Approximations based on perturbation theory are the basis for most of the
quantitative predictions of quantum mechanics, whether in quantum field theory,
many-body physics, chemistry or other domains. Quantum computing provides an
alternative to the perturbation paradigm, but the tens of noisy qubits
currently available in state-of-the-art quantum processors are of limited
practical utility. In this article, we introduce perturbative quantum
simulation, which combines the complementary strengths of the two approaches,
enabling the solution of large practical quantum problems using 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. After introducing the
general perturbative simulation framework, we present an explicit example
algorithm that mimics the Dyson series expansion. We then numerically benchmark
the method for interacting bosons, fermions, and quantum spins in different
topologies, and study different physical phenomena on systems of up to 48
qubits, such as information propagation, charge-spin separation and magnetism.
In addition, we use 5 physical qubits on the IBMQ cloud to experimentally
simulate the 8-qubit Ising model using our algorithm. The result verifies the
noise robustness of our method and illustrates its potential for benchmarking
large quantum processors with smaller ones.Comment: 35 pages, 12 figure
