Space-Time Optimisations for Early Fault-Tolerant Quantum Computation

TL;DR

This paper introduces resource-efficient compilation techniques tailored for early fault-tolerant quantum computers, significantly reducing qubit requirements and optimizing execution time under resource constraints.

Contribution

It develops distillation-adaptive qubit layouts and routing heuristics specifically for early FTQC, achieving up to 60% qubit reduction with minimal overhead.

Findings

Greedy heuristics reduce qubit count by up to 60%.

Techniques achieve 1.2X overhead in execution time.

Results are close to theoretical lower bounds.

Abstract

Fault-tolerance is the future of quantum computing, ensuring error-corrected quantum computation that can be used for practical applications. Resource requirements for fault-tolerant quantum computing (FTQC) are daunting, and hence, compilation techniques must be designed to ensure resource efficiency. There is a growing need for compilation strategies tailored to the early FTQC regime, which refers to the first generation of fault-tolerant machines operating under stringent resource constraints of fewer physical qubits and limited distillation capacity. Present-day compilation techniques are largely focused on overprovisioning of routing paths and make liberal assumptions regarding the availability of distillation factories. Our work develops compilation techniques that are tailored to the needs of early FTQC systems, including distillation-adaptive qubit layouts and routing techniques. In particular, we show that simple greedy heuristics are extremely effective for this problem, offering up to 60% reduction in the number of qubits compared to prior works. Our techniques offer results with an average overhead of 1.2X in execution time for a 53% reduction in qubits against the theoretical lower bounds. As the industry develops early FTQC systems with tens to hundreds of logical qubits over the coming years, our work has the potential to be widely useful for optimising program executions.