Efficiency of classical simulations of a noisy Grover algorithm

TL;DR

This paper investigates how noise affects entanglement dynamics in the Grover algorithm and compares simulation methods, revealing that matrix product density operator simulations can be more efficient than quantum trajectories.

Contribution

It provides a comparative analysis of entanglement measures under noise in Grover's algorithm and demonstrates the potential efficiency of MPDO simulations over quantum trajectories.

Findings

OE captures entanglement reduction during convergence

Deep in the circuit, OE is smaller than TE, indicating more efficient simulations

Noise-rate scaling affects success probabilities in Grover's algorithm

Abstract

We analyze the modification of entanglement dynamics in the Grover algorithm when the qubits are subjected to single-qubit amplitude-damping or phase-flip noise. We compare quantum trajectories with full density-matrix simulations, analyzing the dynamics of averaged trajectory entanglement (TE) and operator entanglement (OE), in the respective state representation. Although not a genuine entanglement measure, both TE and OE are connected to the efficiency of matrix product state simulations and thus of fundamental interest. As in many quantum algorithms, at the end of the Grover circuit entanglement decreases as the system converges towards the target product state. While we find that this is well captured in the OE dynamics, quantum trajectories rarely follow paths of reducing entanglement. Optimized unraveling schemes can lower TE slightly, however we show that deep in the circuit OE is generally smaller than TE. This implies that matrix product density operator (MPDO) simulations of quantum circuits can in general be more efficient than quantum trajectories. In addition, we investigate the noise-rate scaling of success probabilities for both amplitude-damping and phase-flip noise in Grover's algorithm.