Related papers: Topological Obstructions in Quantum Adiabatic Algo…
Towards better understanding of how to design efficient adiabatic quantum algorithms, we study how the adiabatic gap depends on the spectra of the initial and final Hamiltonians in a natural family of test-bed examples. We show that perhaps…
Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of…
The prospect of quantum solutions for complicated optimization problems is contingent on mapping the original problem onto a tractable quantum energy landscape, e.g. an Ising-type Hamiltonian. Subsequently, techniques like adiabatic…
We explore to what extent path-integral quantum Monte Carlo methods can efficiently simulate the tunneling behavior of quantum adiabatic optimization algorithms. Specifically we look at symmetric cost functions defined over n bits with a…
In Amin and Choi \cite{AC09}, we show that an adiabatic quantum algorithm for the NP-hard maximum independent set (MIS) problem on a set of special family of graphs in which there are exponentially many local maxima would have the…
We present a method to split quantum circuits of variational quantum algorithms (VQAs) to allow for parallel training and execution, that maximally exploits the limited number of qubits in hardware to solve large problem instances. We apply…
Two recent preprints [B. Altshuler, H. Krovi, and J. Roland, "Quantum adiabatic optimization fails for random instances of NP-complete problems", arXiv:0908.2782 and "Anderson localization casts clouds over adiabatic quantum optimization",…
The practical implementation of quantum optimization algorithms on noisy intermediate-scale quantum devices requires accounting for their limited connectivity. As such, the Parity architecture was introduced to overcome this limitation by…
The discrete formulation of adiabatic quantum computing is compared with other search methods, classical and quantum, for random satisfiability (SAT) problems. With the number of steps growing only as the cube of the number of variables,…
Optimization problems in finance, physics and computer science are typically very hard to tackle in classical computing and quantum computing could help speed up computations and provide efficient methods for tackling large problems.…
We show enough evidence that a structured version of Adiabatic Quantum Computation (AQC) is efficient for most satisfiability problems. More precisely, when the success probability is fixed beforehand, the computational resources grow…
The quantum approximate optimization algorithm (QAOA) generates an approximate solution to combinatorial optimization problems using a variational ansatz circuit defined by parameterized layers of quantum evolution. In theory, the…
Many quantum algorithms seek to output a specific bitstring solving the problem of interest--or a few if the solution is degenerate. It is the case for the quantum approximate optimization algorithm (QAOA) in the limit of large circuit…
The quantum adiabatic theorem ensures that a slowly changing system, initially prepared in its ground state, will evolve to its final ground state with arbitrary precision. As a first result this thesis extends the original theorem to…
As power systems expand, solving the Unit Commitment Problem (UCP) becomes increasingly challenging due to the dimensional catastrophe, and traditional methods often struggle to balance computational efficiency and solution quality. To…
Recent advances in the field of adiabatic quantum computing and the closely related field of quantum annealers has centered around using more advanced and novel Hamiltonian representations to solve optimization problems. One of these…
In this paper, we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimensional projector…
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…
A challenge with the Quantum Approximate Optimisation Algorithm (QAOA), and variational algorithms in general, is finding good variational parameters, a task which in itself can be NP-hard. Recent work has sought to de-variationalise QAOA…
Quantum annealing solves combinatorial optimization problems by finding the energetic ground states of an embedded Hamiltonian. However, quantum annealing dynamics under the embedded Hamiltonian may violate the principles of adiabatic…