Related papers: Quadratic acceleration of multi-step probabilistic…
With reference to a search in a database of size N, Grover states: "What is the reason that one would expect that a quantum mechanical scheme could accomplish the search in O(square root of N) steps? It would be insightful to have a simple…
We develop an adaptive method for quantum state preparation that utilizes randomness as an essential component and that does not require classical optimization. Instead, a cost function is minimized to prepare a desired quantum state…
Realisation of experiments even on small and medium-scale quantum computers requires an optimisation of several parameters to achieve high-fidelity operations. As the size of the quantum register increases, the characterisation of quantum…
Quantum computers are a highly promising tool for efficiently simulating quantum many-body systems. The preparation of their eigenstates is of particular interest and can be addressed, e.g., by quantum phase estimation algorithms. The…
In this study, we give an extension of Montanaro's arXiv/archive:1504.06987 quantum Monte Carlo method, tailored for computing expected values of random variables that exhibit infinite variance. This addresses a challenge in analyzing…
The method is introduced for fast data processing by reducing the probability amplitudes of undesirable elements. The algorithm has a mathematical description and circuit implementation on a quantum processor. The idea is to make a quick…
The preparation of Hamiltonian eigenstates is essential for many applications in quantum computing; the efficiency with which this can be done is of key interest. A canonical approach exploits the quantum phase estimation (QPE) algorithm.…
Quantum Process Tomography (QPT) methods aim at identifying, i.e. estimating, a quantum process. QPT is a major quantum information processing tool, since it especially allows one to experimentally characterize the actual behavior of…
We develop several algorithms for performing quantum phase estimation based on basic measurements and classical post-processing. We present a pedagogical review of quantum phase estimation and simulate the algorithm to numerically determine…
Approximate combinatorial optimization is a promising use case for quantum computers. The quantum optimization algorithms often employ a fixed ansatz that evolves an unbiased initial state towards states with better values of the optimand,…
We present a probabilistic quantum algorithm for preparing mixed states which, in expectation, are proportional to the solutions of Lyapunov equations -- linear matrix equations ubiquitous in the analysis of classical and quantum dynamical…
Imaginary-time evolution, an important technique in tensor network and quantum Monte Carlo algorithms on classical computers, has recently been adapted to quantum computing. In this study, we focus on probabilistic imaginary-time evolution…
We study numerically the effects of static imperfections and residual couplings between qubits for the quantum phase estimation algorithm with two qubits. We show that the success probability of the algorithm is affected significantly more…
We propose an approach for quantum amplitude estimation (QAE) designed to enhance computational efficiency while minimizing the reliance on quantum resources. Our method leverages quantum computers to generate a sequence of signals, from…
Quantum state preparation is a task to prepare a state with a specific function encoded in the amplitude, which is an essential subroutine in many quantum algorithms. In this paper, we focus on multivariate state preparation, as it is an…
We introduce a classical-quantum hybrid approach to computation, allowing for a quadratic performance improvement in the decision process of a learning agent. In particular, a quantum routine is described, which encodes on a quantum…
A central roadblock to analyzing quantum algorithms on quantum states is the lack of a comparable input model for classical algorithms. Inspired by recent work of the author [E. Tang, STOC'19], we introduce such a model, where we assume we…
The principle of teleportation can be used to perform a quantum computation even before its quantum input is defined. The basic idea is to perform the quantum computation at some earlier time with qubits which are part of an entangled…
Quantum mechanics is well known to accelerate statistical sampling processes over classical techniques. In quantitative finance, statistical samplings arise broadly in many use cases. Here we focus on a particular one of such use cases,…
Simulation of quantum matters is a significant application of quantum computers. In contrast to the unitary operation which can be realized naturally on a quantum computer, the implementation of nonunitary operation, widely used in…