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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…

The Gottesman-Kitaev-Preskill (GKP) quantum error correcting code attracts much attention in continuous variable (CV) quantum computation and CV quantum communication due to the simplicity of error correcting routines and the high tolerance…

Characterization of noise of a quantum harmonic oscillator is important for many experimental platforms. We experimentally demonstrate motional spin-locking spectroscopy, a method that allows us to directly measure the motional noise…

We consider the problem of a generic stabilizer Hamiltonian under local, incoherent Pauli errors. Using two different approaches -- (i) Haah's polynomial formalism arXiv:1204.1063 and (ii) the homological perspective on CSS codes -- we…

Quantum error correction is capable of digitizing quantum noise and increasing the robustness of qubits. Typically, error correction is designed with the target of eliminating all errors - making an error so unlikely it can be assumed that…

Quantum metrology has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on measurement precision, called the Heisenberg…

Quantum error correction codes in continuous variables (also called CV codes, or single-mode bosonic codes) have recently been identified to be a technologically viable option for building fault-tolerant quantum computers. The best-known…

To avoid prohibitive overheads in performing fault-tolerant quantum computation, the decoding problem needs to be solved accurately and at speeds sufficient for fast feedback. Existing decoding systems fail to satisfy both of these…

The Gottesman-Kitaev-Preskill (GKP) quantum error-correcting code has emerged as a key technique in achieving fault-tolerant quantum computation using photonic systems. Whereas [Baragiola et al., Phys. Rev. Lett. 123, 200502 (2019)] showed…

Measurement correlations in quantum systems can exhibit non-local behavior, a fundamental aspect of quantum mechanics with applications such as device-independent quantum information processing. However, the explicit construction of local…

We show that quantum feedback control can be used as a quantum error correction process for errors induced by weak continuous measurement. In particular, when the error model is restricted to one, perfectly measured, error channel per…

We revisit the error correction scheme of real-valued signals when the codeword is corrupted by gross errors on a fraction of entries and a small noise on all the entries. Combining the recent developments of approximate message passing and…

We introduce a class of bosonic quantum error-correcting codes, termed \emph{extended binomial codes}, which generalize the structure of one-mode binomial codes by incorporating ideas from high-rate qubit stabilizer codes. These codes are…

Quantum synchronization offers new possibilities for the exploration of collective dynamics in many-body systems. However, achieving synchronization in many-body quantum systems still faces numerous challenges. Here, we focus on the…

High-rate quantum error correcting codes mitigate the imposing scale of fault-tolerant quantum computers but require efficient generation of non-local, many-body entanglement. We provide a linear-optical architecture with these properties,…

We define a map from an arbitrary quantum circuit to a local Hamiltonian whose ground state encodes the quantum computation. All previous maps relied on the Feynman-Kitaev construction, which introduces an ancillary `clock register' to…

We introduce the hemicubic codes, a family of quantum codes obtained by associating qubits with the $p$-faces of the $n$-cube (for $n>p$) and stabilizer constraints with faces of dimension $(p\pm1)$. The quantum code obtained by identifying…

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.…

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…

Physical platforms such as trapped ions suffer from coherent noise where errors manifest as rotations about a particular axis and can accumulate over time. We investigate passive mitigation through decoherence free subspaces, requiring the…