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Adiabatic quantum computing is a promising route to the computational power afforded by quantum information processing. The recent availability of adiabatic hardware has raised challenging questions about how to evaluate adiabatic quantum…
We give an overview of a quantum adiabatic algorithm for Hilbert's tenth problem, including some discussions on its fundamental aspects and the emphasis on the probabilistic correctness of its findings. For the purpose of illustration, the…
Linear system solvers are widely used in scientific computing, with the primary goal of solving linear system problems. Classical iterative algorithms typically rely on the conjugate gradient method. The rise of quantum computing has…
Quantum computing promises the ability to compute properties of quantum systems exponentially faster than classical computers. Quantum advantage is achieved when a practical problem is solved more efficiently on a quantum computer than on a…
Prime factorization is a difficult problem with classical computing, whose exponential hardness is the foundation of Rivest-Shamir-Adleman (RSA) cryptography. With programmable quantum devices, adiabatic quantum computing has been proposed…
Over the last decades, there have been many proposals for quantum computation. One of the promising candidates is adiabatic quantum computation (AQC). The central idea of AQC is about finding the ground state of a system with a problem…
The adiabatic quantum computation is a universal and robust method of quantum computing. In this architecture, the problem can be solved by adiabatically evolving the quantum processor from the ground state of a simple initial Hamiltonian…
Deutsch-Jozsa algorithm has been implemented via a quantum adiabatic evolution by S. Das et al. [Phys. Rev. A 65, 062310 (2002)]. This adiabatic algorithm gives rise to a quadratic speed up over classical algorithms. We show that a modified…
Advances in quantum algorithms suggest a tentative scaling advantage on certain combinatorial optimization problems. Recent work, however, has also reinforced the idea that barren plateaus render variational algorithms ineffective on large…
One of the most important questions in studying quantum computation is: whether a quantum computer can solve NP-complete problems more efficiently than a classical computer? In 2000, Farhi, et al. (Science, 292(5516):472--476, 2001)…
We demonstrate that the performance of a quantum annealer on hard random Ising optimization problems can be substantially improved using quantum annealing correction (QAC). Our error correction strategy is tailored to the D-Wave Two device.…
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,…
Quantum annealing is a promising algorithm for solving combinatorial optimization problems. It searches for the ground state of the Ising model, which corresponds to the optimal solution of a given combinatorial optimization problem. The…
Adiabatic quantum computing is implemented on specialized hardware using the heuristics of the quantum annealing algorithm. This setup requires the addressed problems to be formatted as discrete quadratic functions without constraints and…
Quantum computers use quantum resources to carry out computational tasks and may outperform classical computers in solving certain computational problems. Special-purpose quantum computers such as quantum annealers employ quantum adiabatic…
A central challenge in the successful implementation of adiabatic quantum algorithms is to maintain the quantum adiabaticity during the entire evolution. However, the energy gap between the ground and the excited states of interacting…
Commercial adiabatic quantum annealers have the potential to solve important NP-hard optimization problems efficiently. The newest generation of those machines additionally allows the user to customize the anneal schedule, that is, the…
We briefly review various computational methods for the solution of optimization problems. First, several classical methods such as Metropolis algorithm and simulated annealing are discussed. We continue with a description of quantum…
In this thesis, I investigate aspects of local Hamiltonians in quantum computing. First, I focus on the Adiabatic Quantum Computing model, based on evolution with a time dependent Hamiltonian. I show that to succeed using AQC, the…
We present a technique that dramatically improves the accuracy of adiabatic state transfer for a broad class of realistic Hamiltonians. For some systems, the total error scaling can be quadratically reduced at a fixed maximum transfer rate.…