The storage and processing of quantum information are susceptible to external noise, resulting in computational errors. A powerful method to suppress these effects is quantum error correction. Typically, quantum error correction is executed in discrete rounds, using entangling gates and projective measurement on ancillary qubits to complete each round of error correction. Here we use direct parity measurements to implement a continuous quantum bit-flip correction code in a resource-efficient manner, eliminating entangling gates, ancillary qubits, and their associated errors. An FPGA controller actively corrects errors as they are detected, achieving an average bit-flip detection efficiency of up to 91%. Furthermore, the protocol increases the relaxation time of the protected logical qubit by a factor of 2.7 over the relaxation times of the bare comprising qubits. Our results showcase resource-efficient stabilizer measurements in a multi-qubit architecture and demonstrate how continuous error correction codes can address challenges in realizing a fault-tolerant system.
The storage and processing of quantum information are susceptible to external noise, resulting in computational errors. A powerful method to suppress these effects is quantum error correction. Typically, quantum error correction is executed in discrete rounds, using entangling gates and projective measurement on ancillary qubits to complete each round of error correction. Here we use direct parity measurements to implement a continuous quantum bit-flip correction code in a resource-efficient manner, eliminating entangling gates, ancillary qubits, and their associated errors. An FPGA controller actively corrects errors as they are detected, achieving an average bit-flip detection efficiency of up to 91%. Furthermore, the protocol increases the relaxation time of the protected logical qubit by a factor of 2.7 over the relaxation times of the bare comprising qubits. Our results showcase resource-efficient stabilizer measurements in a multi-qubit architecture and demonstrate how continuous error correction codes can address challenges in realizing a fault-tolerant system.
Building fault-tolerant quantum computers with large numbers of logical qubits requires both scalable hardware architectures and error-correcting codes that make efficient use of physical qubits. Photonic interconnects address both of these challenges by allowing the physical qubits to be distributed across multiple processors while providing the non-local connectivity necessary to implement resource-efficient codes such as high-rate quantum low-density parity-check (qLDPC) codes. A key requirement for realising this architecture is the ability to perform stabiliser measurements between remote processors, which has not previously been demonstrated experimentally. Here we report the first experimental demonstration of distributed quantum error detection and correction. We generate entanglement between network qubits in two separate trapped-ion processors and use it to perform remote syndrome measurements on data qubits. We first realise a distributed [[2, 1, 1]] repetition code, detecting phase-flip errors on a logical qubit encoded across the two modules in real time and suppressing logical errors. We then combine these mid-circuit syndrome measurements with real-time feedforward to actively correct arbitrary single-qubit Pauli errors on a distributed Bell state. These results provide an experimental foundation for quantum error correction (QEC) across modular quantum architectures.
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 protects fragile quantum information by encoding it into a larger quantum system. These extra degrees of freedom enable the detection and correction of errors, but also increase the operational complexity of the encoded logical qubit. Fault-tolerant circuits contain the spread of errors while operating the logical qubit, and are essential for realizing error suppression in practice. While fault-tolerant design works in principle, it has not previously been demonstrated in an error-corrected physical system with native noise characteristics. In this work, we experimentally demonstrate fault-tolerant preparation, measurement, rotation, and stabilizer measurement of a Bacon-Shor logical qubit using 13 trapped ion qubits. When we compare these fault-tolerant protocols to non-fault tolerant protocols, we see significant reductions in the error rates of the logical primitives in the presence of noise. The result of fault-tolerant design is an average state preparation and measurement error of 0.6% and a Clifford gate error of 0.3% after error correction. Additionally, we prepare magic states with fidelities exceeding the distillation threshold, demonstrating all of the key single-qubit ingredients required for universal fault-tolerant operation. These results demonstrate that fault-tolerant circuits enable highly accurate logical primitives in current quantum systems. With improved two-qubit gates and the use of intermediate measurements, a stabilized logical qubit can be achieved.
