41 research outputs found
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
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
Realizable Hamiltonians for Universal Adiabatic Quantum Computers
It has been established that local lattice spin Hamiltonians can be used for
universal adiabatic quantum computation. However, the 2-local model
Hamiltonians used in these proofs are general and hence do not limit the types
of interactions required between spins. To address this concern, the present
paper provides two simple model Hamiltonians that are of practical interest to
experimentalists working towards the realization of a universal adiabatic
quantum computer. The model Hamiltonians presented are the simplest known
QMA-complete 2-local Hamiltonians. The 2-local Ising model with 1-local
transverse field which has been realized using an array of technologies, is
perhaps the simplest quantum spin model but is unlikely to be universal for
adiabatic quantum computation. We demonstrate that this model can be rendered
universal and QMA-complete by adding a tunable 2-local transverse XX coupling.
We also show the universality and QMA-completeness of spin models with only
1-local Z and X fields and 2-local ZX interactions.Comment: Paper revised and extended to improve clarity; to appear in Physical
Review
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
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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
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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