Related papers: Size dependence of the minimum excitation gap in t…
A major obstacle for quantum optimizers is the reformulation of constraints as a quadratic unconstrained binary optimization (QUBO). Current QUBO translators exaggerate the weight $M$ of the penalty terms. Classically known as the "Big-$M$"…
Adiabatic quantum computers can solve difficult optimization problems (e.g., the quadratic unconstrained binary optimization problem), and they seem well suited to train machine learning models. In this paper, we describe an adiabatic…
A quadratic speedup of the quantum adiabatic algorithm (QAA) for finding independent sets (ISs) in a graph is proven analytically. In comparison to the best classical algorithm with $O(n^2)$ scaling, where $n$ is the number of vertexes, our…
The quantum approximate optimization algorithm (QAOA) has rapidly become a cornerstone of contemporary quantum algorithm development. Despite a growing range of applications, only a few results have been developed towards understanding the…
The computational complexity conjecture of NP $\nsubseteq$ BQP implies that there should be an exponentially small energy gap for Quantum Annealing (QA) of NP-hard problems. We aim to verify how this computation originated gapless point…
Designing quantum algorithms with a speedup over their classical analogs is a central challenge in quantum information science. Motivated by recent experimental observations of a superlinear quantum speedup in solving the Maximum…
Adiabatic quantum computing (AQC) started as an approach to solving optimization problems, and has evolved into an important universal alternative to the standard circuit model of quantum computing, with deep connections to both classical…
We discuss the application of the adiabatic perturbation theory to analyze the dynamics in various systems in the limit of slow parametric changes of the Hamiltonian. We first consider a two-level system and give an elementary derivation of…
We explain why quantum adiabatic evolution and simulated annealing perform similarly in certain examples of searching for the minimum of a cost function of n bits. In these examples each bit is treated symmetrically so the cost function…
Quantum adiabatic algorithm is of vital importance in quantum computation field. It offers us an alternative approach to manipulate the system instead of quantum gate model. Recently, an interesting work arXiv:1805.10549 indicated that we…
Analog quantum algorithms are formulated in terms of Hamiltonians rather than unitary gates and include quantum adiabatic computing, quantum annealing, and the quantum approximate optimization algorithm (QAOA). These algorithms are…
Quantum computation by adiabatic evolution, as described in quant-ph/0001106, will solve satisfiability problems if the running time is long enough. In certain special cases (that are classically easy) we know that the quantum algorithm…
The critical quantum metrology, which exploits the quantum phase transition for high precision measurement, has gained increasing attention recently. The critical quantum metrology with the continuous quantum phase transition, however, is…
We analyze the crossing of a quantum critical point based on exact results for the transverse XY model. In dependence of the change rate of the driving field, the evolution of the ground state is studied while the transverse magnetic field…
We investigate the connection between local minima in the problem Hamiltonian and first order quantum phase transitions during an adiabatic quantum computation. We demonstrate how some properties of the local minima can lead to an extremely…
We extend the family of problems that may be implemented on an adiabatic quantum optimizer (AQO). When a quadratic optimization problem has at least one set of discrete controls and the constraints are linear, we call this a quadratic…
We show that it is possible to use a classical computer to efficiently simulate the adiabatic evolution of a quantum system in one dimension with a constant spectral gap, starting the adiabatic evolution from a known initial product state.…
We present straightforward proofs of estimates used in the adiabatic approximation. The gap dependence is analyzed explicitly. We apply the result to interpolating Hamiltonians of interest in quantum computing.
This paper describes an application of the Quantum Approximate Optimisation Algorithm (QAOA) to efficiently find approximate solutions for computational problems contained in the polynomially bounded NP optimisation complexity class (NPO…
A major drawback of adiabatic quantum computing (AQC) is fulfilling the energy gap constraint, which requires the total evolution time to scale inversely with the square of the minimum energy gap. Failure to satisfy this condition violates…