Related papers: Amplitude amplification and estimation require inv…

Solving non-linear Diophantine systems lies at the mathematical core of integer optimization and cryptography. While the general unbounded problem is undecidable, even over bounded integer domains it remains classically intractable in the…

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…

Over the past few years several quantum machine learning algorithms were proposed that promise quantum speed-ups over their classical counterparts. Most of these learning algorithms either assume quantum access to data -- making it unclear…

Quantum algorithms manipulate the amplitudes of quantum states to find solutions to computational problems. In this work, we present a framework for applying a general class of non-linear functions to the amplitudes of quantum states, with…

Quantum states can in a sense be thought of as generalizations of classical probability distributions, but are more powerful than probability distributions when used for computation or communication. Quantum speedup therefore requires some…

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…

For quantum computation, we investigate the conjecture that the superposition of macroscopically distinct states is necessary for a large quantum speedup. Although this conjecture was supported for a circuit-based quantum computer…

We investigate the reason for the quantum speedup -- quantum algorithms requiring fewer computation steps than their classical counterparts. We extend their representation to the process of setting the problem. The initial measurement…

We present two new quantum algorithms. Our first algorithm is a generalization of amplitude amplification to the case when parts of the quantum algorithm that is being amplified stop at different times. Our second algorithm uses the first…

This paper concerns the Grover algorithm that permits to make amplification of quantum states previously tagged by an Oracle. Grover's algorithm allows searches in an unstructure database of n entries finding a marked element with a…

Algorithms with unitary oracles can be nested, which makes them extremely versatile. An example is the phase estimation algorithm used in many candidate algorithms for quantum speed-up. The search for new quantum algorithms benefits from…

Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…

Amplitude Amplification -- a key component of Grover's Search algorithm -- uses an iterative approach to systematically increase the probability of one or multiple target states. We present novel strategies to enhance the amplification…

This paper focuses on the quantum amplitude estimation algorithm, which is a core subroutine in quantum computation for various applications. The conventional approach for amplitude estimation is to use the phase estimation algorithm, which…

We consider performing phase estimation under the following conditions: we are given only one copy of the input state, the input state does not have to be an eigenstate of the unitary, and the state must not be measured. Most quantum…

Despite intensive research, the physical origin of the speed-up offered by quantum algorithms remains mysterious. No general physical quantity, like, for instance, entanglement, can be singled out as the essential useful resource. Here we…

We investigate the issue of speed-up and the necessity of entanglement in Grover's quantum search algorithm. We find that in a pure state implementation of Grover's algorithm entanglement is present even though the initial and target states…

Classification is at the core of data-driven prediction and decision-making, representing a fundamental task in supervised machine learning. Recently, several quantum machine learning algorithms that use quantum kernels as a measure of…

Identifying the best arm of a multi-armed bandit is a central problem in bandit optimization. We study a quantum computational version of this problem with coherent oracle access to states encoding the reward probabilities of each arm as…

We systematically investigate quantum algorithms and lower bounds for mean estimation given query access to non-identically distributed samples. On the one hand, we give quantum mean estimators with quadratic quantum speed-up given samples…