Related papers: Effective gaps are not effective: quasipolynomial …
Motivated by the quantum adiabatic algorithm (QAA), we consider the scaling of the Hamiltonian gap at quantum first order transitions, generally expected to be exponentially small in the size of the system. However, we show that a quantum…
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.…
The efficient simulation of quantum dynamics and ground states is a central challenge in physics and a key frontier for quantum advantage. While short-time evolution in one-dimensional systems can often be simulated classically, extending…
Recent works have shown that quantum computers can polynomially speed up certain SAT-solving algorithms even when the number of available qubits is significantly smaller than the number of variables. Here we generalise this approach. We…
We present a quantum-inspired classical algorithm that can be used for graph-theoretical problems, such as finding the densest $k$-subgraph and finding the maximum weight clique, which are proposed as applications of a Gaussian boson…
We present a new technique for efficiently transitioning a quantum system from an initial to a final stationary state in less time than is required by an adiabatic (quasi-static) process. Our approach makes use of Nelson's stochastic…
Designing quantum algorithms with a speedup over their classical analogs is a central challenge in quantum information science. Motivated by recent experimental observations of a superlinear quantum speedup in solving the Maximum…
The propagation of errors severely compromises the reliability of quantum computations. The quantum adiabatic algorithm is a physically motivated method to prepare ground states of classical and quantum Hamiltonians. Here, we analyze the…
We prove that a classical computer can efficiently sample from the photon-number probability distribution of a Gaussian state prepared by using an optical circuit that is shallow and local. Our work generalizes previous known results for…
Quantum algorithms profit from the interference of quantum states in an exponentially large Hilbert space and the fact that unitary transformations on that Hilbert space can be broken down to universal gates that act only on one or two…
This paper explores several aspects of the adiabatic quantum computation model. We first show a way that directly maps any arbitrary circuit in the standard quantum computing model to an adiabatic algorithm of the same depth. Specifically,…
We describe a general methodology for enhancing the efficiency of adiabatic quantum computations (AQC). It consists of homotopically deforming the original "Hamiltonian surface" in a way that the redistribution of the Gaussian curvature…
In this paper we develop a classical algorithm of complexity $O(K \, 2^n)$ to simulate parametrized quantum circuits (PQCs) of $n$ qubits, where $K$ is the total number of one-qubit and two-qubit control gates. The algorithm is developed by…
We study several problems related to properties of non-negative matrices that arise at the boundary between quantum and classical probabilistic computation. Our results are twofold. First, we identify a large class of quantum Hamiltonians…
In this work, we present a new diagrammatic method for computing the effective Hamiltonian of driven nonlinear oscillators. At the heart of our method is a self-consistent perturbation expansion developed in phase space, which establishes a…
We propose an adiabatic-elimination formalism in the dispersive regime based on a transition-centric perturbation theory. The perturbative expansion is recast into a diagrammatic framework, while adiabatic elimination is implemented through…
We introduce a simple framework for estimating lower bounds on the runtime of a broad class of adiabatic quantum algorithms. The central formula consists of calculating the variance of the final Hamiltonian with respect to the initial…
We present a hybrid classical-quantum algorithm to solve optimization problems in current quantum computers, whose basic idea is to assist variational quantum eigensolvers (VQE) with adiabatic change of the Hamiltonian. The rational for…
Topological quantum computing promises error-resistant quantum computation without active error correction. However, there is a worry that during the process of executing quantum gates by braiding anyons around each other, extra anyonic…
We propose a hybrid quantum-classical algorithm for approximating the ground state and ground state energy of a Hamiltonian. Once the Ansatz has been decided, the quantum part of the algorithm involves the calculation of two overlap…