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arXiv:1911.12280

Real-time decoding of stabilizer measurements in a bit-flip code

Diego Ristè, Luke C. G. Govia, Brian Donovan, Spencer D. Fallek, William D. Kalfus, Markus Brink, Nicholas T. Bronn, Thomas Ohki

Published Nov 27, 2019• 2 citations
arXivHTMLPDF

Abstract

Although qubit coherence times and gate fidelities are continuously improving, logical encoding is essential to achieve fault tolerance in quantum computing. In most encoding schemes, correcting or tracking errors throughout the computation is necessary to implement a universal gate set without adding significant delays in the processor. Here we realize a classical control architecture for the fast extraction of errors based on multiple cycles of stabilizer measurements and subsequent correction. We demonstrate its application on a minimal bit-flip code with five transmon qubits, showing that real-time decoding and correction based on multiple stabilizers is superior in both speed and fidelity to repeated correction based on individual cycles. Furthermore, the encoded qubit can be rapidly measured, thus enabling conditional operations that rely on feed-forward, such as logical gates. This co-processing of classical and quantum information will be crucial in running a logical circuit at its full speed to outpace error accumulation.

DOI
10.48550/arxiv.1911.12280

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Although qubit coherence times and gate fidelities are continuously improving, logical encoding is essential to achieve fault tolerance in quantum computing. In most encoding schemes, correcting or tracking errors throughout the computation is necessary to implement a universal gate set without adding significant delays in the processor. Here we realize a classical control architecture for the fast extraction of errors based on multiple cycles of stabilizer measurements and subsequent correction. We demonstrate its application on a minimal bit-flip code with five transmon qubits, showing that real-time decoding and correction based on multiple stabilizers is superior in both speed and fidelity to repeated correction based on individual cycles. Furthermore, the encoded qubit can be rapidly measured, thus enabling conditional operations that rely on feed-forward, such as logical gates. This co-processing of classical and quantum information will be crucial in running a logical circuit at its full speed to outpace error accumulation.
Abstract Although qubit coherence times and gate fidelities are continuously improving, logical encoding is essential to achieve fault tolerance in quantum computing. In most encoding schemes, correcting or tracking errors throughout the computation is necessary to implement a universal gate set without adding significant delays in the processor. Here, we realize a classical control architecture for the fast extraction of errors based on multiple cycles of stabilizer measurements and subsequent correction. We demonstrate its application on a minimal bit-flip code with five transmon qubits, showing that real-time decoding and correction based on multiple stabilizers is superior in both speed and fidelity to repeated correction based on individual cycles. Furthermore, the encoded qubit can be rapidly measured, thus enabling conditional operations that rely on feed forward, such as logical gates. This co-processing of classical and quantum information will be crucial in running a logical circuit at its full speed to outpace error accumulation.
Quantum data are susceptible to decoherence induced by the environment and to errors in the hardware processing it. A future fault-tolerant quantum computer will use quantum error correction to actively protect against both. In the smallest error correction codes, the information in one logical qubit is encoded in a two-dimensional subspace of a larger Hilbert space of multiple physical qubits. For each code, a set of non-demolition multi-qubit measurements, termed stabilizers, can discretize and signal physical qubit errors without collapsing the encoded information. Here using a five-qubit superconducting processor, we realize the two parity measurements comprising the stabilizers of the three-qubit repetition code protecting one logical qubit from physical bit-flip errors. While increased physical qubit coherence times and shorter quantum error correction blocks are required to actively safeguard the quantum information, this demonstration is a critical step towards larger codes based on multiple parity measurements.
