Related papers: Classical algorithms for quantum mean values
An important application for near-term quantum computing lies in optimization tasks, with applications ranging from quantum chemistry and drug discovery to machine learning. In many settings --- most prominently in so-called parametrized or…
Quantum algorithms speeding up classical counterparts are proposed for the problems: 1. Recognition of eigenvalues with fixed precision. Given a quantum circuit generating unitary mapping $U$ and a complex number the problem is to determine…
What makes a class of quantum circuits efficiently classically simulable on average? I present a framework that applies harmonic analysis of groups to circuits with a structure encoded by group parameters. Expanding the circuits in a…
A key open question in quantum computing is whether quantum algorithms can potentially offer a significant advantage over classical algorithms for tasks of practical interest. Understanding the limits of classical computing in simulating…
We study quantum algorithms for approximating Lasserre's hierarchy values for polynomial optimization. Let $f,g_1,\ldots,g_m$ be real polynomials in $n$ variables and $f^\star$ the infimum of $f$ over the semialgebraic set $S(g)=\{x:…
We present two methods for the construction of quantum circuits for quantum error-correcting codes (QECC). The underlying quantum systems are tensor products of subsystems (qudits) of equal dimension which is a prime power. For a QECC…
An efficient quantum algorithm is proposed to solve in polynomial time the parity problem, one of the hardest problems both in conventional quantum computation and in classical computation, on NMR quantum computers. It is based on the…
We present quantum algorithms to efficiently perform discriminant analysis for dimensionality reduction and classification over an exponentially large input data set. Compared with the best-known classical algorithms, the quantum algorithms…
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…
The current generation of quantum computing technologies call for quantum algorithms that require a limited number of qubits and quantum gates, and which are robust against errors. A suitable design approach are variational circuits where…
The Quantum Approximate Optimization Algorithm, QAOA, uses a shallow depth quantum circuit to produce a parameter dependent state. For a given combinatorial optimization problem instance, the quantum expectation of the associated cost…
The Quantum Approximate Optimization Algorithm (QAOA) is suggested as a promising application on early quantum computers. Here, a quantum-inspired classical algorithm, the mean-field Approximate Optimization Algorithm (mean-field AOA), is…
Machine learning is a promising application of quantum computing, but challenges remain as near-term devices will have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine…
The Quantum Approximate Optimisation Algorithm is a $p$ layer, time-variable split operator method executed on a quantum processor and driven to convergence by classical outer loop optimisation. The classical co-processor varies individual…
Suppose we have n algorithms, quantum or classical, each computing some bit-value with bounded error probability. We describe a quantum algorithm that uses O(sqrt{n}) repetitions of the base algorithms and with high probability finds the…
Quantum contextuality is a limitation on deterministic hidden variable models, testable in measurement scenarios where outcomes differ under quantum or classical descriptions due to a common set of constraints. When considering measurements…
Quantum-enhanced (i.e., higher performance by quantum effects than any classical methods) mean value estimation of observables is a fundamental task in various quantum technologies; in particular, it is an essential subroutine in quantum…
We introduce a new approach for quantum linear algebra based on quantum subspace states and present three new quantum machine learning algorithms. The first is a quantum determinant sampling algorithm that samples from the distribution…
We discuss a new approach to simulate quantum algorithms using classical probabilistic bits and circuits. Each qubit (a two-level quantum system) is initially mapped to a vector in an eight dimensional probability space (equivalently, to a…
We study the problem of estimating frequency response functions of systems of coupled, classical harmonic oscillators using a quantum computer. The functional form of these response functions can be mapped to a corresponding eigenproblem of…