Related papers: Qubit-oscillator concatenated codes: decoding form…
To be useful, quantum computers will be required to successfully correct errors occurring at the hardware level. Bosonic codes provide a hardware-efficient option for error correction, but fault-tolerance further requires that the available…
Quantum error correction has recently been shown to benefit greatly from specific physical encodings of the code qubits. In particular, several researchers have considered the individual code qubits being encoded with the continuous…
In this work, the efficient quantum error-correction protocol against the general independent noise is constructed with the three-qubit codes. The rules of concatenation are summarized according to the error-correcting capability of the…
We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a…
We propose two schemes to obtain Gottesman-Kitaev-Preskill (GKP) error syndromes by means of linear optical operations, homodyne measurements and GKP ancillae. This includes showing that for a concatenation of GKP codes with a $[n,k,d]$…
(Abridged.) This thesis investigates scalable fault-tolerant quantum computation through the development of bosonic quantum codes, quantum LDPC codes, and decoding protocols that connect continuous-variable and discrete-variable error…
We review some of the recent efforts in devising and engineering bosonic qubits for superconducting devices, with emphasis on the Gottesman-Kitaev-Preskill (GKP) qubit. We present some new results on decoding repeated GKP error correction…
Quantum bits are more robust to noise when they are encoded non-locally. In such an encoding, errors affecting the underlying physical system can then be detected and corrected before they corrupt the encoded information. In 2001,…
Quantum error correction offers a promising path to suppress errors in quantum processors, but the resources required to protect logical operations from noise, especially non-Clifford operations, pose a substantial challenge to achieve…
Color codes are promising quantum error correction (QEC) codes because they have an advantage over surface codes in that all Clifford gates can be implemented transversally. However, thresholds of color codes under circuit-level noise are…
The Gottesman-Kitaev-Preskill (GKP) encoding of a qubit into a bosonic mode is a promising bosonic code for quantum computation due to its tolerance for noise and all-Gaussian gate set. We present a toolkit for phase-space description and…
The Gottesman-Kitaev-Preskill (GKP) code is a promising bosonic quantum error-correcting code, encoding logical qubits into a bosonic mode in such a way that many physically relevant noise types can be corrected effectively. A particularly…
It is known that continuous variable quantum information cannot be protected against naturally occurring noise using Gaussian states and operations only. Noh et al. (PRL 125:080503, 2020) proposed bosonic oscillator-to-oscillator codes…
We introduce and analyze a new type of decoding algorithm called General Color Clustering (GCC), based on renormalization group methods, to be used in qudit color codes. The performance of this decoder is analyzed under code capacity…
In quantum error-correcting code (QECC), many quantum operations and measurements are necessary to correct errors in logical qubits. In the stabilizer formalism, which is widely used in QECC, generators $G_i (i=1,2,..)$ consist of multiples…
Quantum repeaters constitute a promising platform for enabling long distance quantum communication and may ultimately serve as the backbone of a secure quantum internet, a scalable quantum network, or a distributed quantum computer. An…
There are well known necessary and sufficient conditions for a quantum code to correct a set of errors. We study weaker conditions under which a quantum code may correct errors with probabilities that may be less than one. We work with…
Recent advancements in multi-mode Gottesman-Kitaev-Preskill (GKP) codes have shown great promise in enhancing the protection of both discrete and analog quantum information. This broadened range of protection brings opportunities beyond…
We investigate a novel class of quantum error correcting codes to correct errors on both qubits and higher-state quantum systems represented as qudits. These codes arise from an original graph-theoretic representation of sets of quantum…
The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. This dissertation makes a threefold contribution to the mathematical theory of quantum error-correcting codes.…