Quantum error correction (QEC) is essential for achieving low error rates required for fault-tolerant quantum computation. In stabilizer-based codes such as the surface code, errors are inferred from repeated syndrome measurements and corrected by a classical decoder. To prevent error accumulation, decoding must be performed with both high throughput and low latency to keep pace with the QEC cycle and enable real-time feedback for universal logical operations. Here we report a hardware-integrated control architecture featuring an FPGA-based neural-network (NN) decoder and experimentally demonstrate real-time surface-code (distance-3) QEC on a superconducting quantum processor. The system achieves a deterministic closed-loop latency of 550 ns, including 124 ns for NN decoding, enabling feedback corrections within a 1.25 us QEC cycle. We show that real-time decoding and feedback correction achieve logical performance comparable to offline decoding while maintaining robustness against varying error conditions. We further demonstrate mid-circuit feedback correction in non-Clifford logical circuits, where Pauli-frame updating alone becomes insufficient. Our results establish a low-latency hardware architecture for embedded QEC control and provide a pathway towards scalable fault-tolerant quantum computing systems.
Correcting errors in real time is essential for reliable large-scale quantum computations. Realizing this high-level function requires a system capable of several low-level primitives, including single-qubit and two-qubit operations, mid-circuit measurements of subsets of qubits, real-time processing of measurement outcomes, and the ability to condition subsequent gate operations on those measurements. In this work, we use a ten qubit QCCD trapped-ion quantum computer to encode a single logical qubit using the [[7,1,3]][[7,1,3]][[7,1,3]] color code, first proposed by Steane~\cite{steane1996error}. The logical qubit is initialized into the eigenstates of three mutually unbiased bases using an encoding circuit, and we measure an average logical SPAM error of 1.7(6)×10−31.7(6) \times 10^{-3}1.7(6)×10−3, compared to the average physical SPAM error 2.4(8)×10−32.4(8) \times 10^{-3}2.4(8)×10−3 of our qubits. We then perform multiple syndrome measurements on the encoded qubit, using a real-time decoder to determine any necessary corrections that are done either as software updates to the Pauli frame or as physically applied gates. Moreover, these procedures are done repeatedly while maintaining coherence, demonstrating a dynamically protected logical qubit memory. Additionally, we demonstrate non-Clifford qubit operations by encoding a logical magic state with an error rate below the threshold required for magic state distillation. Finally, we present system-level simulations that allow us to identify key hardware upgrades that may enable the system to reach the pseudo-threshold.
Quantum error correction will be essential for quantum computers to realise their full potential. As quantum computers advance towards demonstrating a universal fault-tolerant logical gate set, implementing scalable and low-latency real-time decoding will be crucial to avoid an exponential slowdown and maintain a fast logical clock rate. Here, we demonstrate low-latency feedback with a scalable FPGA decoder integrated into the control system of a superconducting quantum processor. We perform an 8-qubit stability experiment with up to 25 decoding rounds and a sub-microsecond mean decoding time per round, providing strong evidence that the backlog problem will be avoided when the decoder is operated as a streaming decoder on a superconducting hardware with the strictest speed requirements. We observe logical error suppression as the number of decoding rounds is increased. We also implement and time a fast-feedback experiment demonstrating a decoding response time of 9.6 μs for a total of 9 measurement rounds.
Correcting errors in real time is essential for reliable large-scale quantum computations. Realizing this high-level function requires a system capable of several low-level primitives, including single-qubit and two-qubit operations, midcircuit measurements of subsets of qubits, real-time processing of measurement outcomes, and the ability to condition subsequent gate operations on those measurements. In this work, we use a 10-qubit quantum charge-coupled device trapped-ion quantum computer to encode a single logical qubit using the [[7,1,3]] color code, first proposed by Steane [Phys. Rev. Lett. 77, 793 (1996)PRLTAO0031-900710.1103/PhysRevLett.77.793]. The logical qubit is initialized into the eigenstates of three mutually unbiased bases using an encoding circuit, and we measure an average logical state preparation and measurement (SPAM) error of 1.7(2)×10^{-3}, compared to the average physical SPAM error 2.4(4)×10^{-3} of our qubits. We then perform multiple syndrome measurements on the encoded qubit, using a real-time decoder to determine any necessary corrections that are done either as software updates to the Pauli frame or as physically applied gates. Moreover, these procedures are done repeatedly while maintaining coherence, demonstrating a dynamically protected logical qubit memory. Additionally, we demonstrate non-Clifford qubit operations by encoding a T[over ¯]|+⟩_{L} magic state with an error rate below the threshold required for magic state distillation. Finally, we present system-level simulations that allow us to identify key hardware upgrades that may enable the system to reach the pseudothreshold.