Related papers: First order phase transition in the Quantum Adiaba…
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…
Quantum simulation with adiabatic annealing can provide insight into difficult problems that are impossible to study with classical computers. However, it deteriorates when the systems scale up due to the shrinkage of the excitation gap and…
The quantum approximate optimization algorithm (QAOA) is one of the canonical algorithms designed to find approximate solutions to combinatorial optimization problems in current noisy intermediate-scale quantum (NISQ) devices. It is an…
Dimensionality reduction is the fundamental problem for machine learning and pattern recognition. During data preprocessing, the feature selection is often demanded to reduce the computational complexity. The problem of feature selection is…
An explicit proof is developed to reinforce the accuracy of the quantum adiabatic theorem in its original form without any inconsistency and/or violation. Based on this proof, we discuss physical implications that give rise to the violation…
We solve the mean-field-like $p$-spin Ising model under a spatio-temporal inhomogeneous transverse field to study the effects of inhomogeneity on the performance of quantum annealing. We find that the problematic first-order quantum phase…
We use elementary variational arguments to prove, and improve on, gap estimates which arise in simulating quantum circuits by adiabatic evolution.
We show that the rate of closing of the energy gap between the ground state and the first excited state, as a function of system size, behaves in many qualitatively different ways at first-order quantum phase transitions of the…
The use of quantum computing to solve a problem in quantum mechanics is illustrated, step by step, by calculating energies and transition amplitudes in a nonrelativistic quark model. The quantum computations feature the use of variational…
The characterization of quantum phase transitions is a fundamental task for the understanding of quantum phases of matter, with a number of potential applications in quantum technologies. In this work, we use digital quantum simulation as a…
Running quantum circuits on quantum computers does not always generate "clean" results, unlike on a simulator, as noise plays a significant role in any quantum device. To explore this, we experimented with the Quantum Approximate…
Quantum-phase-estimation algorithms are critical subroutines in many applications for quantum computers and in quantum-metrology protocols. These algorithms estimate the unknown strength of a unitary evolution. By using coherence or…
First order phase transitions are ubiquitous in nature, however, this notion is ambiguous and highly debated in the case of quantum systems out of thermal equilibrium. We construct a paradigmatic example which allows for elucidating the key…
We consider quantum and classical first-order transitions, at equilibrium and under out-of-equilibrium conditions, mainly focusing on quench and slow quasi-adiabatic protocols. For these phenomena, we review the finite-size scaling theory…
A major challenge facing adiabatic quantum computing is that algorithm design and error correction can be difficult for adiabatic quantum computing. Recent work has considered addressing his challenge by using coherently controlled…
Solving optimization problems with high performance is the target of existing works of Quantum Approximate Optimization Algorithm (QAOA). With this intention, we propose an advanced QAOA based on incremental learning, where the training…
Quantum adiabatic computation is a novel paradigm for the design of quantum algorithms, which is usually used to find the minimum of a classical function. In this paper, we show that if the initial hamiltonian of a quantum adiabatic…
Integer factorization is a computational problem of fundamental importance in cybersecurity and secure communications, as its difficulty form the basis of modern public-key cryptography. While Shor's algorithm can solve this problem…
Some phase transitions of cosmological interest may be weakly first-order and cannot be analyzed by a simple perturbative expansion around mean field theory. We propose a simple two-scalar model--the cubic anisotropy model--as a foil for…
With progress in quantum technology more sophisticated quantum annealing devices are becoming available. While they offer new possibilities for solving optimization problems, their true potential is still an open question. As the optimal…