Related papers: Quantum error-correcting codes with a covariant en…
Quantum information is vulnerable to environmental noise and experimental imperfections, hindering the reliability of practical quantum information processors. Therefore, quantum error correction (QEC) that can protect quantum information…
Bosonic systems offer unique advantages for quantum error correction, as a single bosonic mode provides a large Hilbert space to redundantly encode quantum information. However, previous studies have been limited to exploiting symmetries in…
(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…
The Gottesman-Kitaev-Preskill (GKP) code is an exciting route to fault-tolerant quantum computing since Gaussian resources and GKP Pauli-eigenstate preparation are sufficient to achieve universal quantum computing. In this work, we provide…
Using transversal gates is a straightforward and efficient technique for fault-tolerant quantum computing. Since transversal gates alone cannot be computationally universal, they must be combined with other approaches such as magic state…
Fault-tolerant quantum computation is a technique that is necessary to build a scalable quantum computer from noisy physical building blocks. Key for the implementation of fault-tolerant computations is the ability to perform a universal…
Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review we consider the formalism of qubit…
Bosonic codes utilize the infinite-dimensional Hilbert space of harmonic oscillators to encode quantum information, offering a hardware-efficient approach to quantum error correction. Designing these codes requires precise geometric…
Covariant codes are quantum codes such that a symmetry transformation on the logical system could be realized by a symmetry transformation on the physical system, usually with limited capability of performing quantum error correction (an…
Bosonic quantum error correction has proven to be a successful approach for extending the coherence of quantum memories, but to execute deep quantum circuits, high-fidelity gates between encoded qubits are needed. To that end, we present a…
Quantum computing relies on quantum error correction for high-fidelity logical operations, but scaling to achieve near-term quantum utility is highly resource-intensive. High-rate quantum LDPC codes can reduce error correction overhead, yet…
Two-level quantum systems, qubits, are not the only basis for quantum computation. Advantages exist in using qudits, d-level quantum systems, as the basic carrier of quantum information. We show that color codes, a class of topological…
Continuous-variable cat codes are encodings into a single photonic or phononic mode that offer a promising avenue for hardware-efficient fault-tolerant quantum computation. Protecting information in a cat code requires measuring the mode's…
Fault-tolerant quantum computation (FTQC) schemes using large block codes that encode $k>1$ qubits in $n$ physical qubits can potentially reduce the resource overhead to a great extent because of their high encoding rate. However, the…
Transversal gates are the simplest form of fault-tolerant gates and are relatively easy to implement in practice. Yet designing codes that support useful transversal operations -- especially non-Clifford or addressable gates -- remains…
We present an approach to one-way quantum computation (1WQC) that can compensate for single-qubit errors, by encoding the logical information residing on physical qubits into five-qubit error-correcting code states. A logical two-qubit…
We introduce simple qubit-encodings and logic gates which eliminate the need for certain difficult single-qubit operations in superconducting phase-qubits, while preserving universality. The simplest encoding uses two physical qubits per…
This work classifies the set of diagonal gates that can implement a single or two-qubit transversal logical gate for qubit stabilizer codes. We show that individual physical gates on the underlying qubits that compose the code are…
An outstanding challenge for quantum information processing using bosonic systems is Gaussian errors such as excitation loss and added thermal noise errors. Thus, bosonic quantum error correction (QEC) is essential. Most bosonic QEC schemes…
We introduce a general framework for weak transversal gates -- probabilistic implementation of logical unitaries realized by local physical unitaries -- and propose a novel partially fault-tolerant quantum computing architecture that…