Simulation of Quantum Circuits via Stabilizer Frames

TL;DR

This paper introduces Quipu, a stabilizer frame-based simulation method that efficiently simulates certain quantum circuits, outperforming existing techniques like QuIDDPro, especially for structured circuits with stabilizer components.

Contribution

The paper presents novel data structures and algorithms for parallel simulation of stabilizer-rich quantum circuits, improving efficiency and scalability over previous methods.

Findings

Quipu simulates quantum arithmetic circuits in polynomial time and space.

It outperforms QuIDDPro in simulating quantum Fourier transform and fault-tolerant circuits.

Quipu can be effectively parallelized, achieving computational speedup.

Abstract

Generic quantum-circuit simulation appears intractable for conventional computers and may be unnecessary because useful quantum circuits exhibit significant structure that can be exploited during simulation. For example, Gottesman and Knill identified an important subclass, called stabilizer circuits, which can be simulated efficiently using group-theory techniques and insights from quantum physics. Realistic circuits enriched with quantum error-correcting codes and fault-tolerant procedures are dominated by stabilizer subcircuits and contain a relatively small number of non-Clifford components. Therefore, we develop new data structures and algorithms that facilitate parallel simulation of such circuits. Stabilizer frames offer more compact storage than previous approaches but require more sophisticated bookkeeping. Our implementation, called Quipu, simulates certain quantum arithmetic circuits (e.g., reversible ripple-carry adders) in polynomial time and space for equal superpositions of $n$-qubits. On such instances, known linear-algebraic simulation techniques, such as the (state-of-the-art) BDD-based simulator QuIDDPro, take exponential time. We simulate quantum Fourier transform and quantum fault-tolerant circuits using Quipu, and the results demonstrate that our stabilizer-based technique empirically outperforms QuIDDPro in all cases. While previous high-performance, structure-aware simulations of quantum circuits were difficult to parallelize, we demonstrate that Quipu can be parallelized with a nontrivial computational speedup.