Bit-flip error correction with superconducting Xmon qubits

S. Kundu, Tanay Roy, Sumeru Hazra +4 more

Christopher D. Wilen, Sohair Abdullah, Noah Kurinsky +11 more

J. Kelly

For quantum computing to become viable, the inherently fallible nature of qubits must be overcome with quantum error correction (QEC). QEC requires coherent qubits, in a configuration compatible with a given QEC scheme, and quantum logic operations with sufficiently low error. In this thesis, we perform a series of targeted experiments to achieve these goals on a path toward realizing the surface code QEC scheme. We first develop the Xmon variant of the transmon qubit, a highly coherent, planar, and frequency tunable superconducting qubit. With coherence demonstrated, we build an array of five Xmon qubits in a configuration compatible with the surface code, and demonstrate quantum logic operations with sufficiently low error to employ the surface code. These logic gates are characterized with randomized benchmarking, a protocol for determining gate error. We find applications of randomized benchmarking beyond the intended use in gate optimization and decoherence characterization, in addition to exploring the fundamental assumptions of randomized benchmarking. Lastly, we build a nine qubit Xmon transmon array and demonstrate correction of environmental bit-flip errors in a precursor to the surface code.

Yao Lu, Eliot Kapit, Samuel Saskin +5 more

Farhan Feroz, A. B. M. Alim Al Islam

Quantum error correction comes from the marriage of quantum mechanics with the theory of error-correcting codes, which is still at the rudimentary stage tackling only 1 qubit to date. As, unlike the classical world, the extent of error in the quantum world is substantially high and unavoidable, scaling up the quantum error correction from 1 qubit to higher is of utmost significane. Therefore, to achive the scaling up, we present a general quantum error correction code that can be adapted for any number of quantum errors (bit-flip error to be specific in our case). This generalized code for bit-flip error correction realizes a delicate blending of using controlled-NOT gates with the notion of quantum entanglement. We augment the blending with majority voting in the final stage of the error correction. We demonstrate efficacy of our proposed error correction code through real experimentation in IBM Qiskit. Our experimental results up to 3-qubit bit-flip errors in the available Qiskit infrastructure confirm a total escape from errors using our proposed error correction code.

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