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arXiv:2608.12803

A Finite-Window Recovery Hierarchy for Local Quantum Memory

Zheng An, Dongyang Cao, Jiangyu Cui

quant-phSubmitted Aug 13, 2026• Announced Aug 14, 2026• 0 citations
arXivHTMLPDF

Abstract

When quantum information initially stored in a local qubit disappears, it need not be lost: it may have moved into nearby degrees of freedom or become inaccessible to shallow local control. We introduce finite-window recoverability as an operational channel benchmark that separates these possibilities. It compares optimal recovery from the target site, recovery by a bounded-depth decoder on a finite window, and the unrestricted optimum for that window. Its operational component, local variational recovery, uses local state preparation, window-local control, and target-qubit Pauli readout to certify recoverable memory beyond the target and quantify how much of the same-window advantage is accessible to shallow control. In a disordered kicked-Ising Floquet chain, a depth-6 decoder on a five-site window realizes $Q^{\mathrm{opt}}_0<Q^{\mathrm{shallow}}_2<Q^{\mathrm{opt}}_2$ across the crossover regime, with positive certified gain for most disorder realizations and substantial shallow-accessibility fractions. The signal differs from target-site persistence and reconstructed coherent-information increments. Positive radius-2 gain also persists when the task is embedded in longer open chains using an independent tensor-network backend. Guided by this hierarchy, we test a carrier-deletion task in which the original target register is reset after the dynamics. A depth-8 decoder repairs the input from a radius-3 surrounding halo with held-out median $F_{\mathrm{avg}}=0.758$, above the single-qubit classical benchmark $2/3$, and outperforms optimal one-, two-, and three-site halo-subwindow counterfactuals. These results establish finite-window recovery as a local-control benchmark for off-site quantum memory, diagnosing both where local quantum information remains and whether bounded-depth control can refocus it.

