Related papers: Universal transversal gates
We re--investigate a plausible proposal for universal quantum gates in Kane's model, in which the authors assumed that electron spin is always downward under a background magnetic field and the value of controlling parameters is varied…
Quantum error correction and fault-tolerance make it possible to perform quantum computations in the presence of imprecision and imperfections of realistic devices. An important question is to find the noise rate at which errors can be…
Which gates are universal for quantum computation? Although it is well known that certain gates on two-level quantum systems (qubits), such as the controlled-not (CNOT), are universal when assisted by arbitrary one-qubit gates, it has only…
It is not a problem to complement a classical bit, i.e. to change the value of a bit, a 0 to a 1 and vice versa. This is accomplished by a NOT gate. Complementing a qubit in an unknown state, however, is another matter. We show that this…
We present a criterion that serves as the basis for a polynomial-time algorithm to decide whether a finite set of qudit gates exponentiated by some Hamiltonians is universal. Our approach formulates universality in Lie algebraic terms and…
One of the largest obstacles to building a quantum computer is gate error, where the physical evolution of the state of a qubit or group of qubits during a gate operation does not match the intended unitary transformation. Gate error stems…
As there is no quantum error correction code with universal set of transversal gates, several approaches have been proposed which, in combination of transversal gates, make universal fault-tolerant quantum computation possible. Magic state…
The surface code is currently the primary proposed method for performing quantum error correction. However, despite its many advantages, it has no native method to fault-tolerantly apply non-Clifford gates. Additional techniques are…
We introduce a generalisation of quantum error correction, relaxing the requirement that a code should identify and correct a set of physical errors on the Hilbert space of a quantum computer exactly, instead allowing recovery up to a…
Using error correcting codes and fault tolerant techniques, it is possible, at least in theory, to produce logical qubits with significantly lower error rates than the underlying physical qubits. Suppose, however, that the gates that act on…
Universal approximation theorems are the foundations of classical neural networks, providing theoretical guarantees that the latter are able to approximate maps of interest. Recent results have shown that this can also be achieved in a…
Transversal gates on quantum error correction codes have been a promising approach for fault-tolerant quantum computing, but are limited by the Eastin-Knill no-go theorem. Existing solutions like gate teleportation and magic state…
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…
Geometric quantum computation offers a potential route to fault-tolerant quantum information processing by exploiting the global nature of geometric phases. However, achieving controlled high-order suppression of multiple error sources…
We investigate the amount of noise required to turn a universal quantum gate set into one that can be efficiently modelled classically. This question is useful for providing upper bounds on fault tolerant thresholds, and for understanding…
What additional gates are needed for a set of classical universal gates to do universal quantum computation? We answer this question by proving that any single-qubit real gate suffices, except those that preserve the computational basis.…
We present a universal framework for quantum error-correcting codes, i.e., the one that applies for the most general quantum error-correcting codes. This framework is established on the group algebra, an algebraic notation for the nice…
Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates achievable with asymptotically vanishing error…
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…
The common security criterion d in quantum key distribution is taken to solve the universal composability problem in quantum key distribution as well as providing good general quantitative security guarantee. In this paper it is shown that…