Related papers: Entropic barriers as a reason for hardness in both…
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…
Run-times of quantum algorithms are often studied via an asymptotic, worst-case analysis. Whilst useful, such a comparison can often fall short: it is not uncommon for algorithms with a large worst-case run-time to end up performing well on…
Of late, we are witnessing spectacular developments in Quantum Information Processing with the availability of Noisy Intermediate-Scale Quantum devices of different architectures and various software development kits to work on quantum…
Large-scale quantum information processing requires the use of quantum error correcting codes to mitigate the effects of noise in quantum devices. Topological error-correcting codes, such as surface codes, are promising candidates as they…
Physically motivated classical heuristic optimization algorithms such as simulated annealing (SA) treat the objective function as an energy landscape, and allow walkers to escape local minima. It has been argued that quantum properties such…
Motivated by recent progress in quantum hardware and algorithms researchers have developed quantum heuristics for optimization problems, aiming for advantages over classical methods. To date, quantum hardware is still error-prone and…
Solving linear systems of equations is essential for many problems in science and technology, including problems in machine learning. Existing quantum algorithms have demonstrated the potential for large speedups, but the required quantum…
Quantum algorithms for combinatorial optimization typically encode constraints as soft penalties within the objective function, which can reduce efficiency and scalability compared to state-of-the-art classical methods that instead exploit…
Boolean satisfiability [1] (k-SAT) is one of the most studied optimization problems, as an efficient (that is, polynomial-time) solution to k-SAT (for $k\geq 3$) implies efficient solutions to a large number of hard optimization problems…
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…
Despite the promise that fault-tolerant quantum computers can efficiently solve classically intractable problems, it remains a major challenge to find quantum algorithms that may reach computational advantage in the present era of noisy,…
Adiabatic quantum programming defines the time-dependent mapping of a quantum algorithm into an underlying hardware or logical fabric. An essential step is embedding problem-specific information into the quantum logical fabric. We present…
A recent paper on quantum walks by Childs et al. [STOC'03] provides an example of a black-box problem for which there is a quantum algorithm with exponential speedup over the best classical randomized algorithm for the problem, but where…
In this paper we show that the performance of the quantum adiabatic algorithm is determined by phase transitions in underlying problem in the presence of transverse magnetic field $\Gamma$. We show that the quantum version of random…
We present the results of a numerical study, with 20 qubits, of the performance of the Quantum Adiabatic Algorithm on randomly generated instances of MAX 2-SAT with a unique assignment that maximizes the number of satisfied clauses. The…
We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. The algorithm can be seen as an analogue of quantum annealing under the restriction of a product state space, where…
In the quantum optimization paradigm, variational quantum algorithms face challenges with hardware-specific and instance-dependent parameter tuning, which can lead to computational inefficiencies. The promising potential of parameter…
Hardware accelerators like quantum annealers or neuromorphic chips are capable of finding the ground state of a Hamiltonian. A promising route in utilizing these devices is via methods from automated reasoning: The problem at hand is first…
We determine the classical and quantum complexities of a specific ensemble of three-satisfiability problems with a unique satisfying assignment for up to N=100 and N=80 variables, respectively. In the classical limit we employ generalized…
The quantum adiabatic unstructured search algorithm is one of only a handful of quantum adiabatic optimization algorithms to exhibit provable speedups over their classical counterparts. With no fault tolerance theorems to guarantee the…