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Unsupervised visual clustering has garnered significant attention in recent times, aiming to characterize distributions of unlabeled visual images through clustering based on a parameterized appearance approach. Alternatively, clustering…
An explicit algorithm for the travelling salesman problem is constructed in the framework of adiabatic quantum computation, AQC. The initial Hamiltonian for the AQC process admits canonical coherent states as the ground state, and the…
We propose a quantum algorithm for solving combinatorial search problems that uses only a sequence of measurements. The algorithm is similar in spirit to quantum computation by adiabatic evolution, in that the goal is to remain in the…
A central goal in quantum computing is the development of quantum hardware and quantum algorithms in order to analyse challenging scientific and engineering problems. Research in quantum computation involves contributions from both physics…
We introduce a perturbative approach to solving the time dependent Schroedinger equation, named adiabatic perturbation theory (APT), whose zeroth order term is the quantum adiabatic approximation. The small parameter in the power series…
Current quantum annealing experiments often suffer from restrictions in connectivity in the sense that only certain qubits can be coupled to each other. The most common strategy to overcome connectivity restrictions so far is by combining…
We propose a framework to solve non-linear and history-dependent mechanical problems based on a hybrid classical computer -- quantum annealer approach. Quantum Computers are anticipated to solve particular operations exponentially faster.…
Quantum annealing promises to be an effective heuristic for complex NP-hard problems. However, clear demonstrations of quantum advantage are wanting, primarily constrained by the difficulty of embedding the problem into the quantum…
We propose a method to speed up the quantum adiabatic algorithm using catalysis by many-body delocalization. This is applied to random-field antiferromagnetic Ising spin models. The algorithm is catalyzed in such a way that the evolution…
Quantum algorithms are prominent in the pursuit of achieving quantum advantage in various computational tasks. However, addressing challenges, such as limited qubit coherence and high error rate in near-term devices, requires extensive…
We give a quantum algorithm for solving instances of the satisfiability problem, based on adiabatic evolution. The evolution of the quantum state is governed by a time-dependent Hamiltonian that interpolates between an initial Hamiltonian,…
We present numerical calculations, and simulations performed on a Rydberg atom quantum simulator, of the adiabatic evolution of many-body quantum systems around a quantum phase transition. We demonstrate that the end-to-end transfer error,…
Continuous-time quantum algorithms for combinatorial optimisation problems, such as quantum annealing, have previously been motivated by the adiabatic principle. A number of continuous-time approaches exploit dynamics, however, and…
The propagation of errors severely compromises the reliability of quantum computations. The quantum adiabatic algorithm is a physically motivated method to prepare ground states of classical and quantum Hamiltonians. Here, we analyze the…
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…
Quantum annealing is a generic name of quantum algorithms to use quantum-mechanical fluctuations to search for the solution of optimization problem. It shares the basic idea with quantum adiabatic evolution studied actively in quantum…
Amongst the most remarkable successes of quantum computation are Shor's efficient quantum algorithms for the computational tasks of integer factorisation and the evaluation of discrete logarithms. In this article we review the essential…
The parametric deformations of quasienergies and eigenvectors of unitary operators are applied to the design of quantum adiabatic algorithms. The conventional, standard adiabatic quantum computation proceeds along eigenenergies of…
The D-Wave adiabatic quantum annealer solves hard combinatorial optimization problems leveraging quantum physics. The newest version features over 1000 qubits and was released in August 2015. We were given access to such a machine,…
Recent advances bring within reach the viability of solving combinatorial problems using a quantum annealing algorithm implemented on a purpose-built platform that exploits quantum properties. However, the question of how to tune the…