Simplification of tensor updates toward performance-complexity balanced quantum computer simulation

TL;DR

This paper compares two tensor update methods, CF and SU, for quantum circuit simulation, showing SU offers similar accuracy with lower computational costs, balancing performance and complexity.

Contribution

It systematically evaluates and demonstrates that the Simple Update method can replace the canonical form in quantum simulations for efficiency without significant accuracy loss.

Findings

SU reduces computational complexity compared to CF

SU achieves comparable accuracy to CF in simulations

Benchmark results confirm SU's efficiency across circuit types

Abstract

Matrix Product States (MPS) provide a powerful framework for simulating quantum circuits. In practical simulations, tensor updates are typically performed in the canonical form (CF), which corresponds to the Schmidt decomposition and improves approximation accuracy. However, maintaining the canonical form introduces significant computational overhead. An alternative approach, known as the Simple Update (SU), does not enforce the Schmidt decomposition and is expected to reduce computational complexity. In this work, we systematically compare the performance and computational cost of SU and CF in quantum circuit simulations. We benchmark both methods on highly entangled circuits and on a QASM benchmark suite covering a wide range of circuit types. Our results show that SU achieves accuracy comparable to CF while reducing computational complexity, indicating that SU provides an efficient alternative for practical quantum circuit simulations.