Related papers: Quantum Circuits and Spin(3n) Groups
Achieving control over the electron spin in quantum dots (artificial atoms) or real atoms promises access to new technologies in conventional and in quantum information processing. Here we review our proposal for quantum computing with…
The power of a quantum circuit is determined through the number of two-qubit entangling gates that can be performed within the coherence time of the system. In the absence of parallel quantum gate operations, this would make the quantum…
With the help of the spin-orbit interaction, we propose a scheme to perform holonomic single qubit gates on the electron spin confined to a quantum dot. The manipulation is done in the absence (or presence) of an applied magnetic field. By…
The implementation of a spin qubit in a quantum ring occupied by one or a few electrons is proposed. Quantum bit involves the Zeeman sublevels of the highest occupied orbital. Such a qubit can be initialized, addressed, manipulated, read…
Two different algorithms are presented for generating a quantum circuit realization of a matrix representing a permutation on $2^n$ letters. All circuits involve $n$ qubits and only use multi--controlled Toffoli gates. The first algorithm…
We consider the Unitary Permutation problem which consists, given $n$ unitary gates $U_1, \ldots, U_n$ and a permutation $\sigma$ of $\{1,\ldots, n\}$, in applying the unitary gates in the order specified by $\sigma$, i.e. in performing…
It has been widely assumed that one-qubit gates in spin-based quantum computers suffer from severe technical difficulties. We show that one-qubit gates can in fact be generated using only modest and presently feasible technological…
Capacitively coupled semiconductor spin qubits hold promise as the building blocks of a scalable quantum computing architecture with long-range coupling between distant qubits. However, the two-qubit gate fidelities achieved in experiments…
The symmetry SU(2) and its geometric Bloch Sphere rendering are familiar for a qubit (spin-1/2) but extension of symmetries and geometries have been investigated far less for multiple qubits, even just a pair of them, that are central to…
Spin-$\frac{1}{2}$ $^{119}$Sn nuclei in a silicon semiconductor could make excellent qubits. Nuclear spins in silicon are known to have long coherence times. Tin is isoelectronic with silicon, so we expect electrons can easily shuttle from…
This article traces a brief history of the use of single electron spins to compute. In classical computing schemes, a binary bit is represented by the spin polarization of a single electron confined in a quantum dot. If a weak magnetic…
We present a universal set of quantum gate operations based on exchange-only spin qubits in a double quantum dot, where each qubit is obtained by three electrons in the (2,1) filling. Gate operations are addressed by modulating…
Quantum algorithms may be described by sequences of unitary transformations called quantum gates and measurements applied to the quantum register of n quantum bits, qubits. A collection of quantum gates is called universal if it can be used…
Implementation of high-dimensional (HD) quantum gates shows very promising perspectives for HD quantum computation. A bipartite quantum system with arbitrary dimensions $n$ and $m$ is termed a quNit-quMit. Here we propose a synthesis scheme…
We study the classical simulatability of commuting quantum circuits with n input qubits and O(log n) output qubits, where a quantum circuit is classically simulatable if its output probability distribution can be sampled up to an…
We discuss a new approach to simulate quantum algorithms using classical probabilistic bits and circuits. Each qubit (a two-level quantum system) is initially mapped to a vector in an eight dimensional probability space (equivalently, to a…
The small footprint of semiconductor qubits is favourable for scalable quantum computing. However, their size also makes them sensitive to their local environment and variations in gate structure. Currently, each device requires tailored…
We give a finite presentation by generators and relations for the group O_n(Z[1/2]) of n-dimensional orthogonal matrices with entries in Z[1/2]. We then obtain a similar presentation for the group of n-dimensional orthogonal matrices of the…
We study the scaling of the convergence of several statistical properties of a recently introduced random unitary circuit ensemble towards their limits given by the circular unitary ensemble (CUE). Our study includes the full distribution…
Quantum circuits with symmetry-respecting gates have attracted broad interest in quantum information science. While recent work has developed a theory for circuits with Abelian symmetries, revealing important distinctions between Abelian…