arXiv subjects

John Blue

Publications and source records attributed to John Blue.

5 recordsLinked to original sources

arXiv2026

Remote entanglement need not be the bottleneck for modular trapped-ion quantum computing

Modularity underpins classical computing; as quantum processors encounter limits on fabrication yield, reliability, and size, they will also need it acutely. The bottleneck to linking modules is producing shared entanglement at sufficient rate, density, and fidelity. Trapped ions hold the best demonstrated photonic links, yet they rely on bulky collection optics that cap how densely links can be packed, and remote entanglement operations trail local gates by two orders of magnitude in rate and fidelity. We synthesize several enabling results $\unicode{x2014}$ single-photon heralding, coherent recoil correction, projective distillation, and trap-integrated photonics $\unicode{x2014}$ into one comprehensive architecture that substantially narrows this gap. Single-photon heralding leads to linear scaling of success probability with detection efficiency, allowing compact integrated photonics to saturate the entanglement rate at a local-operation limit in dense, easy-to-parallelize channels. Addressing its inherent error mechanisms at their source, we project a Bell-pair fidelity of 99.9% at rates and densities compatible with fault-tolerant operations. Remote entanglement then need not remain the bottleneck for modular trapped-ion computing; the limit shifts to the local operations that must improve regardless.

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arXiv2026

Generalized Bicycle Codes as Cyclic Submodules and their Automorphism Structure

Automorphisms of quantum codes, when they exist, offer a pathway toward fault-tolerant gate implementation via qubit relabeling. Although useful, the conditions under which automorphisms appear in a given code remain poorly understood. In this paper, we develop an algebraic framework for systematically analyzing and engineering automorphisms in Generalized Bicycle (GB) codes. Central to our approach is the derivation of a three-space dependency between the polynomial ring space, the parity check matrix space, and the $\mathbb{F}_2^{2\ell}$ qubit space, similar to the structure found in the study of classical cyclic codes. By expressing GB codes as a pair of cyclic submodules of $R_\ell^2$, where $R_\ell \cong \mathbb{F}_2[x]/\langle x^\ell-1\rangle$, we reduce the search for code automorphisms to a deterministic algebraic problem, deriving necessary and sufficient conditions for the existence of block-separable automorphisms built from cyclic shifts, ring automorphisms and block-swaps. We connect these conditions to the fold-transversal gate framework, providing explicit criteria for the existence of $H$-, $S$-, and $CX$-type fold-transversal gates. We further discuss structured bases for logical operators in order to determine the logical action of a given automorphism. Finally, we introduce the Maximal Cube Root (MCR) code family, a family of GB codes constructed around the principle of maximizing automorphism flexibility and fold-CX gates. We demonstrate a collection of $k=2$ MCR codes up to $d=13$ generating the 2-qubit Clifford group via automorphism and fold-transversal gates, with stabilizer weight ranging from 8 to 16, and $k>2$ MCR codes with a minimum of 20 distinct logical gates achievable from automorphisms. This serves as a first demonstration of inverse design: using these methods to build codes around a rich automorphism structure from the ground up.

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arXiv2026

Full Extractors for Logical Processing in Hypergraph Product Codes

Quantum low-density parity-check (QLDPC) codes are promising candidates for practical low-overhead quantum memories. For large-scale fault-tolerant quantum computation, we further need logical processing methods for QLDPC codes. In this work, we construct full extractors---surgery systems capable of measuring arbitrary logical Pauli operators on a code block---for several hypergraph product (HGP) codes. These extractors enable logical processing via Pauli-based computation (PBC) without the compilation overhead observed in prior works. Moreover, our extractors have sizes between $47\%$ and $80\%$ of the base HGP codes, and the extractor-augmented codes can be supported on fixed-connectivity hardware with maximum qubit degree ten. Our approach involves assembling many partial extractors with verifiable fault tolerance into a single full extractor. For a distance $10$ HGP code, circuit-level noise simulations yield logical measurement error rates of approximately $10^{-6}$ at a physical error rate of $0.1\%$. These results demonstrate that extractor architectures, when designed in the fixed-connectivity setting, can achieve the space efficiency of QLDPC codes without introducing compilation overhead compared to surface-code PBC architectures.

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arXiv2025

A log-depth in-place quantum Fourier transform that rarely needs ancillas

When designing quantum circuits for a given unitary, it can be much cheaper to achieve a good approximation on most inputs than on all inputs. In this work we formalize this idea, and propose that such "optimistic quantum circuits" are often sufficient in the context of larger quantum algorithms. For the rare algorithm in which a subroutine needs to be a good approximation on all inputs, we provide a reduction which transforms optimistic circuits into general ones. Applying these ideas, we build an optimistic circuit for the in-place quantum Fourier transform (QFT). Our circuit has depth $O(\log (n / \epsilon))$ for tunable error parameter $\epsilon$, uses $n$ total qubits, i.e. no ancillas, is local for input qubits arranged in 1D, and is measurement-free. The circuit's error is bounded by $\epsilon$ on all input states except an $O(\epsilon)$-sized fraction of the Hilbert space. The circuit is also rather simple and thus may be practically useful. Combined with recent QFT-based fast arithmetic constructions [arXiv:2403.18006], the optimistic QFT yields factoring circuits of nearly linear depth using only $2n + O(n/\log n)$ total qubits. Additionally, we apply our reduction technique to yield an approximate QFT with well-controlled error on all inputs; it is the first to achieve the asymptotically optimal depth of $O(\log (n/\epsilon))$ with a sublinear number of ancilla qubits. The reduction uses long-range gates but no measurements.

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arXiv2025

Machine Learning Decoding of Circuit-Level Noise for Bivariate Bicycle Codes

Fault-tolerant quantum computers will depend crucially on the performance of the classical decoding algorithm which takes in the results of measurements and outputs corrections to the errors inferred to have occurred. Machine learning models have shown great promise as decoders for the surface code; however, this promise has not yet been substantiated for the more challenging task of decoding quantum low-density parity-check (QLDPC) codes. In this paper, we present a recurrent, transformer-based neural network designed to decode circuit-level noise on Bivariate Bicycle (BB) codes. For the $[[72,12,6]]$ BB code, at a physical error rate of $p=0.1\%$, our model achieves logical error rates almost $5$ times lower than belief propagation with ordered statistics decoding (BP-OSD), and roughly $5$ times larger than a most-likely error decoder. Moreover, while BP-OSD has a wide distribution of runtimes with significant outliers, our model has a consistent runtime and is an order-of-magnitude faster than the worst-case times from a benchmark BP-OSD implementation. On the $[[144,12,12]]$ BB code, our model obtains worse logical error rates but maintains the speed advantage. These results provide initial evidence that machine learning decoders can out-perform conventional decoders on small QLDPC codes, but suggest more complex architectures and/or training procedures are necessary to scale to larger code sizes.

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