Realizing Repeated Quantum Error Correction in a Distance-Three Surface Code

Abstract

Quantum computers hold the promise of solving computational problems which are intractable using conventional methods [1]. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited control accuracy [2]. Here, we demonstrate quantum error correction using the surface code, which is known for its exceptionally high tolerance to errors [3][4][5][6]. Using 17 physical qubits in a superconducting circuit we encode quantum information in a distance-three logical qubit building up on recent distance-two error detection experiments [7][8][9]. In an error correction cycle taking only 1.1 µs, we demonstrate the preservation of four cardinal states of the logical qubit. Repeatedly executing the cycle, we measure and decode both bit-and phase-flip error syndromes using a minimum-weight perfect-matching algorithm in an error-modelfree approach and apply corrections in postprocessing. We find a low error probability of 3 % per cycle when rejecting experimental runs in which leakage is detected. The measured characteristics of our device agree well with a numerical model. Our demonstration of repeated, fast and highperformance quantum error correction cycles, together with recent advances in ion traps [10], support our understanding that fault-tolerant quantum computation will be practically realizable.

Realization of an Error-Correcting Surface Code with Superconducting Qubits

“…Note added. Recently, we became aware of a similar work by Sebastian et al [35], which was carried out independently.…”

Scalable High-Performance Fluxonium Quantum Processor

“…Quantum computation and quantum information processing has opened a new frontier in science and technology, with recent advances validating our understanding of the quantum world and revealing the potential for novel applications [1][2][3][4]. Among various platforms, superconducting qubits has emerged as a promising candidate for the implementation of fault-tolerant universal quantum computing [5], with the power of quantum information processing [6,7] and novel quantum error correction schemes [8][9][10][11][12][13][14][15][16][17] having been demonstrated. In addition, quantum simulation [18][19][20][21][22][23][24] and optimization algorithms [25,26] have been implemented using noisy intermediate scale quantum (NISQ) devices [27,28].…”

“…Besides decoherence of physical qubits, crosstalk [40,41], frequency crowding [42,43], and leakage out of the computational subspace [44,45] are also the central problems to overcome upon scaling up. For example, the most popular QEC code for planar architecture, the surface code [29,[46][47][48], has an accurate threshold of approximately 1% and only requires nearest neighbor interactions, yet only small-distance codes have been recently explored in superconducting-circuit architectures based on transmon devices [13][14][15][16][17].…”

Quantum Error Correction with Quantum Autoencoders

“…While performing in-sequence measurements and real-time feedback is experimentally challenging, it has been achieved in various hardware platforms and application contexts [14][15][16][17]. Repeated cycles of quantum error detection and correction are currently studied extensively with superconducting qubits [9,[18][19][20][21]. Experimental demonstrations of QEC that include in-sequence measurements and realtime feedback have been achieved in nitrogen-vacancy centers [13,22], superconducting qubits [23,24], trappedion platforms [12,25] and bosonic qubits [26,27].…”