Improving Gate-Level Simulation of Quantum Circuits

TL;DR

This paper introduces QuIDD, a data structure that enables more efficient classical simulation of certain quantum circuits by exploiting their structure, outperforming existing methods in runtime and memory usage.

Contribution

The paper presents QuIDD, a novel data structure for simulating quantum circuits more efficiently, and demonstrates its advantages through empirical validation with a new simulator.

Findings

QuIDD-based simulation outperforms existing techniques asymptotically.

QuIDD can efficiently simulate specific quantum states like superpositions and basis states.

Certain quantum algorithms can be simulated more efficiently using QuIDDs.

Abstract

Simulating quantum computation on a classical computer is a difficult problem. The matrices representing quantum gates, and the vectors modeling qubit states grow exponentially with an increase in the number of qubits. However, by using a novel data structure called the Quantum Information Decision Diagram (QuIDD) that exploits the structure of quantum operators, a useful subset of operator matrices and state vectors can be represented in a form that grows polynomially with the number of qubits. This subset contains, but is not limited to, any equal superposition of n qubits, any computational basis state, n-qubit Pauli matrices, and n-qubit Hadamard matrices. It does not, however, contain the discrete Fourier transform (employed in Shor's algorithm) and some oracles used in Grover's algorithm. We first introduce and motivate decision diagrams and QuIDDs. We then analyze the runtime and memory complexity of QuIDD operations. Finally, we empirically validate QuIDD-based simulation by means of a general-purpose quantum computing simulator QuIDDPro implemented in C++. We simulate various instances of Grover's algorithm with QuIDDPro, and the results demonstrate that QuIDDs asymptotically outperform all other known simulation techniques. Our simulations also show that well-known worst-case instances of classical searching can be circumvented in many specific cases by data compression techniques.