To solve problems of practical importance1,2, quantum computers probably need to incorporate quantum error correction, in which a logical qubit is redundantly encoded in many noisy physical qubits3–5. The large physical-qubit overhead associated with error correction motivates the search for more hardware-efficient approaches6–18. Here, using a superconducting quantum circuit19, we realize a logical qubit memory formed from the concatenation of encoded bosonic cat qubits with an outer repetition code of distance d = 5 (ref. 10). A stabilizing circuit passively protects cat qubits against bit flips20–24. The repetition code, using ancilla transmons for syndrome measurement, corrects cat qubit phase flips. We study the performance and scaling of the logical qubit memory, finding that the phase-flip correcting repetition code operates below the threshold. The logical bit-flip error is suppressed with increasing cat qubit mean photon number, enabled by our realization of a cat-transmon noise-biased CX gate. The minimum measured logical error per cycle is on average 1.75(2)% for the distance-3 code sections, and 1.65(3)% for the distance-5 code. Despite the increased number of fault locations of the distance-5 code, the high degree of noise bias preserved during error correction enables comparable performance. These results, where the intrinsic error suppression of the bosonic encodings enables us to use a hardware-efficient outer error-correcting code, indicate that concatenated bosonic codes can be a compelling model for reaching fault-tolerant quantum computation. Bosonic qubits can be engineered to feature intrinsic protection against certain kinds of errors, which makes quantum error correction across many bosonic qubits possible with less overhead.
Abstract To build a universal quantum computer from fragile physical qubits, effective implementation of quantum error correction (QEC)1 is an essential requirement and a central challenge. Existing demonstrations of QEC are based on an active schedule of error-syndrome measurements and adaptive recovery operations2, 3, 4, 5, 6, 7 that are hardware intensive and prone to introducing and propagating errors. In principle, QEC can be realized autonomously and continuously by tailoring dissipation within the quantum system1, 8, 9, 10, 11, 12, 13, 14, but so far it has remained challenging to achieve the specific form of dissipation required to counter the most prominent errors in a physical platform. Here we encode a logical qubit in Schrödinger cat-like multiphoton states15 of a superconducting cavity, and demonstrate a corrective dissipation process that stabilizes an error-syndrome operator: the photon number parity. Implemented with continuous-wave control fields only, this passive protocol protects the quantum information by autonomously correcting single-photon-loss errors and boosts the coherence time of the bosonic qubit by over a factor of two. Notably, QEC is realized in a modest hardware setup with neither high-fidelity readout nor fast digital feedback, in contrast to the technological sophistication required for prior QEC demonstrations. Compatible with additional phase-stabilization and fault-tolerant techniques16, 17, 18, our experiment suggests quantum dissipation engineering as a resource-efficient alternative or supplement to active QEC in future quantum computing architectures.
Quantum computation holds the promise of solving certain complex problems exponentially faster than classical computers. However, the high prevalent noise in current quantum devices impedes the accurate execution of even basic algorithms. This can be remedied by protecting quantum information with a quantum error-correcting code, where the logical information of an algorithmic qubit is spread across multiple physical qubits. Individual quantum errors are then located and corrected by the fault-tolerant measurement of multi-qubit stabilizer operators (parity checks). Unfortunately, error correction and fault tolerance both impose large demands on the qubit overhead: hundreds to thousands of physical qubits per logical qubit.
We reduce the spacetime cost of fault tolerance by redesigning key building blocks of an error-corrected quantum computer. First, we develop a combinatorial proof with flag fault tolerance that exponentially reduces the extra qubits needed to measure a stabilizer of any size, while tolerating one fault. We leverage these proofs to then design state preparation circuits for the Steane and Golay codes with 100% yield. Next, we improve error correction on a planar layout by showing that a distance-four code encoding six logical qubits protects information as well as the distance-five surface code, using one-tenth as many physical qubits. Finally, we optimize the time overhead of logical gates in surface code quantum computers by protecting measurement results with a classical code, cutting computation time by a factor of two to six. Our hardware-agnostic optimizations of fault tolerance overheads thus suggest new routes to advance the timeline of error-free quantum computing.