268 research outputs found
Fault-ignorant Quantum Search
We investigate the problem of quantum searching on a noisy quantum computer.
Taking a 'fault-ignorant' approach, we analyze quantum algorithms that solve
the task for various different noise strengths, which are possibly unknown
beforehand. We prove lower bounds on the runtime of such algorithms and thereby
find that the quadratic speedup is necessarily lost (in our noise models).
However, for low but constant noise levels the algorithms we provide (based on
Grover's algorithm) still outperform the best noiseless classical search
algorithm.Comment: v1: 15+8 pages, 4 figures; v2: 19+8 pages, 4 figures, published
version (Introduction section significantly expanded, presentation clarified,
results and order unchanged
Signature Well-being: Toward a More Precise Operationalization of Well-being at the Individual Level
The scientific study of well-being has grown exponentially in recent decades but has primarily focused on the macro level, identifying what generally contributes to well-being. As a result, schools have increased the well-being of students through character strengths and resilience curriculum; institutions have increased employee engagement through aligning interests and strengths; and governments have a new benchmark for success through the deployment of global well-being indices. While great strides have been made at this level, I propose the study of well-being is missing a vital component at the individual level: Signature Well-being. The basis for this proposal is the scientific study of character strengths and the benefits gained from working from one’s signature character strengths. Signature Well-being suggests that, like signature character strengths, there is an element (or combination of elements) of well-being that is energizing, authentic and intuitive. I propose that the elements of well-being should be weighted based on this central element(s) to take into account individual differences and more accurately represent the status a person’s subjective well-being. What is signature then is this unique operationalization of one’s well-being. While the study of well-being at the macro level is a crucial endeavor, the additional study of well-being at the micro level will provide the field a more complete picture from which to build well-being
Searching via walking: How to find a marked subgraph of a graph using quantum walks
We show how a quantum walk can be used to find a marked edge or a marked
complete subgraph of a complete graph. We employ a version of a quantum walk,
the scattering walk, which lends itself to experimental implementation. The
edges are marked by adding elements to them that impart a specific phase shift
to the particle as it enters or leaves the edge. If the complete graph has N
vertices and the subgraph has K vertices, the particle becomes localized on the
subgraph in O(N/K) steps. This leads to a quantum search that is quadratically
faster than a corresponding classical search. We show how to implement the
quantum walk using a quantum circuit and a quantum oracle, which allows us to
specify the resource needed for a quantitative comparison of the efficiency of
classical and quantum searches -- the number of oracle calls.Comment: 4 pages, 2 figure
Quantum searches on highly symmetric graphs
We study scattering quantum walks on highly symmetric graphs and use the
walks to solve search problems on these graphs. The particle making the walk
resides on the edges of the graph, and at each time step scatters at the
vertices. All of the vertices have the same scattering properties except for a
subset of special vertices. The object of the search is to find a special
vertex. A quantum circuit implementation of these walks is presented in which
the set of special vertices is specified by a quantum oracle. We consider the
complete graph, a complete bipartite graph, and an -partite graph. In all
cases, the dimension of the Hilbert space in which the time evolution of the
walk takes place is small (between three and six), so the walks can be
completely analyzed analytically. Such dimensional reduction is due to the fact
that these graphs have large automorphism groups. We find the usual quadratic
quantum speedups in all cases considered.Comment: 11 pages, 6 figures; major revision
Strongly Incompatible Quantum Devices
The fact that there are quantum observables without a simultaneous
measurement is one of the fundamental characteristics of quantum mechanics. In
this work we expand the concept of joint measurability to all kinds of possible
measurement devices, and we call this relation compatibility. Two devices are
incompatible if they cannot be implemented as parts of a single measurement
setup. We introduce also a more stringent notion of incompatibility, strong
incompatibility. Both incompatibility and strong incompatibility are rigorously
characterized and their difference is demonstrated by examples.Comment: 27 pages (AMSart), 6 figure
- …