Abstract
We present a 1D repetition code based on the so-called cat qubits as a viable approach toward hardware-efficient universal and fault-tolerant quantum computation. The cat qubits that are stabilized by a two-photon driven-dissipative process, exhibit a tunable noise bias where the effective bit-flip errors are exponentially suppressed with the average number of photons. We propose a realization of a set of gates on the cat qubits that preserve such a noise bias. Combining these base qubit operations, we build, at the level of the repetition cat qubit, a universal set of fully protected logical gates. This set includes single-qubit preparations and measurements, NOT, controlled-NOT, and controlled-controlled-NOT (Toffoli) gates. Remarkably, this construction avoids the costly magic state preparation, distillation, and injection. Finally, all required operations on the cat qubits could be performed with slight modifications of existing experimental setups.
Highlights
Quantum computers are expected to efficiently solve classically intractable problems
Quantum-errorcorrecting codes (QECCs) are designed [3,4] such that errors induced by the environment do not affect the quantum information
These codes operate by the “fight entanglement with entanglement” mantra: Natural errors arising in physical systems being typically local, the quantum information to be protected is encoded in nonlocal entangled states such that it becomes unlikely that errors can corrupt it, the most popular being the surface code [5,6,7]
Summary
Quantum computers are expected to efficiently solve classically intractable problems. Our approach is different: By employing a cat code as the base qubit, the noise structure is modified in such a way that quantum error correction becomes of similar complexity as classical error correction and can be performed using a simple repetition code This specific noise structure can be preserved for a set of fundamental operations which at the level of the repetition code lead to a universal set of protected logical gates. The infinite-dimensional Hilbert space of the harmonic oscillator that supports the cat qubit state can be exploited to perform various nontrivial gates (such as CNOT and Toffoli) while preserving the noise bias.
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