Environmental records unlock universal quantum computation from thermal decoherence

• URL: http://arxiv.org/abs/2609.16460v1
• Date: Tue, 15 Sep 2026 00:26:12 GMT
• Title: Environmental records unlock universal quantum computation from thermal decoherence
• Abstract summary: At a fixed thermal exposure, the same stabilizer processor can be classically simulable or quantum universal.<n>We give an exact computational classification of energy-counting thermal-idle instruments in a quantum processor.
• Score: 14.068605545952863
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: At a fixed thermal exposure, the same stabilizer processor can be classically simulable or quantum universal, depending on which environmental records its controller retains. We give an exact computational classification of energy-counting thermal-idle instruments in a quantum processor with ideal stabilizer control and independent local Markov baths. The relaxation time $T_1$, homogeneous coherence time $T_2$, and equilibrium excited-state population $p_e$ determine an exact computational boundary at $(1-p_e)T_2/T_1=1$. If every location lies at or below it, branchwise nonnegative stabilizer decompositions give an explicit efficient classical sampler for the adaptive circuit and its full time-resolved exchange record. Above it at a single repeatedly accessible location, a suitable idle duration and no-exchange conditioning supply distillable ancillas and enable universal quantum computation with polynomial overhead. At finite temperature on the resource side, erasing the record at a sufficiently long, unsplit exposure makes the averaged channel stabilizer measure-and-prepare, and even a terminal parity check then yields only simulable branches. Yet at that same exposure, retaining only the bit recording whether any exchange occurred still heralds distillable ancillas, because a thermal round trip restores the parity after its first exchange has already removed the coherence.

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