Dongyang Cao | Searcharxiv

arXiv2026

A Finite-Window Recovery Hierarchy for Local Quantum Memory

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.

quant-ph↗

arXiv2026

Encoding Circuit Satisfiability in Rydberg Atom Arrays

Rydberg atom arrays natively encode the maximum-weight independent set (MWIS) problem through the blockade mechanism, so the Boolean circuit satisfiability problem (Circuit-SAT) can be brought onto the platform once it is reduced to MWIS. The conventional encoding of Circuit-SAT in the Rydberg atom array proceeds through conjunctive normal form (CNF) and incurs a substantial atom overhead. We introduce CAMERA (Circuit-SAT Atom-efficient MWIS Encoding for Rydberg Arrays), a method that provides MWIS encodings of Circuit-SAT instances on the king subgraph geometry of the array. CAMERA represents each logic gate as a compact weighted gadget and assembles the gadgets with a placement and routing compiler inspired by very large scale integration (VLSI) design. On random multi-gate benchmarks, the direct encoding route lowers the atom cost relative to the CNF route by an average factor of $22.4 \pm 1.8$. To demonstrate that the encoding extends from individual weighted gadgets to multi-gate arithmetic blocks, we compile a full adder and a multiplier, verifying each against its complete truth table by exact classical ground state calculations. We further showcase solving a representative Circuit-SAT instance end-to-end, from gate level compilation through a closed-system tensor-network simulation of a hardware-compatible annealing protocol on the encoded 30-atom instance to readout of a satisfying assignment. These results establish a complete encoding and simulation workflow as a proof of principle, and a concrete route toward solving a broader family of combinatorial problems on Rydberg atom arrays.

quant-ph↗