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arXiv:2303.16122

Increasing error tolerance in quantum computers with dynamic bias arrangement

Héctor Bombín, Dawson, Chris, Naomi Nickerson, Mihir Pant, Jordan Sullivan

Published Mar 28, 2023• 5 citations
arXivHTMLPDF

Abstract

Many quantum operations are expected to exhibit bias in the structure of their errors. Recent works have shown that a fixed bias can be exploited to improve error tolerance by statically arranging the errors in beneficial configurations. In some cases an error bias can be dynamically reconfigurable, an example being linear optical fusion where the basis of a fusion failure can be chosen before the measurement is made. Here we introduce methods for increasing error tolerance in this setting by using classical decision-making to adaptively choose the bias in measurements as a fault tolerance protocol proceeds. We study this technique in the setting of linear optical fusion based quantum computing (FBQC). We provide examples demonstrating that by dynamically arranging erasures, the loss tolerance can be tripled when compared to a static arrangement of biased errors while using the same quantum resources: we show that for the best FBQC architecture of Bartolucci et al. (2023) the threshold increases from $2.7\%$ to $7.5\%$ per photon with the same resource state by using dynamic biasing. Our method does not require any specific code structure beyond having a syndrome graph representation. We have chosen to illustrate these techniques using an architecture which is otherwise identical to that in Bartolucci et al. (2023), but deployed together with other techniques, such as different fusion networks, higher loss thresholds are possible.

DOI
10.48550/arxiv.2303.16122

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Many quantum operations are expected to exhibit bias in the structure of their errors. Recent works have shown that a fixed bias can be exploited to improve error tolerance by statically arranging the errors in beneficial configurations. In some cases an error bias can be dynamically reconfigurable, an example being linear optical fusion where the basis of a fusion failure can be chosen before the measurement is made. Here we introduce methods for increasing error tolerance in this setting by using classical decision-making to adaptively choose the bias in measurements as a fault tolerance protocol proceeds. We study this technique in the setting of linear optical fusion based quantum computing (FBQC). We provide examples demonstrating that by dynamically arranging erasures, the loss tolerance can be tripled when compared to a static arrangement of biased errors while using the same quantum resources: we show that for the best FBQC architecture of Bartolucci et al. (2023) the threshold increases from 2.7%2.7\%2.7% to 7.5%7.5\%7.5% per photon with the same resource state by using dynamic biasing. Our method does not require any specific code structure beyond having a syndrome graph representation. We have chosen to illustrate these techniques using an architecture which is otherwise identical to that in Bartolucci et al. (2023), but deployed together with other techniques, such as different fusion networks, higher loss thresholds are possible.
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Quantum error correction is an essential tool for performing reliable quantum information processing tasks under noisy circumstances, and is attracting growing attention today as a crucial element for realizing the fault-tolerant quantum computer. In this article, we introduce two cutting-edge quantum error correction techniques for implementing fault-tolerant quantum computation: the hybrid approach and the fusion-based quantum computation. The hybrid quantum computing utilizes hybrid qubits which combine the advantages of continuous-variable and discrete-variable qubits. The fusion-based quantum error correction offers a way, specialized for photonic quantum information processing, toward fault tolerance based on two-qubit measurement, known as fusion. We demonstrate by numerical simulations that our methods achieve the increased loss threshold and the improved resource efficiency compared to previous photonic proposals.
Qubits with strongly biased noise, in which phase-flip errors are orders of magnitude more frequent than bit-flips, arise both naturally, as in electron and nuclear spins, and by engineering, as in stabilized cat qubits. This noise structure holds the promise of reducing the daunting hardware overhead of fault-tolerant quantum computing, but exploiting it requires physical operations that do not convert frequent phase-flips into rare bit-flips. In this review, we analyze the most prominent fault-tolerant protocols for biased-noise qubits, organized according to the available set of such bias-preserving operations. When this set is restricted to the CZ gate together with preparation and measurement in the X basis, we show that the complexity of the required syndrome extraction gadgets essentially cancels the benefit of the noise bias: at experimentally relevant error rates, one may as well ignore the bias and rely on standard error correction designed for depolarizing noise. The situation changes drastically when a bias-preserving CX gate is available: the hierarchy of errors can then be reflected in the structure of the code, with frequent phase-flips corrected by a dedicated high-threshold code and rare bit-flips by concatenation with a high-rate code. The same hierarchy also enables hardware-efficient preparation of magic states. Finally, as a bias-preserving CX is forbidden in naturally biased platforms and challenging in engineered ones, we present a measurement-based architecture in which a high-fidelity quantum non-demolition readout of multi-qubit Pauli Z operators takes its place, extending these overhead reductions to a much broader range of physical platforms.
We introduce fault-tolerant (FT) architectures for error correction with the XZZX cluster state based on performing measurements of two-qubit Pauli operators Z⊗Z and X⊗X, or fusions, on a collection of few-body entangled resource states. Our construction is tailored to effectively correct noise that predominantly causes faulty X⊗X measurements during fusions. This feature offers a practical advantage in linear optical quantum computing with dual-rail photonic qubits, where failed fusions only erase X⊗X measurement outcomes. By applying our construction to this platform, we find a record-high threshold to fusion failures exceeding 25% in the experimentally relevant regime of nonzero loss rate per photon, considerably simplifying hardware requirements.
**Abstract:** This research details a novel approach to practical quantum error correction (QEC) capable of surpassing current limitations of fixed topological code lattices by employing a dynamically reconfigurable architecture driven by real-time noise profile analysis. The system utilizes a hybrid quantum-classical control loop, continuously adapting the code lattice configuration and decoding algorithms to optimize resilience against specific error syndromes. Projected to achieve a 10-20x improvement in fault tolerance compared to static lattice approaches within five years, this advancement enables scaling of quantum processors to practical qubit counts while minimizing overhead and operational complexity. The methodology involves leveraging established topological code theory (surface codes, color codes, etc.), coupled with advanced machine learning techniques for adaptive lattice configuration and decoding, resulting in a highly robust and practically implementable QEC strategy.
In realistic hardware for quantum computation that possesses fault-tolerance, non-stationary noise and stochastic drift lead to logical failure from the temporal accumulation of errors, not from independent events. Static decoding and fixed calibration techniques are structurally incompatible with this situation because they do not take into account temporal correlations between errors or control-induced back-action of errors. These effects motivate control policies that must track noise evolution across correction cycles, rather than respond to individual syndromes in isolation. We treat fault-tolerant quantum computation as a stochastic control problem, modelled using reduced quantum dynamics in which Pauli error processes are governed by latent noise parameters that vary temporally. From this perspective, logical failure arises through the accumulation of a hazard variable, and the corresponding control objective depends on the full history of observations. Operating under these conditions, a Chronological Deep Q-Network (Ch-DQN) maintains an internal belief state that tracks both noise evolution and accumulated hazard. During training, backward refinement of trajectories is used to sample slowly drifting modes of operation, while runtime inference remains strictly causal. A fractional meta-update stabilizes learning in the presence of non-stationary, control-coupled dynamics. Through multi-distance simulations that incorporate stochastic drift and feedback from decision-making, Ch-DQN suppresses hazard accumulation and extends logical survival time relative to static and recurrent baselines. Error correction in this regime is therefore no longer a static decoding task, but a control process whose success is determined over time by the underlying noise dynamics.