![]() ![]() Both types of code can tolerate errors due to loss and gain of energy quanta, enabling QEC to be performed in a hardware-efficient way. However, in these experiments, the lifetime of the logical qubit still needs to be greatly extended to reach that of the best available physical component, which is regarded as the break-even point for judging whether or not a QEC code can benefit quantum information storage and processing.Īn alternative QEC encoding scheme is to use the large space of an oscillator, which can be used to encode either a continuous-variable or a discrete-variable qubit 28, 29, 30, 31, 32. The past two decades have witnessed remarkable advances in experimental demonstrations of this kind of QEC code in different systems, including nuclear spins 5, 6, nitrogen-vacancy centres in diamond 10, 20, trapped ions 7, 11, 21, 22, 23, photonic qubits 24, silicon spin qubits 25 and superconducting circuits 12, 13, 14, 15, 16, 26, 27. ![]() In conventional QEC schemes 1, 9, the code words of a logical qubit are formed by two highly symmetric entangled states of several physical qubits encoded with some discrete variables. The errors caused by decoherence can be corrected by repetitive application of a quantum error correction (QEC) procedure, whereby the logical qubit is encoded in a high-dimensional Hilbert space, such that different errors project the system into different orthogonal subspaces and thus can be unambiguously identified and corrected without disturbing the stored quantum information. One of the main obstacles for building a quantum computer is environmentally induced decoherence, which destroys the quantum information stored in the qubits. Our work illustrates the potential of hardware-efficient discrete-variable encodings for fault-tolerant quantum computation 19. By applying a pulse featuring a tailored frequency comb to the auxiliary qubit, we can repetitively extract the error syndrome with high fidelity and perform error correction with feedback control accordingly, thereby exceeding the break-even point by about 16% lifetime enhancement. Here we demonstrate a QEC procedure in a circuit quantum electrodynamics architecture 18, where the logical qubit is binomially encoded in photon-number states of a microwave cavity 8, dispersively coupled to an auxiliary superconducting qubit. However, extending the lifetimes of thus-encoded logical qubits beyond the best available physical qubit still remains elusive, which represents a break-even point for judging the practical usefulness of QEC. Over the past decade, repetitive QEC has been demonstrated with various discrete-variable-encoded scenarios 9, 10, 11, 12, 13, 14, 15, 16, 17. In most QEC codes 2, 3, 4, 5, 6, 7, 8, a logical qubit is encoded in some discrete variables, for example photon numbers, so that the encoded quantum information can be unambiguously extracted after processing. Quantum error correction (QEC) aims to protect logical qubits from noises by using the redundancy of a large Hilbert space, which allows errors to be detected and corrected in real time 1.
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