Qubit recycling streamlines quantum computing

Hanru Jiang

Reducing the width of quantum circuits is crucial due to limited number of qubits in quantum devices. This paper revisit an optimization strategy known as qubit recycling (alternatively wire-recycling or measurement- and-reset ), which leverages gate commutativity to reuse discarded qubits, thereby reducing circuit width. We introduce qubit dependency graphs (QDGs) as a key abstraction for this optimization. With QDG, we isolate the computationally demanding components, and observe that qubit recycling is essentially a matrix triangularization problem. Based on QDG and this observation, we study qubit recycling with a focus on complexity, algorithmic, and verification aspects. Firstly, we establish qubit recycling’s NP-hardness through reduction from Wilf’s question, another matrix triangularization problem. Secondly, we propose a QDG-guided solver featuring multiple heuristic options for effective qubit recycling. Benchmark tests conducted on RevLib illustrate our solver’s superior or comparable performance to existing alternatives. Notably, it achieves optimal solutions for the majority of circuits. Finally, we develop a certified qubit recycler that integrates verification and validation techniques, with its correctness proof mechanized in Coq.

Jeremy J. Ramsden

Madhusudan Singh Irish Singh, Bharat S. Rawal

Anna Demming

A team at the US-based firm Atom Computing has reported an improvement in quantum-error reduction in quantum processors based on neutral atoms.

Rowan Brad Quni-Gudzinas

Magic state distillation (MSD) is the canonical route to non-Clifford gates in fault-tolerant quantum computation, but conventional nested factories exhibit qubit occupancy that grows multiplicatively with the number of distillation rounds. Recent work on constant-sized-support distillation protocols with qubit recycling (arXiv:2609.17044v1) proposes to hold the active qubit footprint fixed across rounds by recycling output qubits back into input registers. This paper develops a transparent, fully arithmetized resource-budget model of that proposal. We derive (i) the leading-order error suppression of a two-round 15-to-1 distillation ladder, giving output error 1,500,625 p⁹ for input error p (1.500625 × 10⁻²¹ at p = 10⁻³; 1.500625 × 10⁻¹² at p = 10⁻²); (ii) a peak-occupancy comparison showing that a recycled constant-support factory with a 15-state buffer reduces peak qubit count from 240 to 30, a factor-of-8 reduction; (iii) a recycling error budget showing that, under a stated worst-case linear depolarization model with per-reuse error δ = 10⁻⁵ and input error p₀ = 10⁻³, at most 10 reuses preserve input fidelity within 10% of nominal; and (iv) an energy attribution under one stated convention that yields ≈ 0.55 J per distilled magic state (± 0.07 J) when the model is anchored to a publicly reported benchmark energy of 5.5 × 10⁵ J per inference against a classical baseline of 0.0365 J (ratio 1.5 × 10⁷). All numerical results are analytic projections under explicitly stated assumptions, not simulations; divergences among independent draft analyses are documented in Appendix A, and every claim is attributed in Appendix B. We identify the experimental conditions under which the recycling advantage would be falsified. ## 1. Introduction Fault-tolerant quantum computation requires a gate set executed with error rates far below the threshold of the underlying quantum error-correcting code. For most code families, the transversal or lattice-surgery-accessible gate set i Full text and updates: papers.qnfo.org/papers/constant-sized-support-magic-state-distillation-with-qubit-recycling-a-reconcile/

Teodor Cervinski, Toma Cristian, Mihai Doinea +1 more