Related papers: Scaling of running time of quantum adiabatic algor…
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…
In the last decades, many efforts have focused on analyzing typical-case hardness in optimization and inference problems. Some recent work has pointed out that polynomial algorithms exist, running with a time that grows more than linearly…
Quantum adiabatic optimization seeks to solve combinatorial problems using quantum dynamics, requiring the Hamiltonian of the system to align with the problem of interest. However, these Hamiltonians are often incompatible with the native…
Adiabatic quantum optimization is a procedure to solve a vast class of optimization problems by slowly changing the Hamiltonian of a quantum system. The evolution time necessary for the algorithm to be successful scales inversely with the…
In the last couple of decades, the world has seen several stunning instances of quantum algorithms that provably outperform the best classical algorithms. For most problems, however, it is currently unknown whether quantum algorithms can…
Results are presented of a large-scale simulation of the quantum adiabatic search (QuAdS) algorithm in the presence of noise. The algorithm is applied to the NP-Complete problem Exact Cover 3 (EC3). The noise is assumed to Zeeman-couple to…
We show that by a suitable choice of a time dependent Hamiltonian, Deutsch's algorithm can be implemented by an adiabatic quantum computer. We extend our analysis to the Deutsch-Jozsa problem and estimate the required running time for both…
We illustrate the adiabatic quantum computing solution of the knapsack problem with both integer profits and weights. For problems with $n$ objects (or items) and integer capacity $c$, we give specific examples using both an Ising class…
Quantum computing promises significant improvements of computation capabilities in various fields such as machine learning and complex optimization problems. Recent technological advancements suggest that the adiabatic quantum computing…
This article is a brief introduction to quantum algorithms for the eigenvalue problem in quantum many-body systems. Rather than a broad survey of topics, we focus on providing a conceptual understanding of several quantum algorithms that…
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…
We address lower bounds on the time complexity of algorithms solving the propositional satisfiability problem. Namely, we consider two DPLL-type algorithms, enhanced with the unit clause and pure literal heuristics. Exponential lower bounds…
We propose an adiabatic quantum algorithm for generating a quantum pure state encoding of the PageRank vector, the most widely used tool in ranking the relative importance of internet pages. We present extensive numerical simulations which…
Quantum computation provides exponential speedup for solving certain mathematical problems against classical computers. Motivated by current rapid experimental progress on quantum computing devices, various models of quantum computation…
The quantum speed limit specifies a universal bound of the fidelity between the initial state and the time-evolved state. We apply this method to find a bound of the fidelity between the adiabatic state and the time-evolved state. The bound…
Adiabatic Quantum Computing relies on the quantum adiabatic theorem, which states that a quantum system evolves along its ground state with time if the governing Hamiltonian varies infinitely slowly. However, practical limitations force…
Physical implementations of quantum computation must be scrutinized about their reliability under real conditions, in order to be considered as viable candidates. Among the proposed models, those based on adiabatic quantum dynamics have…
The theoretical investigation of non-adiabatic processes is hampered by the complexity of the coupled electron-nuclear dynamics beyond the Born-Oppenheimer approximation. Classically, the simulation of such reactions is limited by the…
Many problems in quantum information theory can be formulated as optimizations over the sequential outcomes of dynamical systems subject to unpredictable external influences. Such problems include many-body entanglement detection through…
The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous…