Related papers: Schedule path optimization for quantum annealing a…
We provide and analyze examples that counter the widely made claim that tunneling is needed for a quantum speedup in optimization problems. The examples belong to the class of perturbed Hamming-weight optimization problems. In one case,…
Counter-diabatic driving protocols were proposed as a means to do fast changes in the Hamiltonian without exciting transitions. Such driving in principle allows one to realize arbitrarily fast annealing protocols or implement fast…
We introduce an algorithm to perform an optimal adiabatic evolution that operates without an apriori knowledge of the system spectrum. By probing the system gap locally, the algorithm maximizes the evolution speed, thus minimizing the total…
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 typical goal of a quantum simulation is to find the energy levels and eigenstates of a given Hamiltonian. This can be realized by adiabatically varying the system control parameters to steer an initial eigenstate into the eigenstate of…
We present a study of the phase diagram of a random optimization problem in presence of quantum fluctuations. Our main result is the characterization of the nature of the phase transition, which we find to be a first-order quantum phase…
This work explores the relationship between optimal control theory and adiabatic passage techniques in quantum systems. The study is based on a geometric analysis of the Hamiltonian dynamics constructed from the Pontryagin Maximum…
The cost and the error of the adiabatic theorem for preparing the final eigenstate are discussed in terms of path length. Previous studies in terms of the norm of the Hamiltonian and its derivatives with the spectral gap are limited in…
Exploiting the similarity between adiabatic quantum algorithms and quantum phase transitions, we argue that second-order transitions -- typically associated with broken or restored symmetries -- should be advantageous in comparison to…
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…
The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm for finding the minimum eigenvalue of a Hamiltonian that involves the optimization of a parameterized quantum circuit. Since the resulting optimization…
We propose and analyze the use of Bayesian optimization techniques to design quantum annealing schedules with minimal user and resource requirements. We showcase our scheme with results for two paradigmatic spin models. We find that…
The accelerated progress in manufacturing noisy intermediate-scale quantum (NISQ) computing hardware has opened the possibility of exploring its application in transforming approaches to solving computationally challenging problems. The…
Among various algorithms designed to exploit the specific properties of quantum computers with respect to classical ones, the quantum adiabatic algorithm is a versatile proposition to find the minimal value of an arbitrary cost function…
We propose a strategy for modeling the behavior of an adiabatic quantum computer described by an Ising Hamiltonian with $N$ sites and the coordination number $Z$. The method is based on the $1/Z$ expansion for the density matrix of the…
Quantum optimization algorithms offer a promising route to finding the ground states of target Hamiltonians on near-term quantum devices. None the less, it remains necessary to limit the evolution time and circuit depth as much as possible,…
In quantum information processing, the development of fast and robust control schemes remains a central challenge. Although quantum adiabatic evolution is inherently robust against control errors, it typically demands long evolution times.…
Quantum annealing (QA) is a promising approach for not only solving combinatorial optimization problems but also simulating quantum many-body systems such as those in condensed matter physics. However, non-adiabatic transitions constitute a…
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…
Quantum adiabatic evolutions find a broad range of applications in quantum physics and quantum technologies. The traditional form of the quantum adiabatic theorem limits the speed of adiabatic evolution by the minimum energy gaps of the…