History Dependent Quantum Random Walks as Quantum Lattice Gas Automata

Quantum Random Walks (QRW) were first defined as one-particle sectors of Quantum Lattice Gas Automata (QLGA). Recently, they have been generalized to include history dependence, either on previous coin (internal, i.e., spin or velocity) states or on previous position states. These models have the goal of studying the transition to classicality, or more generally, changes in the performance of quantum walks in algorithmic applications. We show that several history dependent QRW can be identified as one-particle sectors of QLGA. This provides a unifying conceptual framework for these models in which the extra degrees of freedom required to store the history information arise naturally as geometrical degrees of freedom on the lattice

When is a quantum cellular automaton (QCA) a quantum lattice gas automaton (QLGA)?

Quantum cellular automata (QCA) are models of quantum computation of particular interest from the point of view of quantum simulation. Quantum lattice gas automata (QLGA - equivalently partitioned quantum cellular automata) represent an interesting subclass of QCA. QLGA have been more deeply analyzed than QCA, whereas general QCA are likely to capture a wider range of quantum behavior. Discriminating between QLGA and QCA is therefore an important question. In spite of much prior work, classifying which QCA are QLGA has remained an open problem. In the present paper we establish necessary and sufficient conditions for unbounded, finite Quantum Cellular Automata (QCA) (finitely many active cells in a quiescent background) to be Quantum Lattice Gas Automata (QLGA). We define a local condition that classifies those QCA that are QLGA, and we show that there are QCA that are not QLGA. We use a number of tools from functional analysis of separable Hilbert spaces and representation theory of associative algebras that enable us to treat QCA on finite but unbounded configurations in full detail.Comment: 37 pages, 7 figures, with changes to explanatory text and updated figures, J. Math. Phys. versio

Adiabatic Quantum Simulation of Quantum Chemistry

We show how to apply the quantum adiabatic algorithm directly to the quantum computation of molecular properties. We describe a procedure to map electronic structure Hamiltonians to 2-body qubit Hamiltonians with a small set of physically realizable couplings. By combining the Bravyi-Kitaev construction to map fermions to qubits with perturbative gadgets to reduce the Hamiltonian to 2-body, we obtain precision requirements on the coupling strengths and a number of ancilla qubits that scale polynomially in the problem size. Hence our mapping is efficient. The required set of controllable interactions includes only two types of interaction beyond the Ising interactions required to apply the quantum adiabatic algorithm to combinatorial optimization problems. Our mapping may also be of interest to chemists directly as it defines a dictionary from electronic structure to spin Hamiltonians with physical interactions

Bounding Polynomial Entanglement Measures for Mixed States

We generalize the notion of the best separable approximation (BSA) and best W-class approximation (BWA) to arbitrary pure-state entanglement measures, defining the best zero-E approximation (BEA). We show that for any polynomial entanglement measure E, any mixed state ρ admits at least one “S decomposition,” i.e., a decomposition in terms of a mixed state on which E is equal to zero, and a single additional pure state with (possibly) nonzero E. We show that the BEA is not, in general, the optimal S decomposition from the point of view of bounding the entanglement of ρ and describe an algorithm to construct the entanglement-minimizing S decomposition for ρ and place an upper bound on E(ρ). When applied to the three-tangle, the cost of the algorithm is linear in the rank d of the density matrix and has an accuracy comparable to a steepest-descent algorithm whose cost scales as d8 log d. We compare the upper bound to a lower-bound algorithm given by C. Eltschka and J. Siewert [Phys. Rev. Lett. 108, 020502 (2012)] for the three-tangle and find that on random rank-2 three-qubit density matrices, the difference between the upper and lower bounds is 0.14 on average. We also find that the three-tangle of random full-rank three-qubit density matrices is less than 0.023 on average

Quantum and Classical Bayesian Agents

We describe a general approach to modeling rational decision-making agents who adopt either quantum or classical mechanics based on the Quantum Bayesian (QBist) approach to quantum theory. With the additional ingredient of a scheme by which the properties of one agent may influence another, we arrive at a flexible framework for treating multiple interacting quantum and classical Bayesian agents. We present simulations in several settings to illustrate our construction: quantum and classical agents receiving signals from an exogenous source, two interacting classical agents, two interacting quantum agents, and interactions between classical and quantum agents. A consistent treatment of multiple interacting users of quantum theory may allow us to properly interpret existing multi-agent protocols and could suggest new approaches in other areas such as quantum algorithm design.Comment: 45 pages, 17 figure

Multipartite quantum entanglement evolution in photosynthetic complexes

We investigate the evolution of entanglement in the Fenna-Matthew-Olson (FMO) complex based on simulations using the scaled hierarchical equations of motion approach. We examine the role of entanglement in the FMO complex by direct computation of the convex roof. We use monogamy to give a lower bound for entanglement and obtain an upper bound from the evaluation of the convex roof. Examination of bipartite measures for all possible bipartitions provides a complete picture of the multipartite entanglement. Our results support the hypothesis that entanglement is maximum primary along the two distinct electronic energy transfer pathways. In addition, we note that the structure of multipartite entanglement is quite simple, suggesting that there are constraints on the mixed state entanglement beyond those due to monogamy. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4742333]. --author-supplied descriptio

The British economy [August 1986]

External events have had a considerable impact on the UK economy. In line with developments elsewhere, UK growth has slowed, interest rates have been reduced and the inflation rate has fallen. However, underlying inflationary pressures in the UK continue to operate with relatively rapid growth of average earnings and substantial growth of private sector liquidity

The Scottish economy [August 1986]

With the inauguration of the quarterly Scottish Business Survey (SBS) in September 1984 there are not two regular up-to-date indicators of trends in the Scottish industrial sector. The combination of the new survey and the long-standing CBI Industrial Trends Survey provides a comprehensive assessment of trends in Scottish industry. The two data sources are essentially complementary, but there are important differences between them

Outlook and appraisal [August 1986]

The results of the July Scottish Business Survey suggest that optimism about the general business climate improved for retailers but deteriorated for manufacturers , wholesalers and construction companies. Overall, the Survey suggests that activity remains constrained by a shortage of sales and orders and that there is fairly widespread spare capacity. Prospects for employment are reported to be poor