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The problem of finding quantum error-correcting codes is transformed into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are…
Probabilistic quantum error correction is an error-correcting procedure which uses postselection to determine if the encoded information was successfully restored. In this work, we deeply analyze probabilistic version of the…
We show that complementary state-specific reconstruction of logical (bulk) operators is equivalent to the existence of a quantum minimal surface prescription for physical (boundary) entropies. This significantly generalizes both sides of an…
Recently, operator quantum error-correcting codes have been proposed to unify and generalize decoherence free subspaces, noiseless subsystems, and quantum error-correcting codes. This note introduces a natural construction of such codes in…
We demonstrate that a classical emulation of quantum gate operations, here represented by an actual analog electronic device, can be modeled accurately as a quantum operation in terms of a universal set of Pauli operators. This observation…
Modelling quantum devices is to find a model according to quantum theory that can explain the result of experiments in a quantum device. We find that usually we cannot correctly identify the model describing the actual physics of the device…
Quantum error correction codes play a central role in the realisation of fault-tolerant quantum computing. Chamon model is a 3D generalization of the toric code. The error correction computation on this model has not been explored so far.…
Topological quantum error correction codes are known to be able to tolerate arbitrary local errors given sufficient qubits. This includes correlated errors involving many local qubits. In this work, we quantify this level of tolerance,…
The so-called "threshold" theorem says that, once the error rate per qubit per gate is below a certain value, indefinitely long quantum computation becomes feasible, even if all of the qubits involved are subject to relaxation processes,…
In quantum tomography, a quantum state or process is estimated from the results of measurements on many identically prepared systems. Tomography can never identify the state or process exactly. Any point estimate is necessarily "wrong" --…
Quantum cellular automata are alternative quantum-computing paradigms to quantum Turing machines and quantum circuits. Their working mechanisms are inherently automated, therefore measurement free, and they act in a translation invariant…
Quantum bits have technological imperfections. Additionally, the capacity of a component that can be implemented feasibly is limited. Therefore, distributed quantum computation is required to scale up quantum computers. This dissertation…
The operation of a quantum computer is considered as a general quantum operation on a mixed state on many qubits followed by a measurement. The general quantum operation is further represented as a Feynman-Vernon double path integral over…
Topological quantum computing has recently proven itself to be a very powerful model when considering large- scale, fully error corrected quantum architectures. In addition to its robust nature under hardware errors, it is a software driven…
We derive necessary and sufficient conditions for the approximate correctability of a quantum code, generalizing the Knill-Laflamme conditions for exact error correction. Our measure of success of the recovery operation is the worst-case…
Quantum devices can process data in a fundamentally different way than classical computers. To leverage this potential, many algorithms require the aid of a quantum Random Access Memory (QRAM), i.e. a module capable of efficiently loading…
Connecting multiple smaller qubit modules by generating high-fidelity entangled states is a promising path for scaling quantum computing hardware. The performance of such a modular quantum computer is highly dependent on the quality and…
We describe a qubit encoded in continuous quantum variables of an rf superconducting quantum interference device. Since the number of accessible states in the system is infinite, we may protect its two-dimensional subspace from small errors…
The purpose of this little survey is to give a simple description of the main approaches to quantum error correction and quantum fault-tolerance. Our goal is to convey the necessary intuitions both for the problems and their solutions in…
Active quantum error correction is a central ingredient to achieve robust quantum processors. In this paper we investigate the potential of quantum machine learning for quantum error correction in a quantum memory. Specifically, we…