Constant-Depth Circuits for Dynamic Simulations of Materials on Quantum Computers

TL;DR

This paper introduces constant-depth quantum circuits for simulating the long-time dynamics of certain 1D materials, significantly reducing circuit complexity and enabling longer simulations on near-term quantum hardware.

Contribution

The authors develop a novel method to generate constant-depth circuits for specific Hamiltonians, allowing arbitrarily long simulations and reduced gate counts compared to standard algorithms.

Findings

Circuits are constant in depth for 1D materials Hamiltonians.

Achieved successful long-time dynamics simulation of up to 5 spins.

Generated circuits with order-of-magnitude fewer gates than traditional methods.

Abstract

Dynamic simulation of materials is a promising application for near-term quantum computers. Current algorithms for Hamiltonian simulation, however, produce circuits that grow in depth with increasing simulation time, limiting feasible simulations to short-time dynamics. Here, we present a method for generating circuits that are constant in depth with increasing simulation time for a subset of one-dimensional materials Hamiltonians, thereby enabling simulations out to arbitrarily long times. Furthermore, by removing the effective limit on the number of feasibly simulatable time-steps, the constant-depth circuits enable Trotter error to be made negligibly small by allowing simulations to be broken into arbitrarily many time-steps. Composed of two-qubit matchgates on nearest-neighbor qubits, these constant-depth circuits are constructed based on a set of multi-matchgate identity relationships. For an $N$-spin system, the constant-depth circuit contains only $\mathcal{O}(N^2)$ CNOT gates. When compared to standard Hamiltonian simulation algorithms, our method generates circuits with order-of-magnitude fewer gates, which allows us to successfully simulate the long-time dynamics of systems with up to 5 spins on available quantum hardware. This paves the way for simulations of long-time dynamics for scientifically and technologically relevant quantum materials, enabling the observation of interesting and important atomic-level physics.