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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…
``Leakage'' errors are particularly serious errors which couple states within a code subspace to states outside of that subspace thus destroying the error protection benefit afforded by an encoded state. We generalize an earlier method for…
The realization of quantum error correction is an essential ingredient for reaching the full potential of fault-tolerant universal quantum computation. Using a range of different schemes, logical qubits can be redundantly encoded in a set…
Quantum Error Correction will be necessary for preserving coherent states against noise and other unwanted interactions in quantum computation and communication. We develop a general theory of quantum error correction based on encoding…
Quantum phase transitions are sudden changes in the ground-state wavefunction of a many-body system that can occur as a control parameter such as a concentration or a field strength is varied. They are driven purely by the competition…
We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances…
Fault-tolerant quantum computers rely on Quantum Error-Correcting Codes (QECCs) to protect information from noise. However, no single error-correcting code supports a fully transversal and therefore fault-tolerant implementation of all…
Intrinsic decoherence in the thermodynamic limit is shown for a large class of many-body quantum systems in the unitary evolution in NMR and cavity QED. The effect largely depends on the inability of the system to recover the phases.…
In this paper we provide a basic introduction of the core ideas and theories surrounding fault-tolerant quantum computation. These concepts underly the theoretical framework of large-scale quantum computation and communications and are the…
The known quantum error-correcting codes are typically built on approximative open-quantum-system models such as Born--Markov master equations. However, it is an open question how such codes perform in actual physical systems that, to some…
The essential insight of quantum error correction was that quantum information can be protected by suitably encoding this quantum information across multiple independently erred quantum systems. Recently it was realized that, since the most…
A quantum error-correcting code with a nonzero error threshold undergoes a mixed-state phase transition when the error rate reaches that threshold. We explore this phase transition for Haar-random quantum codes, in which the logical…
We investigate dynamical quantum phase transitions in disordered quantum many-body models that can support many-body localized phases. Employing $l$-bits formalism, we lay out the conditions for which singularities indicative of the…
We analyze the decoherence induced on a single qubit by the interaction with a two-level boson system with critical internal dynamics. We explore how the decoherence process is affected by the presence of quantum phase transitions in the…
We study the protection of information in nearly critical topological quantum codes, constructed by perturbing topological stabilizer codes towards continuous quantum phase transitions. Our focus is on the transverse-field toric code…
The problem of initializing phase in a quantum computing system is considered. The initialization of phases is a problem when the system is initially present in an entangled state and also in the application of the quantum gate…
Decoherence of quantum states is a major hurdle towards scalable and reliable quantum computing. Lower decoherence (i.e., higher fidelity) can alleviate the error correction overhead and obviate the need for energy-intensive noise reduction…
The accumulation of quantum phase in response to a signal is the central mechanism of quantum sensing, as such, loss of phase information presents a fundamental limitation. For this reason approaches to extend quantum coherence in the…
We investigate the diagonal entropy(DE) of the ground state for quantum many-body systems, including the XY model and the Ising model with next nearest neighbour interactions. We focus on the DE of a subsystem of L continuous spins. We show…
A scheme is presented for protecting one-qubit quantum information against decoherence due to a general environment and local exchange interactions. The scheme operates essentially by distributing information over two pairs of qubits and…