Abstract
The Gottesman-Kitaev-Preskill (GKP) code was proposed in 2001 by Daniel Gottesman, Alexei Kitaev, and John Preskill as a way to encode a qubit in an oscillator. The GKP codewords are coherent superpositions of periodically displaced squeezed vacuum states. Because of the challenge of merely preparing the codewords, the GKP code was for a long time considered to be impractical. However, the remarkable developments in quantum hardware and control technology in the last two decades has made the GKP code a frontrunner in the race to build practical, fault-tolerant bosonic quantum technology. In this Perspective, we provide an overview of the GKP code with emphasis on its implementation in the circuit-QED architecture and present our outlook on the challenges and opportunities for scaling it up for hardware-efficient, fault-tolerant quantum error correction.
Highlights
In 2001, Gottesman, Kitaev, and Preskill published a proposal to encode discrete quantum information in a continuous-variable quantum system, or in other words, “a qubit in an oscillator” [1]
We focus on circuit quantum electrodynamics (cQED) partly because the two authors are working in this field, and because we believe the flexibility and scalability of superconducting circuits make this a promising platform for the long-term goal of constructing a large-scale quantum computer based on bosonic encodings
Most theoretical work on GKP codes assume high-efficiency quadrature measurements [22,23,24,25], it is an open question whether the stringent demands required for scalable, fault-tolerant quantum computing can be met with this approach
Summary
In 2001, Gottesman, Kitaev, and Preskill published a proposal to encode discrete quantum information in a continuous-variable quantum system, or in other words, “a qubit in an oscillator” [1]. A milestone towards this goal of resource-efficient fault tolerance would be to demonstrate basic operations on the encoded GKP states, used to compose error-correction circuits, with fidelities that are comparable or better than the best physical qubits to date These operations include state preparation, entangling gates between two GKP-encoded modes, and measurement. We focus on cQED partly because the two authors are working in this field, and because we believe the flexibility and scalability of superconducting circuits make this a promising platform for the long-term goal of constructing a large-scale quantum computer based on bosonic encodings
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