Related papers: On the representation of Boolean and real function…
Quantum computing employs controllable interactions to perform sequences of logical gates and entire algorithms on quantum registers. This paradigm has been widely explored, e.g., for simulating dynamics of manybody systems by decomposing…
Quantum computation appears to offer significant advantages over classical computation and this has generated a tremendous interest in the field. In this thesis we consider the application of quantum computers to scientific computing and…
With a focus on universal quantum computing for quantum simulation, and through the example of lattice gauge theories, we introduce rather general quantum algorithms that can efficiently simulate certain classes of interactions consisting…
I present a novel use of quantum annealing to solve the Set Splitting Problem using (QUBO) problem formulation. The contribution of the work is in formulating penalty functions that ensure the ground state of the QUBO Hamiltonian…
For a quantum many-body problem, effective Hamiltonians that give exact eigenvalues in reduced model space usually have different expressions, diagrams and evaluation rules from effective transition operators that give exact transition…
A Boolean function is a function that produces a Boolean value output by logical calculation of Boolean inputs. It plays key roles in programing algorithms and design of circuits. Minimization of Boolean function is able to optimize the…
Many quantum algorithms, such as adiabatic algorithms (e.g. AQC) and phase randomisation, require simulating Hamiltonian evolution. In addition, the simulation of physical systems is an important objective in its own right. In many cases,…
Submodular function minimization is a key problem in a wide variety of applications in machine learning, economics, game theory, computer vision, and many others. The general solver has a complexity of $O(n^3 \log^2 n . E +n^4 {\log}^{O(1)}…
Constraint satisfaction or optimisation models -- even if they are formulated in high-level modelling languages -- need to be reduced into an equivalent format before they can be solved by the use of Quantum Computing. In this paper we show…
Quantum simulation, the simulation of quantum processes on quantum computers, suggests a path forward for the efficient simulation of problems in condensed-matter physics, quantum chemistry, and materials science. While the majority of…
Digital quantum simulators are among the most appealing applications of a quantum computer. Here we propose a universal, scalable, and integrated quantum computing platform based on tunable nonlinear electromechanical nano-oscillators. It…
In this paper we introduce the study of quantum boolean functions, which are unitary operators f whose square is the identity: f^2 = I. We describe several generalisations of well-known results in the theory of boolean functions, including…
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-local qubit Hamiltonians with a small set of physically…
We study necessary conditions for the efficient simulation of both bipartite and multipartite Hamiltonians, which are independent of the eigenvalues and based on the algebraic-geometric invariants introduced in [1-2]. Our results indicate…
The mathematical problem of localizing modular functors to neighborhoods of points is shown to be closely related to the physical problem of engineering a local Hamiltonian for a computationally universal quantum medium. For genus $=0$…
This work provides a rigorous and self-contained introduction to numerical methods for Hamiltonian simulation in quantum computing, with a focus on high-order product formulas for efficiently approximating the time evolution of quantum…
Solving continuous variable optimization problems by factorization machine quantum annealing (FMQA) demonstrates the potential of Ising machines to be extended as a solver for integer and real optimization problems. However, the details of…
Current state-of-the-art quantum optimization algorithms require representing the original problem as a binary optimization problem, which is then converted into an equivalent cost Hamiltonian suitable for the quantum device. Implementing…
This paper describes a fundamental correspondence between Boolean functions and projection operators in Hilbert space. The correspondence is widely applicable, and it is used in this paper to provide a common mathematical framework for the…
We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary combinatorial problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted…