Abstract physical traces.
An introduction to quantum annealing
Quantum annealing, or quantum stochastic optimization, is a classical randomized algorithm which provides good heuristics for the solution of hard optimization problems. The algorithm, suggested by the behaviour of quantum systems, is an example of proficuous cross contamination between classical and quantum computer science. In this survey paper we illustrate how hard combinatorial problems are tackled by quantum computation and present some examples of the heuristics provided by quantum annealing....
An introduction to quantum annealing
Quantum annealing, or quantum stochastic optimization, is a classical randomized algorithm which provides good heuristics for the solution of hard optimization problems. The algorithm, suggested by the behaviour of quantum systems, is an example of proficuous cross contamination between classical and quantum computer science. In this survey paper we illustrate how hard combinatorial problems are tackled by quantum computation and present some examples of the heuristics provided by quantum annealing....
Anomalously slow cross symmetry phase relaxation, thermalized non-equilibrated matter and quantum computing beyond the quantum chaos border.
Applications of Graph Spectra in Quantum Physics
Classical computing, quantum computing, and Shor's factoring algorithm
Cluster state computation with quantum-dot charge qubits.
Decoherence of quantum Markov semigroups
Divergence between various estimates of quantized information sources
Entropy generation in a model of reversible computation
We present a model in which, due to the quantum nature of the signals controlling the implementation time of successive unitary computational steps, physical irreversibility appears in the execution of a logically reversible computation.
Extremal quantum states in coupled systems
Introduction to Grassmann manifolds and quantum computation.
Local transition functions of quantum Turing machines
Local Transition Functions of Quantum Turing Machines
Foundations of the notion of quantum Turing machines are investigated. According to Deutsch's formulation, the time evolution of a quantum Turing machine is to be determined by the local transition function. In this paper, the local transition functions are characterized for fully general quantum Turing machines, including multi-tape quantum Turing machines, extending the results due to Bernstein and Vazirani.
Natural quantum operational semantics with predicates
A general definition of a quantum predicate and quantum labelled transition systems for finite quantum computation systems is presented. The notion of a quantum predicate as a positive operator-valued measure is developed. The main results of this paper are a theorem about the existence of generalised predicates for quantum programs defined as completely positive maps and a theorem about the existence of a GSOS format for quantum labelled transition systems. The first theorem is a slight generalisation...
Noise effects in the quantum search algorithm from the viewpoint of computational complexity
We analyse the resilience of the quantum search algorithm in the presence of quantum noise modelled as trace preserving completely positive maps. We study the influence of noise on the computational complexity of the quantum search algorithm. We show that it is only for small amounts of noise that the quantum search algorithm is still more efficient than any classical algorithm.
On the curvature of the space of qubits
The Fisher informational metric is unique in some sense (it is the only Markovian monotone distance) in the classical case. A family of Riemannian metrics is called monotone if its members are decreasing under stochastic mappings. These are the metrics to play the role of Fisher metric in the quantum case. Monotone metrics can be labeled by special operator monotone functions, according to Petz's Classification Theorem. The aim of this paper is to present an idea how one can narrow the set of monotone...
On the factorization criterion for quantum statistics
On the quantum chromatic number of a graph.
On the state complexity of semi-quantum finite automata
Some of the most interesting and important results concerning quantum finite automata are those showing that they can recognize certain languages with (much) less resources than corresponding classical finite automata. This paper shows three results of such a type that are stronger in some sense than other ones because (a) they deal with models of quantum finite automata with very little quantumness (so-called semi-quantum one- and two-way finite automata); (b) differences, even comparing with probabilistic...