arXiv subjects

Maxwell Poster

Publications and source records attributed to Maxwell Poster.

6 recordsLinked to original sources

arXiv2026

Gap-Priced $|T\rangle$-States: Dynamic $|T\rangle$ Post-Selection and Budget-Aware Factory Provisioning

Magic $|T\rangle$-state preparation dominates the cost of fault-tolerant quantum computation on surface codes, yet cultivation and distillation are typically provisioned statically, leaving much of the program's error budget unused. We present Gap-Priced $|T\rangle$ States (GP$|T\rangle$-S), a lattice surgery scheduler and factory allocator that co-optimizes both methods under a total $T$-error budget. GP$|T\rangle$-S uses the complementary gap of each cultivated state as a fidelity estimate and dynamically adjusts the cultivation gap cutoff, converting budget slack into speed by giving the scheduler control over the cultivation post-selection. GP$|T\rangle$-S also characterizes distillation factories by size, $|T\rangle$-state production rate, and budget slack, and introduces cultivating factories that embed cultivation within routing channels, achieving fidelities otherwise requiring two-level distillation at a single-level footprint. GP$|T\rangle$-S organizes these characterizations into a factory catalog, and performs distillation factory allocation over this catalog in tandem with the gap cutoff using dynamic-programming to achieve one of i) minimum spacetime volume, ii) minimum execution time, or iii) minimum space overhead, all within a user-provided $T$-error budget. Across sixteen benchmarks under high and low $T$-error budgets of $10^{-3}$ and $10^{-5}$ respectively, GP$|T\rangle$-S consistently outperforms cultivation-only and single-factory baselines without exceeding the budget, achieving a 5.5$\times$ geometric mean speedup in logical cycle count and a 3.4$\times$ geometric mean reduction in space-time volume.

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arXiv2026

Staying Sober: A Shot-Free Predictor of Logical Error Rates for Concatenated Quantum Error Correcting Codes

Estimating the logical error rate (LER) of a quantum error-correcting (QEC) code by Monte Carlo sampling takes $O(p^{-\lceil d/2 \rceil}/\varepsilon^2)$ samples at physical error rate $p$, code distance $d$ and relative error $\varepsilon$, which becomes intractable at large distances and low error rates, and especially for concatenated codes, whose distance grows as $d^{\ell}$ with the number of levels $\ell$. The fail fast method reduces this cost by sampling the failures of each weight separately, but it only works for unconcatenated codes, and does not model the soft information that the levels of a concatenated code pass to each other. We propose a predictor that takes the stabilizers, the minimum-weight logical operators and, for odd $d$, the logical operators of weight $d + 1$ of a code, and computes, without sampling, the leading monomial $c\,p^{o}$ of the LER when expressed as a polynomial in $p$, at every level of concatenation, in time polynomial in the code parameters and linear in $\ell$ for fixed budgets. We prove that our prediction is exact for any unconcatenated stabilizer code, for every logical observable and arbitrary per-qubit error rates, whenever no budget is exhausted. Furthermore, for concatenated codes, we construct a recursive approach that computes the leading monomial exactly in exponential time, and our predictor approximates this approach. Our predictions match exact enumeration at level 1 on every code we evaluate, and up to three levels for the iceberg code. Using our predictor, we evaluate and compare $37$ code configurations under four noise biases in $48$ core-hours, where Monte Carlo sampling would need more than $10^{12}$ shots at $p = 10^{-3}$ for $113$ of these $148$ cases.

quant-ph↗

arXiv2026

Exploring Asymmetric QEC Code Concatenation

Concatenated quantum error-correcting codes have recently gained popularity because they improve the effective distance of a joint code without requiring the discovery of new codes with desirable parameters. A common building block for such studies is the $[[4,1,2]]$ Iceberg code, the smallest error-detecting code and therefore the one with the lowest resource overhead. However, it has an asymmetric number of $X$ and $Z$ checks, and concatenating it produces skewed logical error rates (LERs) between the $X$ and $Z$ observables. This asymmetry can be mitigated by Clifford-deforming the individual blocks of the concatenation, but the space of possible Hadamard deformations grows doubly exponentially with the number of concatenation levels. We formalize this deformation space and investigate it by proposing six concrete deformation strategies, which we compare under a code capacity (with and without bias) noise model using a concatenated maximum-likelihood soft-information decoder. Among the strategies we study, one one of them achieves near-identical $X$ and $Z$ LERs in a logical-memory experiment while simultaneously reducing the total LER (the sum of the $X$ and $Z$ error rates).

