Related papers: Avoiding coherent errors with rotated concatenated…
The performance of a given quantum error correction (QEC) code depends upon the noise model that is assumed. Independent Pauli noise, applied after each quantum operation, is a simplistic noise model that is easy to simulate and understand…
Mixed-state phases of matter under local decoherence have recently garnered significant attention due to the ubiquitous presence of noise in current quantum processors. One of the key issues is understanding how topological quantum memory…
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…
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…
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.…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
The scheme of entanglement-assisted quantum error-correcting (EAQEC) codes assumes that the ebits of the receiver are error-free. In practical situations, errors on these ebits are unavoidable, which diminishes the error-correcting ability…
Continuous-variable systems protected by bosonic quantum error-correcting codes have emerged as a promising platform for quantum information processing. To date, design of codewords has centered on optimizing the occupation of basis states…
We discuss a method to adapt the codeword stabilized (CWS) quantum code framework to the problem of finding asymmetric quantum codes. We focus on the corresponding Pauli error models for amplitude damping noise and phase damping noise. In…
We construct rotated logical states by applying rotation operators to stabilizer states, extending the logical basis and modifying stabilizer generators. Rotation operators affect the effective code distance $d_R$, which decays…
One of the main problems in quantum information systems is the presence of errors due to noise, and for this reason quantum error-correcting codes (QECCs) play a key role. While most of the known codes are designed for correcting generic…
We propose a method for universal fault-tolerant quantum computation using concatenated quantum error correcting codes. Namely, other than computational basis state preparation as required by the DiVincenzo criteria [1], our scheme requires…
We re-examine a non-Gaussian quantum error correction code designed to protect optical coherent-state qubits against errors due to an amplitude damping channel. We improve on a previous result [Phys. Rev. A 81, 062344 (2010)] by providing a…
In near-term quantum computations that do not employ error correction, noise can proliferate rapidly, corrupting the quantum state and making results unreliable. These errors originate from both decoherence and control imprecision. The…
We compare failure distributions of quantum error correction circuits for stochastic errors and coherent errors. We utilize a fully coherent simulation of a fault tolerant quantum error correcting circuit for a $d=3$ Steane and surface…
Current hardware for quantum computing suffers from high levels of noise, and so to achieve practical fault-tolerant quantum computing will require powerful and efficient methods to correct for errors in quantum circuits. Here, we explore…
Typical stabilizer codes aim to solve the general problem of fault-tolerance without regard for the structure of a specific system. By incorporating a broader representation-theoretic perspective, we provide a generalized framework that…
Stabilizer states are a central resource in quantum information processing, underpinning a wide range of applications. While they can be efficiently generated via Clifford circuits, the presence of coherent errors, such as small-angle…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…