An entanglement-aware quantum computer simulation algorithm

TL;DR

This paper introduces an entanglement-aware quantum simulation algorithm that dynamically adjusts bond dimensions based on fidelity estimates, significantly improving efficiency over fixed bond dimension methods in simulating large quantum systems.

Contribution

The paper presents a novel entanglement-aware algorithm that adaptively manages bond dimensions in MPS simulations using fidelity estimates, enhancing accuracy and efficiency.

Findings

EA algorithm outperforms fixed bond dimension schemes

Simulates 300-qubit circuit in 2 hours with high fidelity

Achieves similar fidelity to traditional methods with less computation

Abstract

The advent of quantum computers promises exponential speed ups in the execution of various computational tasks. While their capabilities are hindered by quantum decoherence, they can be exactly simulated on classical hardware at the cost of an exponential scaling in terms of number of qubits. To circumvent this, quantum states can be represented as matrix product states (MPS), a product of tensors separated by so-called bond dimensions. Limiting bond dimensions growth approximates the state, but also limits its ability to represent entanglement. Methods based on this representation have been the most popular tool at simulating large quantum systems. But how to trust resulting approximate quantum states for such intractable systems sizes ? I propose here a method for inferring the fidelity of an approximate quantum state without direct comparison to its exact counterpart, and use it to design an ``entanglement-aware'' (EA) algorithm for both pure and mixed states. As opposed to state of the art methods which limit bond dimensions up to an arbitrary maximum value, this algorithm receives as input a fidelity, and adapts dynamically its bond dimensions to both local entanglement and noise such that the final quantum state fidelity at least reaches the input fidelity. I show that this algorithm far surpasses standard fixed bond dimension truncation schemes. In particular, a noiseless random circuit of 300 qubits and depth 75 simulated using MPS methods takes one week of computation time, while EA-MPS only needs 2 hours to reach similar quantum state fidelity.