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arXiv2026

ReloQate: Transient Drift Detection and In-Situ Recalibration in Surface Code Quantum Error Correction

Quantum error correction (QEC) promises to exponentially suppress qubit noise, but typically assumes spatially-uniform and temporally-constant noise rates. However, real quantum hardware exhibits variation in noise levels over time, which will be amplified by QEC if not addressed. To mitigate this drift in error rates, we leverage transient information readily available in surface code quantum error correction to predict logical error rates (LER) in real time. We infer a prediction model by sampling physical error rates from real hardware, and mapping detector fire rate (DFR), or parity of stabilizer measurements across QEC rounds, to LER. This allows for on-the-fly LER predictions without the typical characterization overhead required to determine LER. This method can easily be extended to other stabilizer codes. Importantly, we observe that this prediction should be accurate yet conservative (i.e. give an upper estimate) to enable appropriately fast responses to real-time physical error changes. That is, responses should be executed marginally ahead of time to allow for their execution to complete, and minimize time spent (ideally none) above intolerable error rates. More importantly, we pair this predictor with a scheme which remaps drifted logical qubits to fresh tiles in a patch-based architecture while their original tiles are recalibrated. Our results demonstrate DFR-based prediction to be an effective LER predictor, and remapping as a spatially efficient and timely mitigation response for small code distances, both of which are significant steps in furthering practical QEC.

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arXiv2026

Optimizing Logical Mappings for Quantum Low-Density Parity Check Codes

Early demonstrations of fault tolerant quantum systems have paved the way for logical-level compilation. For fault-tolerant applications to succeed, execution must finish with a low total program error rate (i.e., a low program failure rate). In this work, we study a promising candidate for future fault-tolerant architectures with low spatial overhead: the Gross code. Compilation for the Gross code entails compiling to Pauli Based Computation and then reducing the rotations and measurements to the Bicycle ISA. Depending on the configuration of modules and the placement of code modules on hardware, one can reduce the amount of resulting Bicycle instructions to produce a lower overall error rate. We find that NISQ-based, and existing FTQC mappers are insufficient for mapping logical qubits on Gross code architectures because 1. they do not account for the two-level nature of the logical qubit mapping problem, which separates into code modules with distinct measurements, and 2. they naively account only for length two interactions, whereas Pauli-Products are up to length $n$, where $n$ is the number of logical qubits in the circuit. For these reasons, we introduce a two-stage pipeline that first uses hypergraph partitioning to create in-module clusters, and then executes a priority-based algorithm to efficiently assign clusters onto hardware. We find that our mapping policy reduces the error contribution from inter-module measurements, the largest source of error in the Gross Code, by up to $\sim36\%$ in the best case, with an average reduction of $\sim13\%$. On average, we reduce the failure rates from inter-module measurements by $\sim22\%$ with localized factory availability, and by $\sim17\%$ on grid architectures, allowing hardware developers to be less constrained in developing scalable fault tolerant systems due to software driven reductions in program failure rates.

quant-ph↗

arXiv2026

CQM: Cyclic Qubit Mappings

Quantum computers show promise to solve select problems otherwise intractable on classical computers. However, noisy intermediate-scale quantum (NISQ) era devices are currently prone to various sources of error. Quantum error correction (QEC) shows promise as a path towards fault tolerant quantum computing. Surface codes, in particular, have become ubiquitous throughout literature for their efficacy as a quantum error correcting code, and can execute quantum circuits via lattice surgery operations. Lattice surgery also allows for logical qubits to maneuver around the architecture, if there is space for it. Hardware used for near-term demonstrations have both spatially and temporally varying error results in logical qubits. By maneuvering logical qubits around the topology, an average logical error rate (LER) can be enforced. We propose cyclic qubit mappings (CQM), a dynamic remapping technique implemented during compilation to mitigate hardware heterogeneity by expanding and contracting logical qubits. In addition to LER averaging, CQM shows initial promise given it's minimal execution time overhead and effective resource utilization.

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