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The remarkable discovery of Quantum Error Correction (QEC), which can overcome the errors experienced by a bit of quantum information (qubit), was a critical advance that gives hope for eventually realizing practical quantum computers. In principle, a system that implements QEC can actually pass a break-even point and preserve quantum information for longer than the lifetime of its constituent parts. Reaching the break-even point, however, has thus far remained an outstanding and challenging goal. Several previous works have demonstrated elements of QEC in NMR, ions, nitrogen vacancy (NV) centers, photons, and superconducting transmons. However, these works primarily illustrate the signatures or scaling properties of QEC codes rather than test the capacity of the system to extend the lifetime of quantum information over time. Here we demonstrate a QEC system that reaches the break-even point by suppressing the natural errors due to energy loss for a qubit logically encoded in superpositions of coherent states, or cat states of a superconducting resonator. Moreover, the experiment implements a full QEC protocol by using real-time feedback to encode, monitor naturally occurring errors, decode, and correct. As measured by full process tomography, the enhanced lifetime of the encoded information is 320 microseconds without any post-selection. This is 20 times greater than that of the systems transmon, over twice as long as an uncorrected logical encoding, and 10% longer than the highest quality element of the system (the resonators 0, 1 Fock states). Our results illustrate the power of novel, hardware efficient qubit encodings over traditional QEC schemes. Furthermore, they advance the field of experimental error correction from confirming the basic concepts to exploring the metrics that drive system performance and the challenges in implementing a fault-tolerant system.
The typical model for measurement noise in quantum error correction is to randomly flip the binary measurement outcome. In experiments, measurements yield much richer information - e.g., continuous current values, discrete photon counts - which is th
Quantum error correction (QEC) is one of the central concepts in quantum information science and also has wide applications in fundamental physics. The capacity theorems provide solid foundations of QEC. We here provide a general and highly applicabl
To implement fault-tolerant quantum computation with continuous variables, the Gottesman--Kitaev--Preskill (GKP) qubit has been recognized as an important technological element. We have proposed a method to reduce the required squeezing level to real
Quantum operations provide a general description of the state changes allowed by quantum mechanics. The reversal of quantum operations is important for quantum error-correcting codes, teleportation, and reversing quantum measurements. We derive infor
Quantum error correction (QEC) is an essential concept for any quantum information processing device. Typically, QEC is designed with minimal assumptions about the noise process; this generic assumption exacts a high cost in efficiency and performanc