Related papers: Universal quantum processors with arbitrary radix …

We consider algebras underlying Hilbert spaces used by quantum information algorithms. We show how one can arrive at equations on such algebras which define n-dimensional Hilbert space subspaces which in turn can simulate quantum systems on…

A proof is given, which relies on the commutator algebra of the unitary Lie groups, that quantum gates operating on just two bits at a time are sufficient to construct a general quantum circuit. The best previous result had shown the…

In this paper we study universality for quantum gates acting on qudits.Qudits are states in a Hilbert space of dimension d where d is at least two. We determine which 2-qudit gates V have the properties (i) the collection of all 1-qudit…

We analyze the control by electromagnetic fields of quantum systems with infinite dimensional Hilbert space and a discrete spectrum. Based on recent mathematical results, we rigorously show under which conditions such a system can be…

A quantum walk is a time-homogeneous quantum-mechanical process on a graph defined by analogy to classical random walk. The quantum walker is a particle that moves from a given vertex to adjacent vertices in quantum superposition. Here we…

Geometry and dimensionality have played crucial roles in our understanding of the fundamental laws of nature, with examples ranging from curved space-time in general relativity to modern theories of quantum gravity. In quantum many-body…

Any unitary transformation of quantum computational networks is explicitly decomposed, in an exact and unified form, into a sequence of a limited number of one-qubit quantum gates and the two-qubit diagonal gates that have diagonal unitary…

The advent of Quantum Computing has influenced researchers around the world to solve multitudes of computational problems with the promising technology. Feasibility of solutions for computational problems, and representation of various…

The primary resource for quantum computation is Hilbert-space dimension. Whereas Hilbert space itself is an abstract construction, the number of dimensions available to a system is a physical quantity that requires physical resources.…

We construct a simple translationally invariant, nearest-neighbor Hamiltonian on a chain of 10-dimensional qudits that makes it possible to realize universal quantum computing without any external control during the computational process.…

Recently, it is shown that quantum computers can be used for obtaining certain information about the solution of a linear system Ax=b exponentially faster than what is possible with classical computation. Here we first review some key…

A large-scalable quantum computer model, whose qubits are represented by the subspace subtended by the ground state and the single exciton state on semiconductor quantum dots, is proposed. A universal set of quantum gates in this system may…

Any quantum computational network can be constructed with a sequence of the two-qubit diagonal quantum gates and one-qubit gates in two-state quantum systems. The universal construction of these quantum gates in the quantum systems and of…

We describe an approach for characterizing the process of quantum gates using quantum process tomography, by first modeling them in an extended Hilbert space, which includes non-qubit degrees of freedom. To prevent unphysical processes from…

In a recent preprint by Deutsch et al. [1995] the authors suggest the possibility of polynomial approximability of arbitrary unitary operations on $n$ qubits by 2-qubit unitary operations. We address that comment by proving strong lower…

We present a simple quantum circuit that allows for the universal and deterministic manipulation of the quantum state of confined harmonic oscillators. The scheme is based on the selective interactions of the referred oscillator with an…

We prove that universal quantum computation is possible using only (i) the physically natural measurement on two qubits which distinguishes the singlet from the triplet subspace, and (ii) qubits prepared in almost any three different…

Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning…

A unitary 2-design can be viewed as a quantum analogue of a 2-universal hash function: it is indistinguishable from a truly random unitary by any procedure that queries it twice. We show that exact unitary 2-designs on n qubits can be…

We present a novel, computationally efficient approach to accelerate quantum optimal control calculations of large multi-qubit systems used in a variety of quantum computing applications. By leveraging the intrinsic symmetry of finite…