Related papers: Biased Gottesman-Kitaev-Preskill repetition code
The code-capacity threshold of a scalable quantum error correcting stabilizer code can be expressed as a thermodynamic phase transition of a corresponding random-bond Ising model. Here we study the XY and XZZX surface codes under…
Designs for quantum error correction depend strongly on the connectivity of the qubits. For solid state qubits, the most straightforward approach is to have connectivity constrained to a planar graph. Practical considerations may also…
Noise in quantum computing is countered with quantum error correction. Achieving optimal performance will require tailoring codes and decoding algorithms to account for features of realistic noise, such as the common situation where the…
We extend the controlled displacement interaction between a qubit and a harmonic oscillator to the multi-qubit (qudit) case. We define discrete quadratures of the qudit and show how the qudit state can be displaced in these quadratures…
Matching codes are stabilizer codes based on Kitaev's honeycomb lattice model. The hexagonal form of these codes are particularly well-suited to the heavy-hexagon device layouts currently pursued in the hardware of IBM Quantum. Here we show…
The quantum error-correcting code in the continuous-variable (CV) system attracts much attention due to its flexibility and high resistance against specific noise. However, the theory of fault tolerance in CV systems is premature and lacks…
Quantum technologies, encompassing communication, computation, and metrology, rely on the generation and control of non-Gaussian states of light. These states enable secure quantum communication, fault-tolerant quantum computation, and…
A crucial insight for practical quantum error correction is that different types of errors, such as single-qubit Pauli operators, typically occur with different probabilities. Finding an optimal quantum code under such biased noise is a…
Bosonic quantum error correction enables hardware-efficient protection of quantum information by encoding logical qubits in harmonic oscillators. Bosonic grid states, such as Gottesman-Kitaev-Preskill (GKP) states, are particularly…
The minimum-weight perfect matching (MWPM) decoder is a standard decoding strategy for surface codes, but its performance degrades considerably under biased noise. In this paper, a modified surface code, termed the XYZ planar code, is…
Practical utilization of Gottesman-Kitaev-Preskill (GKP) qubits requires not only the preparation of logical basis states, but also the ability to prepare and evaluate arbitrary logical qubit superpositions. Currently, this is typically…
Noise-biased qubits are a promising route toward significantly reducing the hardware overhead associated with quantum error correction. The squeezed cat code, a non-local encoding in phase space based on squeezed coherent states, is an…
We introduce generalized spatially coupled parallel concatenated codes (GSC-PCCs), a class of spatially coupled turbo-like codes obtained by coupling parallel concatenated codes (PCCs) with a fraction of information bits repeated before the…
Quantum repeaters are essential ingredients for quantum networks that link distant quantum modules such as quantum computers and sensors. Motivated by distributed quantum computing and communication, quantum repeaters that relay…
Bosonic quantum error-correcting codes offer a viable direction towards reducing the hardware overhead required for fault-tolerant quantum information processing. A broad class of bosonic codes, namely rotation-symmetric codes, can be…
We consider a topological stabilizer code on a honeycomb grid, the "XYZ$^2$" code. The code is inspired by the Kitaev honeycomb model and is a simple realization of a "matching code" discussed by Wootton [J. Phys. A: Math. Theor. 48, 215302…
Local update recovery seeks to maintain quantum information by applying local correction maps alternating with and compensating for the action of noise. Motivated by recent constructions based on quantum LDPC codes in the finite-dimensional…
Color code is a promising topological code for fault-tolerant quantum computing. Insufficient research on the color code has delayed its practical application. In this work, we address several key issues to facilitate practical…
Repetition code forms a fundamental basis for quantum error correction experiments. To date, it stands as the sole code that has achieved large distances and extremely low error rates. Its applications span the spectrum of evaluating…
With the Gottesman-Kitaev-Preskill (GKP) encoding, Clifford gates and error correction can be carried out using simple Gaussian operations. Still, non-Clifford gates, required for universality, require non-Gaussian elements. In their…