Perturbative quantum simulation

TL;DR

This paper introduces perturbative quantum simulation, combining perturbation theory and quantum computing to efficiently simulate large quantum systems on limited noisy hardware, demonstrated through numerical and experimental results.

Contribution

It presents a novel perturbative quantum simulation method that enables large-scale quantum system simulation on noisy intermediate-scale quantum hardware.

Findings

Numerical benchmarks for bosons, fermions, and spins up to 48 qubits.

Experimental demonstration on IBM quantum cloud showing noise robustness.

Potential for benchmarking large quantum processors with smaller ones.

Abstract

Approximation based on perturbation theory is the foundation for most of the quantitative predictions of quantum mechanics, whether in quantum many-body physics, chemistry, quantum field theory or other domains. Quantum computing provides an alternative to the perturbation paradigm, yet state-of-the-art quantum processors with tens of noisy qubits are of limited practical utility. Here, we introduce perturbative quantum simulation, which combines the complementary strengths of the two approaches, enabling the solution of large practical quantum problems using limited noisy intermediate-scale quantum hardware. The use of a quantum processor eliminates the need to identify a solvable unperturbed Hamiltonian, while the introduction of perturbative coupling permits the quantum processor to simulate systems larger than the available number of physical qubits. We present an explicit perturbative expansion that mimics the Dyson series expansion and involves only local unitary operations, and show its optimality over other expansions under certain conditions. We numerically benchmark the method for interacting bosons, fermions, and quantum spins in different topologies, and study different physical phenomena, such as information propagation, charge-spin separation, and magnetism, on systems of up to $48$ qubits only using an $8+1$ qubit quantum hardware. We experimentally demonstrate our scheme on the IBM quantum cloud, verifying its noise robustness and illustrating its potential for benchmarking large quantum processors with smaller ones.