Related papers: A quantum-walk-inspired adiabatic algorithm for gr…
Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links.…
This paper presents an advanced DAG-based algorithm for datapath synthesis that targets area minimization using logic-level resource sharing. The problem of identifying common specification logic is formulated using unweighted graph…
We propose a method to obtain optimal protocols for adiabatic ground-state preparation near the adiabatic limit, extending earlier ideas from [D. A. Sivak and G. E. Crooks, Phys. Rev. Lett. 108, 190602 (2012)] to quantum non-dissipative…
In Amin and Choi \cite{AC09}, we show that an adiabatic quantum algorithm for the NP-hard maximum independent set (MIS) problem on a set of special family of graphs in which there are exponentially many local maxima would have the…
Adiabatic quantum algorithms represent a promising approach to universal quantum computation. Whilst in a closed system these algorithms are limited by avoided level crossings, where the gap becomes exponentially small in the system size,…
In this work, we generalize the recently-introduced graph composition framework to the non-boolean setting. A quantum algorithm in this framework is represented by a hypergraph, where each hyperedge is adjacent to multiple vertices. The…
In this paper, we propose algorithms for the graph isomorphism (GI) problem that are based on the eigendecompositions of the adjacency matrices. The eigenvalues of isomorphic graphs are identical. However, two graphs $ G_A $ and $ G_B $ can…
We present the implementation of an algorithm for graph isomorphism testing, based on ideas about number of walks (of sufficiently large length) between vertices. The algorithm is expanded for strongly regular graphs (SRG-s) by testing the…
Continuous-time quantum walks and adiabatic quantum evolution are two general techniques for quantum computing, both of which are described by Hamiltonians that govern their evolutions by Schr\"odinger's equation. In the former, the…
Quantum annealing is a proposed combinatorial optimization technique meant to exploit quantum mechanical effects such as tunneling and entanglement. Real-world quantum annealing-based solvers require a combination of annealing and classical…
We propose a protocol to realize nonadiabatic geometric quantum computation of small-amplitude Schr\"odinger cat qubits via invariant-based reverse engineering. We consider a system with a two-photon driven Kerr nonlinearity, which provides…
We develop a time-dependent real-space renormalization-group approach which can be applied to Hamiltonians with time-dependent random terms. To illustrate the renormalization-group analysis, we focus on the quantum Ising Hamiltonian with…
The two main approaches to quantum computing are gate-based computation and analog computation, which are polynomially equivalent in terms of complexity, and they are often seen as alternatives to each other. In this work, we present a…
A single-loop scenario is proposed to realize nonadiabatic geometric quantum computation. Conventionally, a so-called multi-loop approach is used to remove the dynamical phase accumulated in the operation process for geometric quantum…
We consider a classical and superadiabatic version of an iterative quantum adiabatic algorithm to solve combinatorial optimization problems. This algorithm is deterministic because it is based on purely classical dynamics, that is, it does…
Continuous-time quantum walks provide a natural framework to tackle the fundamental problem of finding a node among a set of marked nodes in a graph, known as spatial search. Whether spatial search by continuous-time quantum walk provides a…
We demonstrate the possibility of (sub)exponential quantum speedup via a quantum algorithm that follows an adiabatic path of a gapped Hamiltonian with no sign problem. This strengthens the superpolynomial separation recently proved by…
The theoretical analysis of the Adiabatic Quantum Computation protocol presents several challenges resulting from the difficulty of simulating, with classical resources, the unitary dynamics of a large quantum device. We present here a…
We introduce a method for the problem of learning the structure of a Bayesian network using the quantum adiabatic algorithm. We do so by introducing an efficient reformulation of a standard posterior-probability scoring function on graphs…
The quantum walk formalism is a widely used and highly successful framework for modeling quantum systems, such as simulations of the Dirac equation, different dynamics in both the low and high energy regime, and for developing a wide range…