论文库

Large language models (LLMs) have recently demonstrated the ability to generate parameters for variational quantum circuits without conventional optimization. However, the conditions under which this approach is effective remain unclear. Here, we investigate a frozen, general-purpose LLM that generates complete circuit parameter vectors from symbolic circuit and Hamiltonian descriptions, with optional iterative energy feedback. We evaluate the approach on general random Hamiltonians, structured parent Hamiltonians, and molecular systems. For general Hamiltonians, LLM-generated parameters exhibit larger energy errors than conventional Adam optimization, while additional feedback generally provides limited improvement. In contrast, for structured Hamiltonians, the LLM can generate promising low-energy parameter configurations, suggesting that identifiable physical and mathematical structure facilitates parameter inference. We also show that direct LLM predictions of minimum energies can violate the Hamiltonian spectral lower bound, whereas generated circuit parameters allow independent evaluation of physically realizable energy expectation values. Finally, we investigate blind circuit interpretation and find that the LLM can predict measurement outcomes even when it fails to identify the underlying quantum algorithm. These findings highlight the role of problem structure, the limitations of iterative LLM optimization, and the importance of independently verifiable predictions in quantum parameter programming.

Low-depth syndrome extraction for Calderbank-Shor-Steane (CSS) quantum low-density parity-check codes can be formulated as a proper ordered edge-coloring problem subject to quantum parity constraints. A proper edge-coloring of the CSS Tanner graph ensures that each data or ancilla qubit participates in at most one two-qubit gate per layer, but does not guarantee a valid interleaving of the X- and Z-check measurements as for every overlapping X/Z check pair, the number of shared data qubits on which the X interaction precedes the Z interaction must be even. The minimum number of colors in a proper ordered edge-coloring satisfying the quantum parity constraints equals the minimum two-qubit depth when each stabilizer check is measured with a single ancilla. We introduce local automorphism-aware syndrome compilation (LocalASC), which reduces the constraint system to edge-orbit variables under a subgroup of the Tanner graph automorphisms and lifts each feasible orbit assignment to the full graph. Although the $6$-layer degree lower bound is unattainable for the published weight-$6$ IBM bivariate bicycle codes, we show that this is not universal among two-block CSS codes. Among code instances for which the maximum check weight equals the maximum Tanner graph degree, LocalASC finds depth-optimal syndrome-extraction schedules for several two-block CSS codes with odd component weights, including instances with unequal odd weights. We also obtain lower-bound-saturating syndrome-extraction schedules for several quantum Tanner codes satisfying the same degree condition. To obtain the subgroups used by LocalASC without computing the full automorphism group of the Tanner graph, we construct translation subgroups for two-block group-algebra CSS codes over abelian groups. For quantum Tanner codes, we give conditions under which square-complex symmetries extend to Tanner graph automorphisms.

We present new upper and lower bounds on the minimum distance of certain generalized bicycle (GB) codes that go beyond the capabilities of techniques based on classical codes. These bounds are shown to capture the true minimum distance for specific subclasses within the GB family. In particular, we demonstrate the existence of two highly degenerate GB code families with parameters $[\![d^2+1,2,d]\!]_2$ for odd $d \geq 3$ and $[\![d^2,2,d]\!]_2$ for even $d \geq 4$, both having qubit connectivity of four, similar to that of surface codes. For the odd-distance family, we analyze the structure of low-weight logical Pauli operators and establish the existence of a fault-tolerant logical CNOT gate between the two logical qubits, achievable via a simple relabeling of data qubits. Next, using nearly self-inverse polynomials, we extend our results to construct an infinite class of connectivity-six GB codes with an improved rate. For GB codes based on these polynomials, we further present a technique to realize transversal logical CNOT gates via data-qubit permutations. We further construct syndrome extraction schemes for our connectivity four GB families that avoid reductions in minimum distance due to circuit-level faults propagating from check qubits to data qubits. Finally, we numerically evaluate the logical error rate performance of the mentioned connectivity four families of GB codes under circuit-level noise, obtaining thresholds comparable to those of rotated surface codes.

Hardware executions of the quantum approximate optimization algorithm (QAOA) are often validated by comparing the device's mean cost with a simulation, a check that can miss what matters for optimization. Under global depolarization, the mean normalized gap and the floor-corrected probability of every set of bitstrings, the optimum included, retain the same fraction of their noiseless improvement over uniform sampling. We test this prediction with depth-2, transferred-angle QAOA circuits for binary subproblems of an alternating-direction decomposition on the IBM Heron processor \texttt{ibm\_marrakesh}, with and without dynamical decoupling and twirling. At 12 qubits, the main-family circuits retained 29\% to 46\% of their mean-gap improvement but only 5\% to 15\% of their probability of the optimum, lower on at least nine of ten instances per run. Near-optimal bitstrings were lost about as much as the optimum, whereas the avoidance of poor bitstrings was retained best. In the first submission, a device-matched noise model reproduced the pattern but overestimated the retention of the optimum five- to eightfold. On a rugged planted family, the device found the optimum in 62\% of 768-shot blocks (noiseless: 98\%), within the range of local heuristics. Validations of optimization circuits should report retention of the optimum and of near-optimal sets.

Quantum algorithms for machine learning, chemistry, and cryptanalysis often assume coherent access to classical data at negligible physical cost. We instead treat data loading as a hardware process and quantify the dynamic energetic cost of a quantum random access memory (QRAM) query on a superconducting processor. Using the metric-noise-resource framework, we relate query fidelity and power to gate duration, relative two-qubit drive strength, and the distribution of attenuation across a multi-stage refrigerator, while accounting for thermal photons and gate errors. We analyze the linear-depth multiplexer and the noise-resilient bucket-brigade architectures, adapting the latter to a native superconducting gate set and refining its fidelity analysis using the fully decomposed gate schedule. For a representative bucket-brigade QRAM query with a $12$-qubit address register we obtain a query fidelity of $0.969$. The query consumes $3.51\times10^{-4}\,\mathrm{J}$ of dynamic energy, corresponding to an average dynamic power of $4.38\,\mathrm{W}$ and a peak of $64.4\,\mathrm{W}$. Our optimization shows that, at fixed target fidelity, the operating point and attenuation profile can change the average power by a factor of two or more.

We implement reference renewal to reconsider retained physical quantum-service results under a prespecified protocol. Twelve transitions retained six results each; ten completed renewal, eight met the prespecified endpoint, and five succeeded using retained results alone. The exact one-sided p=0.0546875 does not establish the recovery hypothesis. Incomplete references, binding failures and sequential waits expose operational limits. Offline reconstruction recovers decisions from preserved counts. Retrospective binding-plus-oracle checking accepts all 60 usable-transition results without renewal. With the exact oracle also supplying calibration scores, the study does not demonstrate incremental numerical-correctness utility of renewal.