Reversible Lifetime Semantics for Quantum Programs

TL;DR

This paper introduces a semantic model for reversible quantum computation using scope-bounded uncomputation, enabling early qubit reclamation, reducing circuit depth, and clarifying parameter passing semantics.

Contribution

It presents a formal semantic framework for uncomputation in quantum programming, linking lifetime analysis with program correctness and resource management.

Findings

Early reclamation reduces circuit depth and peak qubit usage.

Semantic lifetime and restoration invariants ensure safe uncomputation.

Parameter passing semantics are derived from lifetime discipline.

Abstract

Reversible computation requires that intermediate data be explicitly undone rather than discarded. In quantum programming, this principle appears as uncomputation, usually treated as a technical cleanup mechanism. We instead present uncomputation as a semantic foundation. In the Qutes language, we introduce a formal model of \emph{Scope-Bounded Liveness-Guided Uncomputation}, where lexical scope bounds variable lifetime and static liveness and entanglement analysis determine the earliest safe reclamation point. We define semantic lifetime and a Restoration Invariant ensuring that temporary quantum information disappears once it becomes semantically irrelevant. We prove compositional correctness under nested scopes and show that early reclamation can reduce circuit depth by avoiding critical-path overhead and can bound peak live qubits through disciplined ancilla reuse. Finally, we show that parameter passing semantics emerges from the same lifetime discipline, with pass-by-value and pass-by-reference corresponding to different lifetime boundaries, and we characterize the constraints (irreversibility, persistent entanglement, and aliasing) under which automatic uncomputation must be restricted.