Related papers: Effective gaps are not effective: quasipolynomial …

Simulating the time-evolution of quantum mechanical systems is BQP-hard and expected to be one of the foremost applications of quantum computers. We consider classical algorithms for the approximation of Hamiltonian dynamics using…

Understanding NP-complete problems is a central topic in computer science. This is why adiabatic quantum optimization has attracted so much attention, as it provided a new approach to tackle NP-complete problems using a quantum computer.…

We introduce a family of Hamiltonian systems for measurement-based quantum computation with continuous variables. The Hamiltonians (i) are quadratic, and therefore two body, (ii) are of short range, (iii) are frustration-free, and (iv)…

Sampling from the stationary distribution is one of the fundamental tasks of Markov chain-based algorithms and has important applications in machine learning, combinatorial optimization and network science. For the quantum case, qsampling…

Quantum algorithms are of great interest for their possible use in optimization problems. In particular, variational algorithms that use classical counterparts to optimize parameters hold promise for use in currently existing devices.…

In this paper we present a simulation environment enhanced with parallel processing which can be used on personal computers, based on a high-level user interface developed on Mathematica\copyright which is connected to C++ code in order to…

Simulation of realistic classical mechanical systems is of great importance to many areas of engineering such as robotics, dynamics of rotating machinery and control theory. In this work, we develop quantum algorithms to estimate quantities…

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…

The ability to efficiently prepare ground states of quantum Hamiltonians via adiabatic protocols is typically limited by the smallest energy gap encountered during the quantum evolution. This presents a key obstacle for quantum simulation…

A common trick for designing faster quantum adiabatic algorithms is to apply the adiabaticity condition locally at every instant. However it is often difficult to determine the instantaneous gap between the lowest two eigenvalues, which is…

This paper summarizes a quantum algorithm of [R.D. Somma, et.al., Phys. Rev. Lett. 101, 130504 (2008)] that simulates a classical annealing process for solving discrete optimization problems. The complexity of the quantum algorithm scales…

We present a framework for quantum computation, similar to Adiabatic Quantum Computation (AQC), that is based on the quantum Zeno effect. By performing randomised dephasing operations at intervals determined by a Poisson process, we are…

Solving partial differential equations for extremely large-scale systems within a feasible computation time serves in accelerating engineering developments. Quantum computing algorithms, particularly the Hamiltonian simulations, present a…

Non-smooth optimization models play a fundamental role in various disciplines, including engineering, science, management, and finance. However, classical algorithms for solving such models often struggle with convergence speed,…

We describe an efficient approximation algorithm for evaluating the ground-state energy of the classical Ising Hamiltonian with linear terms on an arbitrary planar graph. The running time of the algorithm grows linearly with the number of…

We determine the complexity of several constraint satisfaction problems using the quantum adiabatic algorithm in its simplest implementation. We do so by studying the size dependence of the gap to the first excited state of "typical"…

We describe an algorithm that computes the ground state energy and correlation functions for 2-local Hamiltonians in which interactions between qubits are weak compared to single-qubit terms. The running time of the algorithm is polynomial…

Quantum adiabatic computation is a novel paradigm for the design of quantum algorithms, which is usually used to find the minimum of a classical function. In this paper, we show that if the initial hamiltonian of a quantum adiabatic…

Computing using a continuous-time evolution, based on the natural interaction Hamiltonian of the quantum computer hardware, is a promising route to building useful quantum computers in the near-term. Adiabatic quantum computing, quantum…

The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise quantum walks have shown much potential as a frame- work for developing new quantum algorithms.…