Testing a Quantum Computer

The problem of quantum test is formally addressed. The presented method attempts the quantum role of classical test generation and test set reduction methods known from standard binary and analog circuits. QuFault, the authors software package generates test plans for arbitrary quantum circuits using the very efficient simulator QuIDDPro[1]. The quantum fault table is introduced and mathematically formalized, and the test generation method explained.Comment: 15 pages, 17 equations, 27 tables, 8 figure

Simulation of Electronic Structure Hamiltonians Using Quantum Computers

Over the last century, a large number of physical and mathematical developments paired with rapidly advancing technology have allowed the field of quantum chemistry to advance dramatically. However, the lack of computationally efficient methods for the exact simulation of quantum systems on classical computers presents a limitation of current computational approaches. We report, in detail, how a set of pre-computed molecular integrals can be used to explicitly create a quantum circuit, i.e. a sequence of elementary quantum operations, that, when run on a quantum computer, obtains the energy of a molecular system with fixed nuclear geometry using the quantum phase estimation algorithm. We extend several known results related to this idea and discuss the adiabatic state preparation procedure for preparing the input states used in the algorithm. With current and near future quantum devices in mind, we provide a complete example using the hydrogen molecule of how a chemical Hamiltonian can be simulated using a quantum computer.Chemistry and Chemical Biolog

Quantum Computing for Molecular Energy Simulations

Over the last century, a large number of physical and mathematical developments paired with rapidly advancing technology have allowed the field of quantum chemistry to advance dramatically. However, the lack of computationally efficient methods for the exact simulation of quantum systems on classical computers presents a limitation of current computational approaches. We report, in detail, how a set of pre-computed molecular integrals can be used to explicitly create a quantum circuit, i.e. a sequence of elementary quantum operations, that, when run on a quantum computer, to obtain the energy of a molecular system with fixed nuclear geometry using the quantum phase estimation algorithm. We extend several known results related to this idea and discuss the adiabatic state preparation procedure for preparing the input states used in the algorithm. With current and near future quantum devices in mind, we provide a complete example using the hydrogen molecule, of how a chemical Hamiltonian can be simulated using a quantum computer.Chemistry and Chemical Biolog

Community Detection in Quantum Complex Networks

Determining community structure is a central topic in the study of complex networks, be it technological, social, biological or chemical, in static or interacting systems. In this paper, we extend the concept of community detection from classical to quantum systems---a crucial missing component of a theory of complex networks based on quantum mechanics. We demonstrate that certain quantum mechanical effects cannot be captured using current classical complex network tools and provide new methods that overcome these problems. Our approaches are based on defining closeness measures between nodes, and then maximizing modularity with hierarchical clustering. Our closeness functions are based on quantum transport probability and state fidelity, two important quantities in quantum information theory. To illustrate the effectiveness of our approach in detecting community structure in quantum systems, we provide several examples, including a naturally occurring light-harvesting complex, LHCII. The prediction of our simplest algorithm, semiclassical in nature, mostly agrees with a proposed partitioning for the LHCII found in quantum chemistry literature, whereas our fully quantum treatment of the problem uncovers a new, consistent, and appropriately quantum community structure.Comment: 16 pages, 4 figures, 1 tabl

The Computational Power of Minkowski Spacetime

The Lorentzian length of a timelike curve connecting both endpoints of a classical computation is a function of the path taken through Minkowski spacetime. The associated runtime difference is due to time-dilation: the phenomenon whereby an observer finds that another's physically identical ideal clock has ticked at a different rate than their own clock. Using ideas appearing in the framework of computational complexity theory, time-dilation is quantified as an algorithmic resource by relating relativistic energy to an $n$th order polynomial time reduction at the completion of an observer's journey. These results enable a comparison between the optimal quadratic \emph{Grover speedup} from quantum computing and an $n=2$ speedup using classical computers and relativistic effects. The goal is not to propose a practical model of computation, but to probe the ultimate limits physics places on computation.Comment: 6 pages, LaTeX, feedback welcom

Testing a Quantum Computer

We address the problem of quantum test set generation using measurement from a single basis and the single fault model. Experimental physicists currently test quantum circuits exhaustively, meaning that each n-bit permutative circuit requires ζ x 2n tests to assure functionality, and for an m stage permutative circuit proven not to function properly the current method requires ζ x 2n x m tests as the upper bound for fault localization, where zeta varies with physical implementation. Indeed, the exhaustive methods complexity grows exponentially with the number of qubits, proportionally to the number of stages in a quantum circuit and directly with zeta. This testability bound grows still exponentially with the attempted verification of quantum effects, such as the emission of a quantum source. The exhaustive method will soon not be feasible for practical application provided the number of qubits increases even a small number from the current state of the art. An algorithm is presented making fault detection feasible both now and in the foreseeable future for quantum circuits. The presented method attempts the quantum role of classical test generation and test set reduction methods known from standard binary and analog circuits. The quantum fault table is introduced, and the test generation method explained, we show that all faults can be detected that impact calculations from the computational basis. It is believed that this fundamental research will lead to the simplification of testing for commercial quantum computers

Chiral Quantum Walks

Given its importance to many other areas of physics, from condensed matter physics to thermodynamics, time-reversal symmetry has had relatively little influence on quantum information science. Here we develop a network-based picture of time-reversal theory, classifying Hamiltonians and quantum circuits as time-symmetric or not in terms of the elements and geometries of their underlying networks. Many of the typical circuits of quantum information science are found to exhibit time-asymmetry. Moreover, we show that time-asymmetry in circuits can be controlled using local gates only, and can simulate time-asymmetry in Hamiltonian evolution. We experimentally implement a fundamental example in which controlled time-reversal asymmetry in a palindromic quantum circuit leads to near-perfect transport. Our results pave the way for using time-symmetry breaking to control coherent transport, and imply that time-asymmetry represents an omnipresent yet poorly understood effect in quantum information science.Comment: 9 pages, 4 figures, REVTeX 4.1 - published versio