Related papers: Spectral Gap Analysis for Efficient Tunneling in Q…
We study the asymptotic behavior of the spectral gap of simple barrier tunneling problems, which are related to using quantum annealing to find the global optimum of cost functions defined over n bits. Specifically we look at the problem of…
Quantum annealing is guaranteed to find the ground state of optimization problems in the adiabatic limit. Recent work [Phys. Rev. X 6, 031010 (2016)] has found that for some barrier tunneling problems, quantum annealing can be run much…
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…
Several previous works have investigated the circumstances under which quantum adiabatic optimization algorithms can tunnel out of local energy minima that trap simulated annealing or other classical local search algorithms. Here we…
We explore to what extent path-integral quantum Monte Carlo methods can efficiently simulate the tunneling behavior of quantum adiabatic optimization algorithms. Specifically we look at symmetric cost functions defined over n bits with a…
Perturbed Hamming weight problems serve as examples of optimization instances for which the adiabatic algorithm provably out performs classical simulated annealing. In this work we study the efficiency of the adiabatic algorithm for solving…
Adiabatic quantum computing is a framework for quantum computing that is superficially very different to the standard circuit model. However, it can be shown that the two models are computationally equivalent. The key to the proof is a…
Quantum annealing is a promising algorithm for solving combinatorial optimization problems. It searches for the ground state of the Ising model, which corresponds to the optimal solution of a given combinatorial optimization problem. The…
In adiabatic quantum annealing, the speed with which an anneal can be run, while still achieving a high final ground state fidelity, is dictated by the size of the minimum gap that appears between the ground and first excited state in the…
In the circuit model of quantum computing, amplitude amplification techniques can be used to find solutions to NP-hard problems defined on $n$-bits in time $\text{poly}(n) 2^{n/2}$. In this work, we investigate whether such general…
Quantum annealing (QA) is a method for solving combinatorial optimization problems. We can estimate the computational time for QA using the adiabatic condition. The adiabatic condition consists of two parts: an energy gap and a transition…
Tunneling is often claimed to be the key mechanism underlying possible speedups in quantum optimization via quantum annealing (QA), especially for problems featuring a cost function with tall and thin barriers. We present and analyze…
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.…
Adiabatic quantum optimization offers a new method for solving hard optimization problems. In this paper we calculate median adiabatic times (in seconds) determined by the minimum gap during the adiabatic quantum optimization for an NP-hard…
The quantum adiabatic theorem ensures that a slowly changing system, initially prepared in its ground state, will evolve to its final ground state with arbitrary precision. As a first result this thesis extends the original theorem to…
We explore the relationship between two figures of merit for an adiabatic quantum computation process: the success probability $P$ and the minimum gap $\Delta_{min}$ between the ground and first excited states, investigating to what extent…
The ability to tune quantum tunneling is key for achieving selectivity in manipulation of individual particles in quantum technology applications. In this work we count electron escape events out of a time-dependent confinement potential,…
The Quantum Approximate Optimization Algorithm (QAOA) is a leading approach for combinatorial optimization on near-term quantum devices, yet its scalability is limited by the difficulty of optimizing \(2p\) variational parameters for a…
The time or cost of simulating a quantum circuit by adiabatic evolution is determined by the spectral gap of the Hamiltonians involved in the simulation. In "standard" constructions based on Feynman's Hamiltonian, such a gap decreases…
In this review we consider the performance of the quantum adiabatic algorithm for the solution of decision problems. We divide the possible failure mechanisms into two sets: small gaps due to quantum phase transitions and small gaps due to…