacting electrons

Prethermal quasiconserved observables in Floquet quantum systems

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