Comments
23 pages, 16 figures; includes Methods and appendices

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When quantum information initially stored in a local qubit disappears, it need not be lost: it may have moved into nearby degrees of freedom or become inaccessible to shallow local control. We introduce finite-window recoverability as an operational channel benchmark that separates these possibilities. It compares optimal recovery from the target site, recovery by a bounded-depth decoder on a finite window, and the unrestricted optimum for that window. Its operational component, local variational recovery, uses local state preparation, window-local control, and target-qubit Pauli readout to certify recoverable memory beyond the target and quantify how much of the same-window advantage is accessible to shallow control. In a disordered kicked-Ising Floquet chain, a depth-6 decoder on a five-site window realizes Q0opt<Q2shallow<Q2optQ^{\mathrm{opt}}_0<Q^{\mathrm{shallow}}_2<Q^{\mathrm{opt}}_2Q0opt​<Q2shallow​<Q2opt​ across the crossover regime, with positive certified gain for most disorder realizations and substantial shallow-accessibility fractions. The signal differs from target-site persistence and reconstructed coherent-information increments. Positive radius-2 gain also persists when the task is embedded in longer open chains using an independent tensor-network backend. Guided by this hierarchy, we test a carrier-deletion task in which the original target register is reset after the dynamics. A depth-8 decoder repairs the input from a radius-3 surrounding halo with held-out median Favg=0.758F_{\mathrm{avg}}=0.758Favg​=0.758, above the single-qubit classical benchmark 2/32/32/3, and outperforms optimal one-, two-, and three-site halo-subwindow counterfactuals. These results establish finite-window recovery as a local-control benchmark for off-site quantum memory, diagnosing both where local quantum information remains and whether bounded-depth control can refocus it.
Erase the apparent carrier. Recover the qubit from its halo. Then ask a different clock. This preregistration separates an ordinary quantum-memory qualification from a distinct timing test. Test A evolves a logical qubit through a frozen local channel, physically resets its original carrier, and asks whether a finite surrounding window can recover it. Test B asks whether that independently reconstructed channel fidelity controls a separate timing-covariance frontier. Test A: where is the recoverable channel? Ri(ω)=∣0⟩ ⁣⟨0∣i⊗Tr⁡iω, \mathcal R_i(\omega)=|0\rangle\!\langle0|_i\otimes\operatorname{Tr}_i\omega, Ri​(ω)=∣0⟩⟨0∣i​⊗Tri​ω, Qdel=2Favg(Ndel,id⁡)−1,Fedel=1+3Qdel4. Q_{\rm del}=2F_{\rm avg}(\mathcal N_{\rm del},\operatorname{id})-1, \qquad \boxed{F_e^{\rm del}=\frac{1+3Q_{\rm del}}4.} Qdel​=2Favg​(Ndel​,id)−1,Fedel​=41+3Qdel​​.​ Target-only and every smaller halo subwindow remain optimized counterfactuals. A physical reset, sham reset, hidden-record injection, boundary ladder, and complete terminal record are required before the recovery layer qualifies. Test B: does the memory verifier intertwine with an independent timing projector? W†MeW=Palign,ηT=Tr⁡(ρPalign), \boxed{W^\dagger M_eW=P_{\rm align}}, \qquad \eta_T=\operatorname{Tr}(\rho P_{\rm align}), W†Me​W=Palign​​,ηT​=Tr(ρPalign​), UT⋆=inf⁡2det⁡ΣTΩ. \mathcal U_T^\star =\inf 2\sqrt{\det\Sigma_{T\Omega}}. UT⋆​=inf2detΣTΩ​​. On the certified canonical branch, the sealed QTT target is ηT=Fedel,UT⋆=1−Fedel. \boxed{ \eta_T=F_e^{\rm del}, \qquad \mathcal U_T^\star=1-F_e^{\rm del}. } ηT​=Fedel​,UT⋆​=1−Fedel​.​ No complement coefficient is fitted. Five fidelity corridors, a radius/depth ladder, one-third untouched holdouts, topology twins, full covariance, global five-sigma decisions, at least 95% planned power, and transfer to a second record technology are frozen before data. The external computation is a feasibility anchor, not the timing target An, Cao, and Cui report carrier-deletion recovery in a local kicked-Ising memory. Their result qualifies the plausibility of Test A. Their reported Q=0.516Q=0.516Q=0.516 is explicitly forbidden from constructing Test B. The public source archive lacks the exact arrays and scripts, so exact replication remains pending. Five terminal outcomes INELIGIBLE_NO_THEORY_VERDICT REGISTERED_QTT_CONSEQUENCE_FALSIFIED QTT_CANDIDATE QUALIFIED_OTHER_OR_CROSS_CHANNEL_ANOMALY AMBIGUOUS_OR_UNDERPOWERED Any failed eligibility gate terminates without a theory verdict. A positive result requires the full multirung shape, not one selected point. An off-target anomaly is preserved rather than discarded or used as a post-hoc rescue. Immutable protocol seal eb0640b25c1d0bde56cacc7f25d9ce4304594833e4aa937ed50293a1faafc849 This is a separate sealed extension. It changes no target, threshold, classifier, protocol hash, or file in the parent test under concept DOI 10.5281/zenodo.21902885. Public anchors Completed-record fan-out and timing-access framework Observation as Access Quantum Traction Theory: Main Book External finite-window recovery paper The PDF is the default preview. The reconstruction archive contains the sealed JSON, classifier, eighteen-gate and raw-terminal templates, Stage-0 handoff, verifier, external audit, adversarial review, metadata, and checksums.
We derive an explicit test of whether a reduced quantum-memory model overstates recoverability. For channels with orthogonal logical outputs in distinguishable sectors, the minimum recovery error follows directly from differences between environmental record amplitudes, without numerical recovery optimization. Applying this test to two-excitation oscillator–qubit and four-qubit encodings reveals that matching single-loss responses need not preserve finite-time recoverability. Under collective loss, the four-qubit encoding is perfectly recoverable, whereas oscillator emission records reveal logical information. The resulting unavoidable error initially grows as the cube of storage time. The test quantifies omitted-level effects and benchmarks reduced models and recovery algorithms.
