Related papers: A Dequantized Algorithm for the Guided Local Hamil…
Understanding commuting local Hamiltonians (CLHs) is at the heart of many questions in quantum computational complexity and quantum physics: quantum error correcting codes, quantum NP, the PCP conjecture, topological order and more.
Quantum computation can be achieved by preparing an appropriate initial product state of qudits and then letting it evolve under a fixed Hamiltonian. The readout is made by measurement on individual qudits at some later time. This approach…
Variational quantum algorithms are proposed to solve relevant computational problems on near term quantum devices. Popular versions are variational quantum eigensolvers and quantum ap- proximate optimization algorithms that solve ground…
Finding the ground energy of a quantum system is a fundamental problem in condensed matter physics and quantum chemistry. Existing classical algorithms for tackling this problem often assume that the ground state has a succinct classical…
It is well-known in physics that the limit of large quantum spin $S$ should be understood as a semiclassical limit. This raises the question of whether such emergent classicality facilitates the approximation of computationally hard quantum…
Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning techniques to impressive results in regression, classification, data-generation and reinforcement learning tasks.…
Quantum algorithms that can speed up certain tasks, such as factorisation and unstructured search, have driven a decades-long development of quantum computers and quantum technologies. Yet, outside specialized applications, quantum…
The goal of the present account is to review our efforts to obtain and apply a ``collective'' Hamiltonian for a few, approximately decoupled, adiabatic degrees of freedom, starting from a Hamiltonian system with more or many more degrees of…
A majority of numerical scientific computation relies heavily on handling and manipulating matrices, such as solving linear equations, finding eigenvalues and eigenvectors, and so on. Many quantum algorithms have been developed to advance…
Quantum algorithms on the noisy intermediate-scale quantum (NISQ) devices are expected to simulate quantum systems that are classically intractable to demonstrate quantum advantages. However, the non-negligible gate error on the NISQ…
Using quantum devices supported by classical computational resources is a promising approach to quantum-enabled computation. One example of such a hybrid quantum-classical approach is the variational quantum eigensolver (VQE) built to…
We obtain sufficient conditions for the efficient simulation of a continuous variable quantum algorithm or process on a classical computer. The resulting theorem is an extension of the Gottesman-Knill theorem to continuous variable quantum…
We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression that are comparable to their quantum analogues. De-quantizing such algorithms has received a flurry of…
Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the…
Efficiently simulating quantum circuits on classical computers is a fundamental challenge in quantum computing. This paper presents a novel theoretical approach that achieves substantial speedups over existing simulators for a wide class of…
We introduce a quantum decomposition algorithm (QDA) that decomposes the problem $\frac{\partial \rho}{\partial t}=\mathcal{L}\rho=\lambda \rho$ into a summation of eigenvalues times phase-space variables. One interesting feature of QDA…
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…
The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly…
The conventional Hamiltonian $H= p^2+ V_N(x)$, where the potential $V_N(x)$ is a polynomial of degree $N$, has been studied intensively since the birth of quantum mechanics. In some cases, its spectrum can be determined by combining the WKB…
We prove several new results concerning the pure quantum polynomial hierarchy (pureQPH). First, we show that QMA(2) is contained in pureQSigma2, that is, two unentangled existential provers can be simulated by competing existential and…