Bosonic qubits and the Gottesman-Kitaev-Preskill code

Short answer: The Gottesman-Kitaev-Preskill (GKP) code, proposed in 2001, encodes a qubit in the states of an oscillator rather than in a two-level system. Reviews say it was long considered impractical because the codewords are hard to prepare, but that advances in hardware and control have made it a frontrunner for hardware-efficient, fault-tolerant bosonic quantum technology. Reported experiments have reached the error-correction break-even point, and these are research results, not products.

What is the physical structure of the GKP code?

The GKP code was proposed in 2001 by Daniel Gottesman, Alexei Kitaev, and John Preskill as a method to encode a qubit in an oscillator. Its codewords are defined as coherent superpositions of periodically displaced squeezed vacuum states. A 2023 review says encoding quantum information into harmonic oscillators is considered a hardware-efficient approach to mitigating noise.

While early quantum error correction codes were designed for information stored in discrete variables, the GKP code applies the concept to information stored in quantum states characterized by continuous variables. Although the code is widely recognized for its promise in quantum computation, it also facilitates near-optimal quantum communication rates in bosonic channels. Furthermore, it offers the ability to safeguard arbitrary quantum states of oscillators, extending its utility beyond simple qubit protection.

Why was the GKP code initially considered impractical?

For a long time, the GKP code was considered impractical due to the significant challenge of merely preparing the codewords. The requirement to generate coherent superpositions of periodically displaced squeezed vacuum states posed substantial technical hurdles for early experimental setups.

The 2021 Perspective says developments in quantum hardware and control technology over the last two decades have made the GKP code a frontrunner in the race to build practical, fault-tolerant bosonic quantum technology.

What experimental progress has been achieved?

A 2020 review reports that bosonic quantum error correction has been demonstrated to reach the break-even point. This milestone means the lifetime of a logical qubit is enhanced to exceed that of any individual components composing the experimental system. The review calls superconducting quantum circuits and bosonic encodings in superconducting microwave modes appealing platforms for quantum error correction.

Beyond reaching the break-even point, universal gate sets and fault-tolerant operations on bosonic codes are also realized. The review says this pushes quantum information processing towards the quantum error correction era. Recent experimental progress specifically in superconducting circuit architectures has been emphasized in reviews of the field. Theoretical advancements have also occurred in multimode GKP qubit codes and oscillators-to-oscillators (O2O) codes, expanding the scope of the technology beyond single-mode implementations.

How does the GKP code compare to other bosonic codes?

Various codes have been proposed to encode a qubit into an oscillator, including cat codes, binomial codes, and GKP codes. The 2023 review says these codes are among the first to reach a break-even point for quantum error correction. While cat codes and binomial codes are also reviewed in the context of bosonic quantum error correction, the GKP code is distinguished by its specific structure of periodically displaced squeezed vacuum states.

The GKP code is noted for facilitating near-optimal quantum communication rates in bosonic channels, a capability that distinguishes it from codes focused solely on qubit protection. It also offers the ability to safeguard arbitrary quantum states of oscillators. Reviews of the field discuss the opportunities of bosonic codes in various quantum applications, with the GKP code highlighted for its theoretical advancements in multimode configurations and its role in hardware-efficient, fault-tolerant quantum error correction.

FAQ

What is a bosonic qubit?

A qubit encoded in a harmonic oscillator rather than in a two-level system. Proposed codes include cat codes, binomial codes and GKP codes.

What is the GKP code?

A 2001 proposal by Gottesman, Kitaev and Preskill. Its codewords are coherent superpositions of periodically displaced squeezed vacuum states.

Why was it considered impractical?

According to a 2021 PRX Quantum Perspective, because of the challenge of merely preparing the codewords.

What does break-even mean?

That the lifetime of a logical qubit is enhanced to exceed that of any individual component of the experimental system, as defined in a 2020 review.

Is this deployed technology?

No. The sources are reviews of laboratory research, mainly in superconducting circuits.