The measurements reported here separate maximum contiguous depth from nominal depth as the variable governing initialization gradient visibility in identity-fragmented hardware-efficient variational circuits, and extend the fragmented branch to 106 qubits. Three separately written implementations of a reduced active-window evaluator agree pairwise, to displayed precision, on every per-sample gradient, and the window evaluation is verified against full-register simulation at small size, against closed forms for the two shallowest prefix depths, and by window-width convergence. At fixed parameter location, the quantity barren-plateau statements concern, the prefix-depth-one gradient variance is one eighth analytically and is measured consistent with that value at both 65,536 and 10^6 qubits. A matched-nominal-depth comparison over the tested sizes yields suppression exponents 0.688 unfragmented against 0.011 fragmented; these are finite-size values and are not asymptotic exponents. A dense-topology control, in which the backward cone fills the register for both branches, retains the separation, which rules out cone width as the controlling variable. At exactly simulable sizes the fragmented circuit trains to 10^−3 relative energy error while the matched monolithic baseline collapses; asymptotic trainability is not established. The single-block 10^6-qubit circuit then trains off the identity point under translation-invariant parameters, exactly on certified causal-cone windows, and multistart search over the six shared angles reaches an energy density within 1.8% of the infinite-chain value. That residual is not a boundary effect, and is not the expressivity limit of identity fragmentation: relaxing translation invariance to period-two angles - twelve parameters, the same window - raises the correlation energy recovered beyond the best product state from 35.1% to 87.8%. Optima are best-found under local search; global optimality is not certified. The regimes trained here are classically simulable by construction; no claim of quantum advantage is made.
Quantum reservoir computing processes temporal information through driven many-body dynamics, but its performance is ultimately limited by how accurately past inputs can be extracted from finite measurements. Here we formulate this limitation as a local multiparameter estimation problem and introduce a delay-space quantum Fisher information matrix to quantify the distinguishability of information stored at different delays. This perspective identifies Fisher-orthogonal memory as a measurement-efficient design principle: different delays should perturb the reservoir state along mutually Fisher-orthogonal directions. We first analyze the single-qubit limit using the Gill--Massar bound, revealing an optimal write-store-routing trade-off. Guided by this structure, we construct solvable multi-qubit reservoirs based on Clifford routing orbits and Singer-cycle Pauli algebra. The resulting dynamics yield diagonal delay-space QFIMs with analytically programmable fading profiles. Under finite-shot local Pauli readout, these reservoirs retain sharp memory windows that are absent in a validation-selected Ising baseline. Their product-task behavior is governed by second-order responses inherited from the same Pauli-routing algebra. Our results provide an analytically controlled route toward measurement-efficient quantum reservoir computing.
A quantum record can have locally accessible populations while its distinguishing phase remains correlated with a distant source. We study this access boundary in a specified finite recording apparatus with a returning, vacuum/one-excitation source. Source-position weights give finite-time cutoff bounds without removing any physical hopping or return coupling. For an initially far-tagged record and its incoherent mixture, every reader in a declared position-preserving local-control class obeys a phase-visibility envelope and a necessary access-time inequality. A separate finite local probe shows why that state-discrimination limit is not an unrestricted limit on distinguishing two dynamical laws: fresh local coherence can reveal a stipulated added dephaser without recovering the old record phase. We construct a bounded, degree-three reader accessing only source positions 1–32. With the initial tag fixed at position 65, exact finite-source arrival certificates and an analytical tail comparison yield recovery uniformly over every finite total source length at least 65. Accessible control faults are charged against the arrived signed-phase norm, while source-moving drift is charged against the full norm. At the fixed deadline 25.02/J, the matched phase-dependent difference between coherent and archive-gated dynamics exceeds 0.005, including the stated simultaneous control faults and four additional absolute response allowances of 0.008 each. Complementary results cover a vacuum-ready source and a stronger endpoint-prepared finite example. The conclusions are conditional on the supplied model, preparations, common realized controls and calibration bounds. They are not a switchable-fundamental-law experiment, a nuisance-independent classifier, an optimal-speed theorem or an end-to-end formal verification. The supporting Lean companion contains 59 declarations in eight modules with accepted returned Mac compilation, type and axiom evidence; physical analytical interfaces remain explicit hypotheses or outside that subset. The deposit files include the main manuscript, technical supplement and full research/reproduction package.
Abstract Decoherence suppresses interference, but an observer’s ability to reconstruct a classical pointer value depends on additional resources: distinguishable conditional environmental states, an allowed measurement, sufficient accessible fragments, and sufficiently independent records. We provide an explicit minimal quantum-to-operational bridge that places these requirements in one chain. A system qubit is correlated with conditional environmental qubit states, permitting exact expressions for residual coherence, quantum mutual information, pointer Holevo information, accessible information, and Helstrom discrimination error. Full density-matrix calculations validate the formulas across 280 endpoint and interior cases. An accessible-sector/hidden-bath construction shows that coherence can fall below 2.3 × 10⁻⁵ while the observer’s record information and error remain fixed at 0.0803 bits and 0.4009. Measurement policies shift recovery thresholds: for record overlap 0.8 and error tolerance 0.05, collective or optimized adaptive-local discrimination requires four fragments, a fixed canonical-basis measurement requires six, and repeated one-fragment Helstrom measurements followed by classical decoding require seven. More importantly, records matched at the one-fragment level can have radically different collective behavior. For a binary pointer, the common-mode classical channel has an exact accessible-information ceiling of 1 − h₂(0.1) = 0.5310 bits, while the noncommuting hidden-memory ensemble approaches the same Holevo-information ceiling; matched independent records approach one bit and zero error. Disjoint observer counts and unanimous agreement likewise depend on shared error structure. Finally, declared local measurements induce classical record channels that are subjected to held-out model selection, predictive checks, abstention, and simultaneous finite-sample threshold certification. The resulting framework supplies the validated quantum-to-operational record model used in the companion analysis of operational capacity bounds for distinguishable decoherent histories.