Surface code quantum computing by lattice surgery. Fault-tolerant parity readout on a shuttling-based trapped-ion quantum computer. Fault-tolerant control of an error-corrected qubit. Fault-tolerant operation of a logical qubit in a diamond quantum processor. Benchmarking quantum computers: the five-qubit error correcting code. State preservation by repetitive error detection in a superconducting quantum circuit. Quantum error correction in a solid-state hybrid spin register. Experimental repetitive quantum error correction. Demonstration of sufficient control for two rounds of quantum error correction in a solid state ensemble quantum information processor. Quantum error correction for quantum memories. PhD thesis, California Institute of Technology (1997). Stabilizer Codes and Quantum Error Correction.
Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory. Quantum codes on a lattice with boundary. Realization of real-time fault-tolerant quantum error correction. Exponential suppression of bit or phase errors with cyclic error correction. Logical-qubit operations in an error-detecting surface code. Repeated quantum error detection in a surface code. Quantum measurements and gates by code deformation. Fault-tolerant quantum computation with high threshold in two dimensions. Fault-tolerant quantum computation by anyons. 37th Conference on Foundations of Computer Science 56 pp (IEEE, 1996). Quantum computing in the NISQ era and beyond. Our demonstration of repeated, fast and high-performance quantum error-correction cycles, together with recent advances in ion traps 10, support our understanding that fault-tolerant quantum computation will be practically realizable. The measured characteristics of our device agree well with a numerical model. We find a low logical error probability of 3% per cycle when rejecting experimental runs in which leakage is detected. Repeatedly executing the cycle, we measure and decode both bit-flip and phase-flip error syndromes using a minimum-weight perfect-matching algorithm in an error-model-free approach and apply corrections in post-processing. In an error-correction cycle taking only 1.1 μs, we demonstrate the preservation of four cardinal states of the logical qubit. Using 17 physical qubits in a superconducting circuit, we encode quantum information in a distance-three logical qubit, building on recent distance-two error-detection experiments 7, 8, 9. Here we demonstrate quantum error correction using the surface code, which is known for its exceptionally high tolerance to errors 3, 4, 5, 6. For fault-tolerant operation, quantum computers must correct errors occurring owing to unavoidable decoherence and limited control accuracy 2. Quantum computers hold the promise of solving computational problems that are intractable using conventional methods 1.
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