Efficient and practical Hamiltonian simulation from time-dependent product formulas

In this work we propose an approach for implementing time-evolution of a quantum system using product formulas. The quantum algorithms we develop have provably better scaling (in terms of gate complexity and circuit depth) than a naive application of well-known Trotter formulas, for systems where th...

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Bibliographic Details
Published in:arXiv.org 2024-06
Main Authors: Jan Lukas Bosse, Childs, Andrew M, Derby, Charles, Gambetta, Filippo Maria, Montanaro, Ashley, Santos, Raul A
Format: Article
Language:English
Subjects:
Algorithms
Computer simulation
Evolution
Gates (circuits)
Ising model
Mathematical models
Quantum computers
Quantum theory
Qubits (quantum computing)
Time dependence
Online Access:Get full text
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Summary:In this work we propose an approach for implementing time-evolution of a quantum system using product formulas. The quantum algorithms we develop have provably better scaling (in terms of gate complexity and circuit depth) than a naive application of well-known Trotter formulas, for systems where the evolution is determined by a Hamiltonian with different energy scales (i.e., one part is "large" and another part is "small"). Our algorithms generate a decomposition of the evolution operator into a product of simple unitaries that are directly implementable on a quantum computer. Although the theoretical scaling is suboptimal compared with state-of-the-art algorithms (e.g., quantum signal processing), the performance of the algorithms we propose is highly competitive in practice. We illustrate this via extensive numerical simulations for several models. For instance, in the strong-field regime of the 1D transverse-field Ising model, our algorithms achieve an improvement of one order of magnitude in both the system size and evolution time that can be simulated with a fixed budget of 1000 arbitrary 2-qubit gates, compared with standard Trotter formulas.
ISSN:2331-8422