Optimal Quantum Circuit Cuts with Application to Clustered Hamiltonian Simulation
Aram W. Harrow, Angus Lowe
Abstract
We study methods to replace entangling operations with random local operations in a quantum computation, at the cost of increasing the number of required executions. First, we consider “spacelike cuts” where an entangling unitary is replaced with random local unitaries. We propose an entanglement measure for quantum dynamics, the , which bounds the cost in a procedure for this replacement based on two copies of the Hadamard test. In the terminology of prior work, this procedure yields a quasiprobability decomposition with minimal 1-norm in a number of cases, which addresses an open question of Piveteau and Sutter. As an application, we give an improved algorithm for clustered Hamiltonian simulation. Specifically we show that interactions can be removed at a cost, which is exponential in the sum of their strengths times the evolution time, and vanishing in the limit of weak interactions. We also give an improved upper bound on the cost of replacing wires with measure-and-prepare channels using “timelike cuts.” We prove a matching information-theoretic lower bound when estimating output probabilities.