Related papers: Symmetric extendibility for qudits and tolerable e…
Quantum error correction (QEC) is a key concept in quantum computation as well as many areas of physics. There are fundamental tensions between continuous symmetries and QEC. One vital situation is unfolded by the Eastin--Knill theorem,…
Quantum error correction will be a necessary component towards realizing scalable quantum computers with physical qubits. Theoretically, it is possible to perform arbitrarily long computations if the error rate is below a threshold value.…
Quantum error correcting codes have a distance parameter, conveying the minimum number of single spin errors that could cause error correction to fail. However, the success thresholds of finite per-qubit error rate that have been proven for…
A semi-quantum key distribution (SQKD) protocol allows two users, one of whom is restricted in their quantum capabilities, to establish a shared secret key, secure against an all-powerful adversary. In this paper, we design a new SQKD…
In this short review, I draw attention to new developments in the theory of fault tolerance in quantum computation that may give concrete direction to future work in the development of superconducting qubit systems. The basics of quantum…
Quantum error correction and symmetry arise in many areas of physics, including many-body systems, metrology in the presence of noise, fault-tolerant computation, and holographic quantum gravity. Here we study the compatibility of these two…
Graph states are generalized from qubits to collections of $n$ qudits of arbitrary dimension $D$, and simple graphical methods are used to construct both additive and nonadditive quantum error correcting codes. Codes of distance 2…
We investigate the performance of a quantum error-correcting code when pushed beyond its intended capacity to protect information against errors, presenting formulae for the probability of failure when the errors affect more qudits than…
We make a detailed analysis of error mechanisms, gate fidelity, and scalability of proposals for quantum computation with neutral atoms in addressable (large lattice constant) optical lattices. We have identified possible limits to the size…
The quantum computing scheme described in Phys. Rev. Lett. 98, 190504 (2007), when viewed as a cluster state computation, features a 3-D cluster state, novel adjustable strength error correction capable of correcting general errors through…
Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited…
Variations of phase-matching measurement-device-independent quantum key distribution (PM-MDI QKD) protocols have been investigated before, but it was recently discovered that this type of protocol (under the name of twin-field QKD) can beat…
We present a theoretical framework for state-adaptive quantum error correction that bridges the gap between quantum computing and error correction paradigms. By incorporating knowledge of quantum states into the error correction process, we…
In this paper, we place bounds on when it is impossible to purify a noisy two-qubit state if all the gates used in the purification protocol are subject to adversarial local, independent, noise. It is found that the gate operations must be…
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…
It is pointed out that treatments of the error correcting code in current quantum key distribution protocols of the BB84 type are not correct under joint attack, and the general interpretation of the trace distance security criterion is…
Two types of errors can occur when discriminating pairs of quantum states. Asymmetric state discrimination involves minimizing the probability of one type of error, subject to a constraint on the other. We give explicit expressions bounding…
Quantum key distribution (QKD) allows for communication with security guaranteed by quantum theory. The main theoretical problem in QKD is to calculate the secret key rate for a given protocol. Analytical formulas are known for protocols…
Realizing the potential of quantum computing will require achieving sufficiently low logical error rates. Many applications call for error rates in the $10^{-15}$ regime, but state-of-the-art quantum platforms typically have physical error…
There are well known necessary and sufficient conditions for a quantum code to correct a set of errors. We study weaker conditions under which a quantum code may correct errors with probabilities that may be less than one. We work with…