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First page of The wiring sets a phase-blind quantum memory's gap, the weight caps its coherence

The wiring sets a phase-blind quantum memory's gap, the weight caps its coherence

Ruini Qian, Zhaobin Lyu, Zelong Yin, Jingjing Hu, Dengfeng Li, Shuoming An

quant-ph Sep 26, 2026 · v2
formalization quantum
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TL;DR
Key algebraic identities (pump-invisibility of stabilizer-preserving noise, rank-one jump gain terms, pump boundary algebra) are machine-checked in Lean 4, with formalizations on Zenodo.
Abstract
Engineered dissipation corrects errors, yet a memory's phase decays. What the memory's gap measures is not settled. Here we show that when each jump resets one basis state, the wiring can set the gap time while the phase keeps its rate. Under dephasing the gap time spans two orders across wirings; the phase does not. In this class, a contrast on two or more qubits fades faster than a bare qubit at any distance; no such pump power substitutes. The ceiling is two over the qubits the contrast spans. A two-branch pump can escape it at distance three; a two-clock test runs on published data.
Problem

Engineered-dissipation quantum memories are often judged by their Liouvillian gap. It is unclear whether that gap measures how long the stored logical phase survives.

Approach

The authors study phase-blind pumps whose rank-one jumps reset computational-basis error states to code states. They analyze a four-qubit plaquette and other codes under dephasing and amplitude damping, and prove an envelope bound on the decay of weight-w contrasts. They also study two-branch (rank-two) pumps that can carry the phase. Core identities, including the pump-boundary and noise-only algebra and the jump gain terms, are machine-checked in Lean 4.

Results

Changing the wiring moves the gap time by about two orders of magnitude while the phase lifetime stays fixed, bounded by T_X <= T_2/w, which is below break-even for w>=2. Rank-two pumps can beat this ceiling at code distance three; for the five-qubit code, T_X reaches 1059.6 μs. A two-clock test applied to published data shows the gap and the logical coherence are decoupled.