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Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring…
Only a few classes of quantum algorithms are known which provide a speed-up over classical algorithms. However, these and any new quantum algorithms provide important motivation for the development of quantum computers. In this article new…
Two-stage stochastic programming is a problem formulation for decision-making under uncertainty. In the first stage, the actor makes a best "here and now" decision in the presence of uncertain quantities that will be resolved in the future,…
Starting from the Quantum-Phase-Estimate (QPE) algorithm, a method is proposed to construct entangled states that describe correlated many-body systems on quantum computers. Using operators for which the discrete set of eigenvalues is…
We study the simultaneous estimation of multiple phases as a discretised model for the imaging of a phase object. We identify quantum probe states that provide an enhancement compared to the best quantum scheme for the estimation of each…
With a combination of the quantum repeater and the cluster state approaches, we show that efficient quantum computation can be constructed even if all the entangling quantum gates only succeed with an arbitrarily small probability $p$. The…
In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…
Quantum computing promises the ability to compute properties of quantum systems exponentially faster than classical computers. Quantum advantage is achieved when a practical problem is solved more efficiently on a quantum computer than on a…
Quantum-limited amplifiers increase the amplitude of quantum signals at the price of introducing additional noise. Quantum purification protocols operate in the reverse way, by reducing the noise while attenuating the signal. Here we…
We introduce a local concept of speed-up applicable to intermediate stages of a quantum algorithm. We use it to analyse the complementary roles played by quantum parallel computation and quantum measurement in yielding the speed-up. A…
In former work, we showed that a quantum algorithm is the sum over the histories of a classical algorithm that knows in advance 50% of the information about the solution of the problem - each history is a possible way of getting the…
Insofar as quantum computation is faster than classical, it appears to be irreversible. In all quantum algorithms found so far the speed-up depends on the extra-dynamical irreversible projection representing quantum measurement. Quantum…
Quantum phase estimation is one of the critical building blocks of quantum computing. For early fault-tolerant quantum devices, it is desirable for a quantum phase estimation algorithm to (1) use a minimal number of ancilla qubits, (2)…
Here we explore which heuristic quantum algorithms for combinatorial optimization might be most practical to try out on a small fault-tolerant quantum computer. We compile circuits for several variants of quantum accelerated simulated…
Quantum state preparation by adiabatic evolution is currently rendered ineffective by the long implementation times of the underlying quantum circuits, comparable to the decoherence time of present and near-term quantum devices. These…
Fault-tolerant quantum computations require alternating quantum and classical computations, where the classical computations prove vital in detecting and correcting errors in the quantum computation. Recently, interest in using these…
Quantum Phase Estimation is a crucial component of several front-running quantum algorithms. Improving the efficiency and accuracy of QPE is currently a very active field of research. In this work, we present a hybrid quantum-classical…
This paper generalizes the quantum amplitude amplification and amplitude estimation algorithms to work with non-boolean oracles. The action of a non-boolean oracle $U_\varphi$ on an eigenstate $|x\rangle$ is to apply a state-dependent…
It is a fundamental principle of quantum theory that an unknown state cannot be copied or, as a consequence, an unknown optical signal cannot be amplified deterministically and perfectly. Here we describe a protocol that provides…
While quantum algorithms for simulation exhibit better asymptotic scaling than their classical counterparts, they currently cannot be implemented on real-world devices. Instead, chemists and computer scientists rely on costly classical…