Related papers: Unitary operator bases as universal averaging sets

Based on local unitary operators acting on a n-dimensional Hilbert-space, we investigate selective and collective operator basis sets for N-particle quantum networks. Selective cluster operators are used to derive the properties of general…

Let $\ket{\0}$ and $\ket{\1}$ be two states that are promised to come from known subsets of orthogonal subspaces, but are otherwise unknown. Our paper probes the question of what can be achieved with respect to the basis…

We provide algebraic criteria for the unitarity of linear quantum cellular automata, i.e. one dimensional quantum cellular automata. We derive these both by direct combinatorial arguments, and by adding constraints into the model which do…

Simulating physical systems on near-term quantum computers often requires preparing states within constrained subspaces, like those with fixed particle number or spin. We use Lie algebraic techniques to prove that hardware-efficient gates…

Hilbert space operators may be mapped onto a space of ordinary functions (operator symbols) equipped with an associative (but noncommutative) star-product. A unified framework for such maps is reviewed. Because of its clear probabilistic…

Given a preferred orthonormal basis $B$ in the Hilbert space of a quantum system we define a measure of the coherence generating power of a unitary operation with respect to $B$. This measure is the average coherence generated by the…

We consider dual unitary operators and their multi-leg generalizations that have appeared at various places in the literature. These objects can be related to multi-party quantum states with special entanglement patterns: the sites are…

Measurement-based quantum computation describes a scheme where entanglement of resource states is utilized to simulate arbitrary quantum gates via local measurements. Recent works suggest that symmetry-protected topologically non-trivial,…

A quantum processor is a programmable quantum circuit in which both the data and the program, which specifies the operation that is carried out on the data, are quantum states. We study the situation in which we want to use such a processor…

Measurement based (MB) quantum computation allows for universal quantum computing by measuring individual qubits prepared in entangled multipartite states, known as graph states. Unless corrected for, the randomness of the measurements…

We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and circuits are naturally interpretable in such structures. We consider…

The existence of universal quantum computers has been theoretically well established. However, building up a real quantum computer system not only relies on the theory of universality, but also needs methods to satisfy requirements on other…

In this paper we present a quantization of Cellular Automata. Our formalism is based on a lattice of qudits, and an update rule consisting of local unitary operators that commute with their own lattice translations. One purpose of this…

Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems, and solving large…

A quantum processor (the programmable gate array) is a quantum network with a fixed structure. A space of states is represented as tensor product of data and program registers. Different unitary operations with the data register correspond…

Any method for estimating the ensemble average of arbitrary operator (observables or not, including the density matrix) relates the quantity of interest to a complete set of observables, i.e. a quorum}. This corresponds to an expansion on…

Iterates of quantum operations and their convergence are investigated in the context of mean ergodic theory. We discuss in detail the convergence of the iterates and show that the uniform ergodic theorem plays an essential role. Our results…

We show that every correctable subsystem for an arbitrary noise operation can be recovered by a unitary operation, where the notion of recovery is more relaxed than the notion of correction insofar as it does not protect the subsystem from…

We consider pseudo-unitary quantum systems and discuss various properties of pseudo-unitary operators. In particular we prove a characterization theorem for block-diagonalizable pseudo-unitary operators with finite-dimensional diagonal…

We consider the problem of estimating quantum observables on a collection of qubits, given as a linear combination of Pauli operators, with shallow quantum circuits consisting of single-qubit rotations. We introduce estimators based on…