arXiv subjects

Anqi Gong

Publications and source records attributed to Anqi Gong.

7 recordsLinked to original sources

arXiv2026

Magic State Distillation via Codes over Binary Extension Fields

Fault-tolerant quantum computation architectures are frequently bottlenecked by the overhead of producing high-fidelity magic states. In this work, we use algebraic geometric techniques to construct codes over binary extension fields $\mathbb{F}_{2^s}$, thus discovering new protocols for the distillation of qubit magic states, where our focus is on the regime of practical qubit-based quantum computing architectures. To do this, we show that multi-qubit gates of interest such as $\text{CS}$, $\text{CCZ}$, and $\text{TOF}\# = \text{CCZ}_{123}\text{CCZ}_{345}$, can be packaged into simple gates over the larger fields, and we derive simple algebraic conditions in the extension fields allowing the distillation of these gates. Because they are derived from Galois qudits, the corresponding qubits codes naturally handle the correlated errors present on such multi-qubit states. Moreover, the protocols we discover are extremely compact; for example, we show that 4 $\text{CS}$ states can be distilled to 1 $\text{CS}$ state at distance 2, using only 4 logical qubits. For a case study, we consider the distillation of $\text{CS}$ and $\text{CCZ}$ states from injected $\text{T}$ and $\text{CS}$ states. When optimized for magic state production per unit time, or logical spacetime volume, we find that our protocols outperform the state-of-the-art in almost every situation, both at input error rates $10^{-3}$ (direct injection), and $10^{-6}$ (allowing some cultivation pre-injection).

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arXiv2026

Entangling logical qubits without physical operations

Fault-tolerant logical entangling gates are essential for scalable quantum computing, but are limited by the error rates and overheads of physical two-qubit gates and measurements. To address this limitation, we introduce phantom codes-quantum error-correcting codes that realize entangling gates between all logical qubits in a code block purely through relabelling of physical qubits during compilation, yielding perfect fidelity with no spatial or temporal overhead. We present a systematic study of such codes. First, we identify phantom codes using complementary numerical and analytical approaches. We exhaustively enumerate all $2.71 \times 10^{10}$ inequivalent CSS codes up to $n=14$ and identify additional instances up to $n=21$ via SAT-based methods. We then construct higher-distance phantom-code families using quantum Reed-Muller codes and the binarization of qudit codes. Across all identified codes, we characterize other supported fault-tolerant logical Clifford and non-Clifford operations. Second, through end-to-end noisy simulations with state preparation, full QEC cycles, and realistic physical error rates, we demonstrate scalable advantages of phantom codes over the surface code across multiple tasks. We observe a one-to-two order-of-magnitude reduction in logical infidelity at comparable qubit overhead for GHZ-state preparation and Trotterized many-body simulation tasks, given a modest preselection acceptance rate. Our work establishes phantom codes as a viable architectural route to fault-tolerant quantum computation with scalable benefits for workloads with dense local entangling structure, and introduces general tools for systematically exploring the broader landscape of quantum error-correcting codes.

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arXiv2025

Decoding quantum low density parity check codes with diffusion

An efficient decoder is essential for quantum error correction, and data-driven neural decoders have emerged as promising, flexible solutions. Here, we introduce a diffusion model framework to infer logical errors from syndrome measurements in quantum low-density parity-check codes. Using the bivariate bicycle code with realistic circuit-level noise, we show that masked diffusion decoders are more accurate, often faster on average, and always faster in the worst case than other state-of-the-art decoders, including belief propagation with ordered statistics decoding (BP-OSD) and autoregressive neural decoders. We show that by using fewer diffusion steps during inference one can gain significant speed at minimal cost in accuracy. By examining the factored attention from our trained neural network we find that, despite being trained solely on paired samples of syndrome-logical errors, this diffusion decoder learns the structure of the quantum codes. We also compare both masked and continuous diffusion decoders on code-capacity noise models, finding that masked diffusion decoders scale better than continuous diffusion decoders.

