Related papers: Generators and Roots of Quantum Logic Gates
This note presents a simple and unified formulation of the most fundamental structures used in quantum information with qubits, arbitrary dimension qudits, and quantum continuous variables. This \emph{general quantum variables} construction…
Quantum computers are expected to be able to solve mathematical problems that cannot be solved using conventional computers. Many of these problems are of practical importance, especially in the areas of cryptography and secure…
Representations of Quantum Groups U_q (g_n), g_n any semi simple Lie algebra of rank n, are constructed from arbitrary representations of rank n-1 quantum groups for q a root of unity. Representations which have the maximal dimension and…
Simplest models of two- and three-terminal Quantum Quantum Gates are suggested in form of a quantum ring with few one-dimensional quantum wires attached to it and several point-wise govering electrodes inside the ring which are charged by a…
We propose the use of a trapped electron to implement quantum logic operations. The fundamental controlled-NOT gate is shown to be feasible. The two quantum bits are stored in the internal and external (motional) degrees of freedom.
It is shown that anisotropic spin chains with gapped bulk excitations and magnetically ordered ground states offer a promising platform for quantum computation, which bridges the conventional single-spin-based qubit concept with recently…
Some notes about quantum physics, an interpretation if one wishes, are put forward, insisting on `closely following the mathematics/formalism, the `nuts and bolts of what quantum physics says'. These, basically well-known, issues seem to…
Usually the generators of a quantum group are assumed to be commutative with the noncommuting coordinates of a quantum plane. We have relaxed the assumption and investigated its consequences. Not only does a two-parameter quantum group…
We examine the following problem: given a collection of Clifford gates, describe the set of unitaries generated by circuits composed of those gates. Specifically, we allow the standard circuit operations of composition and tensor product,…
A historical review is given of the emergence of the idea of the quantum logic gate from the theory of reversible Boolean gates. I highlight the quantum XOR or controlled NOT as the fundamental two-bit gate for quantum computation. This…
In quantum mechanics, the connection between the operator algebraic realization and the logical models of measurement of state observables has long been an open question. In the approach that is presented here, we introduce a new…
First some old as well as new results about P.I. algebras, Ore extensions, and degrees are presented. Then quantized $n\times r$ matrices as well as quantized factor algebras of $M_q(n)$ are analyzed. The latter are the quantized function…
Recent research in generalizing quantum computation from 2-valued qudits to d-valued qudits has shown practical advantages for scaling up a quantum computer. A further generalization leads to quantum computing with hybrid qudits where two…
We report the realization of an elementary quantum processor based on a linear crystal of trapped ions. Each ion serves as a quantum bit (qubit) to store the quantum information in long lived electronic states. We present the realization of…
The Clifford$+T$ gate set is commonly used to perform universal quantum computation. In such setup the $T$ gate is typically much more expensive to implement in a fault-tolerant way than Clifford gates. To improve the feasibility of…
Quantum computation is a continuously growing research area which is based on nature and resources of quantum mechanics, as superposition and entanglement. In its quantum circuits version, the use of convenient and appropriate gates is…
The controlled-not gate and the single qubit gates are considered elementary gates in quantum computing. It is natural to ask how many such elementary gates are needed to implement more elaborate gates or circuits. Recall that a…
Hamiltonian encoding was introduced as a technique for revealing the mechanism of controlled quantum systems. It does so by decomposing the evolution into pathways between the computational basis states, where each pathway has an associated…
Quantum logic gates can perform calculations much more efficiently than their classical counterparts. However, the level of control needed to obtain a reliable quantum operation is correspondingly higher. In order to evaluate the…
Quantum gates are essential for the realization of quantum computer and have been implemented in various types of two-level systems. However, high-dimensional quantum gates are rarely investigated both theoretically and experimentally even…