Node Replacement based Approximate Quantum Simulation with Decision Diagrams

TL;DR

This paper introduces a novel node replacement method using Locality Sensitive Hashing to improve approximate quantum circuit simulation with decision diagrams, achieving better memory-accuracy trade-offs and scalability for complex circuits.

Contribution

It proposes a new node replacement strategy with LSH to enhance decision diagram-based quantum simulation, outperforming previous approximate methods in efficiency and scalability.

Findings

Achieves superior memory-accuracy trade-off in quantum circuit simulation.

Demonstrates good scalability with increasing circuit size and depth.

Shows a linear or better trade-off between memory and fidelity for quantum supremacy circuits.

Abstract

Simulating a quantum circuit with a classical computer requires exponentially growing resources. Decision diagrams exploit the redundancies in quantum circuit representation to efficiently represent and simulate quantum circuits. But for complicated quantum circuits like the quantum supremacy benchmark, there is almost no redundancy to exploit. Therefore, it often makes sense to do a trade-off between simulation accuracy and memory requirement. Previous work on approximate simulation with decision diagrams exploits this trade-off by removing less important nodes. In this work, instead of removing these nodes, we try to find similar nodes to replace them, effectively slowing down the fidelity loss when reducing the memory. In addition, we adopt Locality Sensitive Hashing (LSH) to drastically reduce the computational complexity for searching for replacement nodes. Our new approach achieves a better memory-accuracy trade-off for representing a quantum circuit with decision diagrams with minimal run time overhead. Notably, our approach shows good scaling properties when increasing the circuit size and depth. For the first time, a strong better-than-linear trade-off between memory and fidelity is demonstrated for a decision diagram based quantum simulation when representing the quantum supremacy benchmark circuits at high circuit depths, showing the potential of drastically reducing the resource requirement for approximate simulation of the quantum supremacy benchmarks on a classical computer.