Related papers: The Quantum Adiabatic Algorithm applied to random …
Many quantum algorithms make use of oracles which evaluate classical functions on a superposition of inputs. In order to facilitate implementation, testing, and resource estimation of such algorithms, we present quantum circuits for…
Variational Quantum Algorithms have emerged as a leading paradigm for near-term quantum computation. In such algorithms, a parameterized quantum circuit is controlled via a classical optimization method that seeks to minimize a…
A reinforcement algorithm solves a classical optimization problem by introducing a feedback to the system which slowly changes the energy landscape and converges the algorithm to an optimal solution in the configuration space. Here, we use…
Adiabatic quantum control protocols have been of wide interest to quantum computation due to their robustness and insensitivity to their actual duration of execution. As an extension of previous quantum learning algorithms, this work…
The adiabatic gauge potential (AGP) is the generator of unitary transformations which preserve the eigenbasis of a quantum Hamiltonian under parametric variation. While its usefulness in quantum mechanics has been thoroughly demonstrated in…
We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the…
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 present a perturbative method to estimate the spectral gap for adiabatic quantum optimization, based on the structure of the energy levels in the problem Hamiltonian. We show that for problems that have exponentially large number of…
We present a robust pulse optimization method for adiabatic population transfer and adiabatic quantum computation. The approach relies on identifying control pulses that keep the evolving quantum system close to its instantaneous ground…
Randomized protocols are procedures that incorporate probabilistic choices during their execution and they play a central role in quantum algorithms, spanning Hamiltonian simulation, noise mitigation, and measurement tasks. In practical…
In this paper we study the performance of the quantum adiabatic algorithm on random instances of two combinatorial optimization problems, 3-regular 3-XORSAT and 3-regular Max-Cut. The cost functions associated with these two clause-based…
Quantum cooling has demonstrated its potential in quantum computing, which can reduce the number of control channels needed for external signals. Recent progress also supports the possibility of maintaining quantum coherence in large-scale…
Estimating partition functions of Ising spin glasses is a cornerstone of statistical physics and computational science, yet it remains classically challenging due to its $\#$P-hard complexity. While Jarzynski's equality offers a theoretical…
Grover's algorithm can be employed in global optimization methods providing, in some cases, a quadratic speedup over classical algorithms. This paper describes a new method for continuous global optimization problems that uses a classical…
We present a rigorous proof that quantum circuit algorithm can be transformed into quantum adiabatic algorithm with the exact same time complexity. This means that from a quantum circuit algorithm of $L$ gates we can construct a quantum…
The design of new quantum algorithms has proven to be an extremely difficult task. This paper considers a different approach to the problem, by studying the problem of 'quantum state generation'. This approach provides intriguing links…
The quest for real-time dynamic optimization solutions in the process industry represents a formidable computational challenge, particularly within the realm of applications like model-predictive control, where rapid and reliable…
The classical simulation of quantum systems typically requires exponential resources. Recently, the introduction of a machine learning-based wavefunction ansatz has led to the ability to solve the quantum many-body problem in regimes that…
Modern adiabatic quantum computers (AQC) are already used to solve difficult combinatorial optimisation problems in various domains of science. Currently, only a few applications of AQC in computer vision have been demonstrated. We review…
This is a set of lecture notes for a graduate-level course on quantum algorithms, with an emphasis on quantum optimization algorithms. It is developed for applied mathematicians and engineers, and requires no previous background in quantum…