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arXiv:quant-ph/0505153 · Physical Review Letters

Quantum Error Correction in Spatially Correlated Quantum Noise

Rochus Klesse, Sandra Frank

Published Nov 30, 2005• 65 citations
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Abstract

We consider quantum error correction of quantum noise that is created by a local interaction of qubits with a common bosonic bath. The possible exchange of bath bosons between qubits gives rise to spatial and temporal correlations in the noise. We find that these kinds of noise correlations have a strong negative impact on quantum error correction.

DOI
10.1103/physrevlett.95.230503

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We consider quantum error correction of quantum noise that is created by a local interaction of qubits with a common bosonic bath. The possible exchange of bath bosons between qubits gives rise to spatial and temporal correlations in the noise. We find that these kinds of noise correlations have a strong negative impact on quantum error correction.
Correlated noise across multiple qubits poses a significant challenge for achieving scalable and fault-tolerant quantum processors. Despite recent experimental efforts to quantify this noise in various qubit architectures, a comprehensive understanding of its role in qubit dynamics remains elusive. Here, we present an analytical study of the dynamics of driven qubits under spatially correlated noise, including both Markovian and non-Markovian noise. Surprisingly, we find that, while correlated classical noise only leads to correlated decoherence without increasing the quantum coherence in the system, the correlated quantum noise can be exploited to generate entanglement. In particular, we reveal that, in the quantum limit, pure dephasing noise induces a coherent long-range two-qubit Ising interaction that correlates distant qubits. In contrast, for purely transverse noise when qubits are subjected to coherent drives, the correlated quantum noise induces both coherent symmetric exchange and Dzyaloshinskii-Moriya interaction between the qubits, as well as correlated relaxation, both of which give rise to significant entanglement. Remarkably, in this case, we uncover that the system exhibits distinct dynamical phases in different parameter regimes. Finally, we reveal the impact of spatio-temporally correlated 1/f noise on the decoherence rate, and how its temporal correlations restore lost entanglement. Our analysis not only offers critical insights into designing effective error mitigation strategies to reduce harmful effects of correlated noise, but also enables tailored protocols to leverage and harness noise-induced correlations for quantum information processing.
Abstract Quantum systems can be used to measure various quantities in their environment with high precision. Often, however, their sensitivity is limited by the decohering effects of this same environment. Dynamical decoupling schemes are widely used to filter environmental noise from signals, but their performance is limited by the spectral properties of the signal and noise at hand. Quantum error correction schemes have therefore emerged as a complementary technique without the same limitations. To date, however, they have failed to correct the dominant noise type in many quantum sensors, which couples to each qubit in a sensor in the same way as the signal. Here we show how quantum error correction can correct for such noise, which dynamical decoupling can only partially address. Whereas dynamical decoupling exploits temporal noise correlations in signal and noise, our scheme exploits spatial correlations. We give explicit examples in small quantum devices and demonstrate a method by which error-correcting codes can be tailored to their noise.
Quantum systems can be used to measure various quantities in their environment with high precision. Often, however, their sensitivity is limited by the decohering effects of this same environment. Dynamical decoupling schemes are widely used to filter environmental noise from signals, but their performance is limited by the spectral properties of the signal and noise at hand. Quantum error correction schemes have therefore emerged as a complementary technique without the same limitations. To date, however, they have failed to correct the dominant noise type in many quantum sensors, which couples to each qubit in a sensor in the same way as the signal. Here we show how quantum error correction can correct for such noise, which dynamical decoupling can only partially address. Whereas dynamical decoupling exploits temporal noise correlations in signal and noise, our scheme exploits spatial correlations. We give explicit examples in small quantum devices and demonstrate a method by which error-correcting codes can be tailored to their noise.
Quantum error correction is a solution to preserve the fidelity of quantum information encoded in physical systems subject to noise. However, unfavorable correlated errors could be induced even for non-interacting qubits through the environment (bath), when they are "packed" together. The question is, to what extent can we treat the noise induced by the bath as independent? In the context of the spin-boson model, we show that, under some reasonable constraints, the independent noise approximation could be valid. On the other hand, in the strongly correlated limit, we show how the method of decoherence free subspace can be made applicable. Combining these two methods makes fault-tolerant quantum computation promising in fighting against correlated errors.
The path to fault-tolerant quantum computing hinges on hardware that scales while remaining compatible with quantum error correction (QEC). Silicon spin qubits are a leading hardware candidate because they combine industrial fabrication compatibility with a nanoscale footprint that could accommodate millions of qubits on a chip. However, their suitability for QEC remains uncertain since spatially correlated noise naturally emerges from the resulting close proximity of qubits. These correlations increase the likelihood of simultaneous errors and erode the redundancy that QEC depends on. Here we quantify the spatial extent of noise correlations in a five-qubit silicon array and assess their impact on QEC. We identify two distinct sources of correlated noise: global magnetic field drifts that generate perfectly correlated fluctuations, and charge noise from two-level fluctuators that produces short-range correlations decaying within neighboring qubits. While magnetic drifts represent a critical correlated noise source that can compromise QEC, they can be mitigated. In contrast, the measured charge noise correlations are moderate, electrically tunable, and compatible with fault-tolerant operation with minimal qubit overhead. Our results establish quantitative benchmarks for correlated noise and clarify how such correlations impact the viability of quantum error correction in scalable qubit arrays.