Novel methods for classical simulation of quantum circuits via ZX-calculus

Thesis

With the limitations of today's 'NISQ era' quantum hardware, classical simulation of quantum computations is an essential tool for understanding the quantum advantage and optimising quantum algorithms and systems. However, without the features unique to quantum computers, simulating such computations with classical hardware is (believed to be) a necessarily inefficient endeavour. For a general class of quantum circuits, any classical simulator requires a resource overhead which grows exponentially with one metric or another. Two notable and widely used techniques are tensor contraction and stabiliser decomposition. The former suffers from both space and time complexities that scale exponentially with the interconnectedness (or treewidth) of the circuit, while the latter is limited by a time complexity that scales exponentially with the number of 'non-Clifford' gates in the circuit. Recent years have seen the graphical language of ZX-calculus applied to this problem, with a particular growing body of research utilising its benefits to discover more efficient stabiliser decompositions. This in turn reduces the growth rate of the exponential time complexity, thereby rendering ever larger and more complex quantum circuits classically simulable.

This thesis expands upon this literature by presenting various new techniques and approaches by which the ZX-calculus may be used to classically simulate quantum circuits with improved efficiencies. This work includes a new perspective on optimising stabiliser decomposition strategies, focusing on improved heuristics and decomposition patterns rather than on discovering wholly new decompositions. Also included is extensive use of GPU hardware to parallelise the workload, particularly used in conjunction with a parameterisation of the ZX-calculus which allows large sets of similar circuits to be reasoned upon as single entities. Lastly, this thesis features a hybrid method of classical simulation which leverages of the strengths of both tensor contraction and stabiliser decomposition approaches, optimising a balance between these techniques. Ultimately, the chapters ahead demonstrate how these new techniques can greatly increase the scope of classical simulation by reducing the runtime of this task by orders of magnitude and providing a foundation for further research.

Authors: Sutcliffe, M

• DOI: 10.5287/ora-m860yzbyj
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: quantum circuit simulation; classical simulation; stabiliser decomposition; quantum computing; tensor contraction; quantum information; quantum software; ZX-calculus; gpu parallelism
• Subjects: Quantum computing