168 research outputs found
Combinatorial algorithms for perturbation theory and application on quantum computing
Quantum computing is an emerging area between computer science and physics. Numerous problems in quantum computing involve quantum many-body interactions. This dissertation concerns the problem of simulating arbitrary quantum many-body interactions using realistic two-body interactions. To address this issue, a general class of techniques called perturbative reductions (or perturbative gadgets) is adopted from quantum complexity theory and in this dissertation these techniques are improved for experimental considerations. The idea of perturbative reduction is based on the mathematical machinery of perturbation theory in quantum physics. A central theme of this dissertation is then to analyze the combinatorial structure of the perturbation theory as it is used for perturbative reductions
Solving Set Cover with Pairs Problem using Quantum Annealing
Here we consider using quantum annealing to solve Set Cover with Pairs (SCP), an NP-hard combinatorial optimization problem that plays an important role in networking, computational biology, and biochemistry. We show an explicit construction of Ising Hamiltonians whose ground states encode the solution of SCP instances. We numerically simulate the time-dependent Schrödinger equation in order to test the performance of quantum annealing for random instances and compare with that of simulated annealing. We also discuss explicit embedding strategies for realizing our Hamiltonian construction on the D-wave type restricted Ising Hamiltonian based on Chimera graphs. Our embedding on the Chimera graph preserves the structure of the original SCP instance and in particular, the embedding for general complete bipartite graphs and logical disjunctions may be of broader use than that the specific problem we deal with
Quantum Circuit Design for Solving Linear Systems of Equations
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 aspects of the algorithm from the standpoint of finding its efficient
quantum circuit implementation using only elementary quantum operations, which
is important for determining the potential usefulness of the algorithm in
practical settings. Then we present a small-scale quantum circuit that solves a
2x2 linear system. The quantum circuit uses only 4 qubits, implying a tempting
possibility for experimental realization. Furthermore, the circuit is
numerically simulated and its performance under different circuit parameter
settings is demonstrated.Comment: 7 pages, 3 figures. The errors are corrected. For the general case,
discussions are added to account for recent results. The 4x4 example is
replaced by a 2x2 one due to recent experimental efforts. The 2x2 example was
devised at the time of writing v1 but not included in v1 for brevit
Analysis of a thaumasite attack in a railway tunnel
Concrete linings failed before the acceptance of a railway tunnel in a north mountain area of China. A series of experiments were done to analyze the cause of this case. Thaumasite, ettringite, gypsum and calcite were found in the deteriorated concrete linings. The composition of on-situ soil and water samples were also analyzed. Though the sulfate concentration soil behind the linings are not very high, the underground water bring plenty of sulfate after its upsteam flow through a gypsum stratum. It is the external sulfate that induce the deterioration in a low temperature environment which is suitable for thaumasite formation
- …