2018/11/24 by H. W. L. Naus, Naus, H. W. L., R. Versluis +1
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Quantum-Dot Cellular Automata
paper · pdf · doi:10.48550/arxiv.1811.09832
openalex publication_date 2018/11/24 · openalex created_date 2022/08/01 · openalex updated_date 2026/07/28
Surface codes based on stabilizer circuits may pave the way for large scale\nfault-tolerant quantum computation. The surface code uses only single- and\ntwo-qubit gates and the error threshold falls close to 1% for a large range of\nerrors. Among the most promising candidates to physically implement such\ncircuits and codes are superconducting qubits coupled by resonators. We\ninvestigate a X and Z stabilizing circuit realized by two data qubits, two\nancillas and four resonators. The aim is to assess the consequences of unitary\nevolution of the interacting system, in particular for given stable initial\nstates, on fidelities and error syndrome probabilities. We model the system\nwith a Jaynes-Tavis-Cummings Hamiltonian and construct the low-excitation level\nevolution operators. The analysis is limited to two stable input states. We\nassume an ideal system with perfect gates, perfect measurements and no\ndecoherence or leakage. Our analysis shows that the capture probabilities after\nthe execution of a single stabilizer round are not equal to 100%, but vary\nbetween 99.2% and 99.99%. This is caused solely by the unitary evolution of the\ninteracting system. Two consecutive rounds of stabilizer measurements result in\ncapture probability values that depend heavily on the duration of the\nevolution, but vary between 0% and 99%. Also due to the unitary evolution, the\nfinal state of the data qubits leaves the the four-dimensional subspace, which\nresults in a state fidelity oscillating between 0 and 1. Even if an error on\nthe qubits is captured, the correcting operation on the qubit will not bring\nthe qubit to the original state. The errors induced by the Hamiltonian\nevolution of the system cannot be interpreted nor classified as commonly\nappearing errors. Additional or augmented quantum error correction may be\nrequired to compensate these effects of resonator-qubit interaction.\n