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arXiv:cond-mat/0609441

Protected qubit based on a superconducting current mirror

Alexei Kitaev

Published Sep 19, 2006• 20 citations
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Abstract

We propose a qubit implementation based on exciton condensation in capacitively coupled Josephson junction chains. The qubit is protected in the sense that all unwanted terms in its effective Hamiltonian are exponentially suppressed as the chain length increases. We also describe an implementation of a universal set of quantum gates. Most gates also offer exponential error suppression. The only gate that is not intrinsically fault-tolerant needs to be realized with about 50% precision, provided the other gates are exact.

DOI
10.48550/arxiv.cond-mat/0609441

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We propose a qubit implementation based on exciton condensation in capacitively coupled Josephson junction chains. The qubit is protected in the sense that all unwanted terms in its effective Hamiltonian are exponentially suppressed as the chain length increases. We also describe an implementation of a universal set of quantum gates. Most gates also offer exponential error suppression. The only gate that is not intrinsically fault-tolerant needs to be realized with about 50% precision, provided the other gates are exact.
We propose a protected qubit which is `dual' to a suggestion of a superconducting current mirror qubit [A. Kitaev, arXiv:0609441 (2006)]. Our construction can be regarded as the magnetic analogue of Kitaev's proposal: it inherits the intrinsic fault-tolerance of the current mirror qubit, but may perform better than it in the laboratory, since magnetic noise is generally less of a problem than electric noise. We adapt the scheme for universal fault-tolerant quantum computation proposed by Kitaev to our construction.
We analyze the accuracy of quantum phase gates acting on ``0-$\ensuremath{\pi}$ qubits'' in superconducting circuits, where the gates are protected against thermal and Hamiltonian noise by continuous-variable quantum error-correcting codes. The gates are executed by turning on and off a tunable Josephson coupling between an LCLCLC oscillator and a qubit or pair of qubits; assuming perfect qubits, we show that the gate errors are exponentially small when the oscillator's impedance L/C\sqrt{L/C}L/C​ is large compared to $\ensuremath{\hbar}/4{e}^{2}\ensuremath{\approx}1\phantom{\rule{4pt}{0ex}}\mathrm{k}\ensuremath{\Omega}$. The protected gates are not computationally universal by themselves, but a scheme for universal fault-tolerant quantum computation can be constructed by combining them with unprotected noisy operations. We validate our analytic arguments with numerical simulations.
Abstract A quantum processor might execute certain computational tasks exponentially faster than a classical processor. Here, using superconducting quantum circuits we design a powerful universal quantum processor with the structure of symmetric all-to-all capacitive connection. We present the Hamiltonian and use it to demonstrate a full set of qubit operations needed in the programmable universal quantum computations. With the device the unwanted crosstalk and ZZ -type couplings between qubits can be effectively suppressed by tuning gate voltages, and the design allows efficient and high-quality couplings of qubits. Within available technology, the scheme may enable a practical programmable universal quantum computer.
Protected superconducting qubits such as the 000-πππ qubit promise to substantially suppress error rates, facilitating fault-tolerant quantum computing with fewer qubits. Measuring these qubits is challenging due to their protected nature, and thus far no concrete proposal exists for how to measure them without breaking their protection. Here we show how to perform protected measurements of the 000-πππ qubit in two orthogonal bases. The protection of these measurements is facilitated by their quantum non-demolition nature, allowing faults on ancillary measurement qubits to be tolerated. As experimental progress pushes protected qubits further into the low error-rate regime, our techniques will be crucial for fault-tolerant universal control.