Improved T counts and active volume estimates for high-level arithmetic subroutines

2025/04/28 by Sam Heavey, Heavey, Sam
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Quantum-Dot Cellular Automata

paper · pdf · doi:10.48550/arxiv.2504.19626

openalex publication_date 2025/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Surface code based quantum computers show great promise for fault-tolerant quantum computing, but most architectures needlessly increase the spacetime volume of a computation due to qubits sitting idly during a computation. Active volume architectures, with long-range connectivity, aim to remove idle spacetime volume leaving only the spacetime volume that logically contributes to a computation. In this work we optimise and derive the active volumes for several industry-leading low- and high-level arithmetic subroutines and achieve significant T-count reductions. We discuss a simple method for estimating and optimising active volumes using orientated ZX diagrams. We also demonstrate that circuit structure, beyond gate counts alone, impacts the active volume of a subroutine and therefore should be taken into consideration when designing circuits.

Citations

• How to compute a 256-bit elliptic curve private key with only 50 million Toffoli gates
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• Interleaving: Modular architectures for fault-tolerant photonic quantum computing
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• Novel constructions for the fault-tolerant Toffoli gate
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• Layered architecture for quantum computing
• Quantum Addition Circuits and Unbounded Fan-Out
• Interacting Quantum Observables: Categorical Algebra and Diagrammatics
• Polynomial-time quantum algorithms for Pell's equation and the principal ideal problem
• A logarithmic-depth quantum carry-lookahead adder
• Universal quantum computation with ideal Clifford gates and noisy ancillas
• Topological quantum memory
• Fault-tolerant quantum computation by anyons

Related

• Active volume: An architecture for efficient fault-tolerant quantum computers with limited non-local connections
• An Improved Volumetric Metric for Quantum Computers via more Representative Quantum Circuit Shapes
• The FLuid Allocation of Surface code Qubits (FLASQ) cost model for early fault-tolerant quantum algorithms
• Stacking the Odds: Full-Stack Quantum System Design Space Exploration
• Time versus Hardware: Reducing Qubit Counts with a (Surface Code) Data Bus