Related papers: Canonical Construction of Quantum Oracles
Several prominent quantum computing algorithms--including Grover's search algorithm and Shor's algorithm for finding the prime factorization of an integer--employ subcircuits termed 'oracles' that embed a specific instance of a mathematical…
A foundational question in quantum computational complexity asks how much more useful a quantum state can be in a given task than a comparable, classical string. Aaronson and Kuperberg showed such a separation in the presence of a quantum…
We propose a couple of oracle construction methods for quantum pattern matching. We in turn show that one of the construct can be used with the Grover's search algorithm for exact and partial pattern matching, deterministically. The other…
We present a polynomial-time quantum algorithm making a single query (in superposition) to a classical oracle, such that for every state $|\psi\rangle$ there exists a choice of oracle that makes the algorithm construct an exponentially…
Grover's search algorithm was originally proposed for circuit-based quantum computers. A crucial part of it is to query an oracle -- a black-box unitary operation. Generation of this oracle is formally beyond the original algorithm design.…
Grover's algorithm is a well-known contribution to quantum computing. It searches one value within an unordered sequence faster than any classical algorithm. A fundamental part of this algorithm is the so-called oracle, a quantum circuit…
The search for "a quantum needle in a quantum haystack" is a metaphor for the problem of finding out which one of a permissible set of unitary mappings---the oracles---is implemented by a given black box. Grover's algorithm solves this…
We propose a Hamiltonian-based quantum state preparation method implemented via a shallow parametrized quantum circuit. The approach learns the parameters of a diagonal Hamiltonian through a classical training phase, while the quantum…
A quantum computer promises efficient processing of certain computational tasks that are intractable with classical computer technology. While basic principles of a quantum computer have been demonstrated in the laboratory, scalability of…
A quantum computer encodes information in quantum states and runs quantum algorithms to surpass the classical counterparts by exploiting quantum superposition and quantum correlation. Grover's quantum search algorithm is a typical quantum…
We describe a quantum algorithm to prepare an arbitrary pure state of a register of a quantum computer with fidelity arbitrarily close to 1. Our algorithm is based on Grover's quantum search algorithm. For sequences of states with suitably…
Quantum state preparation is an important class of quantum algorithms that is employed as a black-box subroutine in many algorithms, or used by itself to generate arbitrary probability distributions. We present a novel state preparation…
In a previous paper [quant-ph/0408045] we described a quantum algorithm to prepare an arbitrary state of a quantum register with arbitrary fidelity. Here we present an alternative algorithm which uses a small number of quantum oracles…
The quantum guesswork quantifies the minimum number of queries needed to guess the state of a quantum ensemble if one is allowed to query only one state at a time. Previous approaches to the computation of the guesswork were based on…
In this paper, we present an algorithm for preparing quantum states of the form $\sum_{i=0}^{n-1} \alpha_i |i\rangle$, where the coefficients $\alpha_i$ are specified by a quantum oracle. Our method achieves this task twice as fast as the…
Quantum algorithms use the principles of quantum mechanics, as for example quantum superposition, in order to solve particular problems outperforming standard computation. They are developed for cryptography, searching, optimisation,…
A typical oracle problem is finding which software program is installed on a computer, by running the computer and testing its input-output behaviour. The program is randomly chosen from a set of programs known to the problem solver. As…
The steadily growing research interest in quantum computing - together with the accompanying technological advances in the realization of quantum hardware - fuels the development of meaningful real-world applications, as well as…
Quantum state preparation is an important ingredient for other higher-level quantum algorithms, such as Hamiltonian simulation, or for loading distributions into a quantum device to be used e.g. in the context of optimization tasks such as…
This paper presents an enhancement to Grover's search algorithm for instances where the number of items (or the size of the search problem) $N$ is not a power of 2. By employing an efficient algorithm for the preparation of uniform quantum…