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arXiv2024

Computation with quantum Reed-Muller codes and their mapping onto 2D atom arrays

We give a fault tolerant construction for error correction and computation using two punctured quantum Reed-Muller (PQRM) codes. In particular, we consider the $[[127,1,15]]$ self-dual doubly-even code that has transversal Clifford gates (CNOT, H, S) and the triply-even $[[127,1,7]]$ code that has transversal T and CNOT gates. We show that code switching between these codes can be accomplished using Steane error correction. For fault-tolerant ancilla preparation we utilize the low-depth hypercube encoding circuit along with different code automorphism permutations in different ancilla blocks, while decoding is handled by the high-performance classical successive cancellation list decoder. In this way, every logical operation in this universal gate set is amenable to extended rectangle analysis. The CNOT exRec has a failure rate approaching $10^{-9}$ at $10^{-3}$ circuit-level depolarizing noise. Furthermore, we map the PQRM codes to a 2D layout suitable for implementation in arrays of trapped atoms and try to reduce the circuit depth of parallel atom movements in state preparation. The resulting protocol is strictly fault-tolerant for the $[[127,1,7]]$ code and practically fault-tolerant for the $[[127,1,15]]$ code. Moreover, each patch requires a permutation consisting of $7$ sub-hypercube swaps only. These are swaps of rectangular grids in our 2D hypercube layout and can be naturally created with acousto-optic deflectors (AODs). Lastly, we show for the family of $[[2^{2r},{2r\choose r},2^r]]$ QRM codes that the entire logical Clifford group can be achieved using only permutations, transversal gates, and fold-transversal gates.

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arXiv2024

Toward Low-latency Iterative Decoding of QLDPC Codes Under Circuit-Level Noise

We introduce a sliding window decoder based on belief propagation (BP) with guided decimation for the purposes of decoding quantum low-density parity-check codes in the presence of circuit-level noise. Windowed decoding keeps the decoding complexity reasonable when, as is typically the case, repeated rounds of syndrome extraction are required to decode. Within each window, we employ several rounds of BP with decimation of the variable node that we expect to be the most likely to flip in each round, Furthermore, we employ ensemble decoding to keep both decimation options (guesses) open in a small number of chosen rounds. We term the resulting decoder BP with guided decimation guessing (GDG). Applied to bivariate bicycle codes, GDG achieves a similar logical error rate as BP with an additional OSD post-processing stage (BP+OSD) and combination-sweep of order 10. For a window size of three syndrome cycles, a multi-threaded CPU implementation of GDG achieves a worst-case decoding latency of 3ms per window for the [[144,12,12]] code.

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arXiv2023

Graph Neural Networks for Enhanced Decoding of Quantum LDPC Codes

In this work, we propose a fully differentiable iterative decoder for quantum low-density parity-check (LDPC) codes. The proposed algorithm is composed of classical belief propagation (BP) decoding stages and intermediate graph neural network (GNN) layers. Both component decoders are defined over the same sparse decoding graph enabling a seamless integration and scalability to large codes. The core idea is to use the GNN component between consecutive BP runs, so that the knowledge from the previous BP run, if stuck in a local minima caused by trapping sets or short cycles in the decoding graph, can be leveraged to better initialize the next BP run. By doing so, the proposed decoder can learn to compensate for sub-optimal BP decoding graphs that result from the design constraints of quantum LDPC codes. Since the entire decoder remains differentiable, gradient descent-based training is possible. We compare the error rate performance of the proposed decoder against various post-processing methods such as random perturbation, enhanced feedback, augmentation, and ordered-statistics decoding (OSD) and show that a carefully designed training process lowers the error-floor significantly. As a result, our proposed decoder outperforms the former three methods using significantly fewer post-processing attempts. The source code of our experiments is available online.

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arXiv2023

Improved Logical Error Rate via List Decoding of Quantum Polar Codes

The successive cancellation list decoder (SCL) is an efficient decoder for classical polar codes with low decoding error, approximating the maximum likelihood decoder (MLD) for small list sizes. Here we adapt the SCL to the task of decoding quantum polar codes and show that it inherits the high performance and low complexity of the classical case, and can approximate the quantum MLD for certain channels. We apply SCL decoding to a novel version of quantum polar codes based on the polarization weight (PW) method, which entirely avoids the need for small amounts of entanglement assistance apparent in previous quantum polar code constructions. When used to find the precise error pattern, the quantum SCL decoder (SCL-E) shows competitive performance with surface codes of similar size and low-density parity check codes of similar size and rate. The SCL decoder may instead be used to approximate the probability of each equivalence class of errors, and then choose the most likely class. We benchmark this class-oriented decoder (SCL-C) against the SCL-E decoder and find a noticeable improvement in the logical error rate. This improvement stems from the fact that the contributions from just the low-weight errors give a reasonable approximation to the error class probabilities. Both SCL-E and SCL-C maintain the complexity O(LN logN) of SCL for code size N and list size L. We also show that the list decoder can be used to gain insight into the weight distribution of the codes and how this impacts the effect of degenerate errors.

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