Related papers: First-order transitions and the performance of qua…
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.…
The Quantum Approximate Optimization Algorithm and its generalization to Quantum Alternating Operator Ansatz (QAOA) is a promising approach for applying quantum computers to challenging problems such as combinatorial optimization and…
We study the eigenlevel spectrum of quantum adiabatic algorithm for 3-satisfiability problem, focusing on single-solution instances. The properties of the ground state and the associated gap, crucial for determining the running time of the…
We show, for quantum annealing, that a certain type of inhomogeneous driving of the transverse field erases first-order quantum phase transitions in the p-body interacting mean-field-type model with and without longitudinal random field.…
We introduce and review briefly the phenomenon of quantum annealing and analog computation. The role of quantum fluctuation (tunneling) in random systems with rugged (free) energy landscapes having macroscopic barriers are discussed to…
Adiabatic quantum algorithms are characterized by their run time and accuracy. The relation between the two is essential for quantifying adiabatic algorithmic performance, yet is often poorly understood. We study the dynamics of a…
Adiabatic quantum computation employs a slow change of a time-dependent control function (or functions) to interpolate between an initial and final Hamiltonian, which helps to keep the system in the instantaneous ground state. When the…
Quantum annealing is a generic name of quantum algorithms to use quantum-mechanical fluctuations to search for the solution of optimization problem. It shares the basic idea with quantum adiabatic evolution studied actively in quantum…
While there are various approaches to benchmark physical processors, recent findings have focused on computational phase transitions. This is due to several factors. Importantly, the hardest instances appear to be well-concentrated in a…
In this paper we analyze the performance of the Quantum Adiabatic Evolution algorithm on a variant of Satisfiability problem for an ensemble of random graphs parametrized by the ratio of clauses to variables, $\gamma=M/N$. We introduce a…
We analyze the complexity of the quantum optimization algorithm based on adiabatic evolution for the set partition problem. We introduce a cost function defined on a logarithmic scale of the partition residues so that the total number of…
Quantum computation by adiabatic evolution, as described in quant-ph/0001106, will solve satisfiability problems if the running time is long enough. In certain special cases (that are classically easy) we know that the quantum algorithm…
In this Letter, we numerically present the possibility of the first-order phase transition occurring through the thermal fluctuation in the early universe. We find that when the temperature is slightly higher than the mass scale of the…
The preparation of a given quantum state on a quantum computing register is a typically demanding operation, requiring a number of elementary gates that scales exponentially with the size of the problem. Using the adiabatic theorem for…
First order quantum phase transitions (1QPTs) are signaled, in the thermodynamic limit, by discontinuous changes in the ground state properties. These discontinuities affect expectation values of observables, including spatial correlations.…
The observation that concepts from quantum information has generated many alternative indicators of quantum phase transitions hints that quantum phase transitions possess operational significance with respect to the processing of quantum…
Natural systems often exhibit chaotic behavior in their space-time evolution. Systems transiting between chaos and order manifest a potential to compute, as shown with cellular automata and artificial neural networks. We demonstrate that…
Classical optimization problems can be solved by adiabatically preparing the ground state of a quantum Hamiltonian that encodes the problem. The performance of this approach is determined by the smallest gap encountered during the…
The smallness of the variation rate of the hamiltonian matrix elements compared to the (square of the) energy spectrum gap is usually believed to be the key parameter for a quantum adiabatic evolution. However it is only perturbatively…
We demonstrate that first-order phase transitions in 1+1-dimensional nonequilibrium systems with fluctuating ordered phases are impossible, provided that there are no additional conservation laws, long-range interactions, macroscopic…