Related papers: Quantum oracles for the finite element method
Quantum algorithms for scientific computing require modules implementing fundamental functions, such as the square root, the logarithm, and others. We require algorithms that have a well-controlled numerical error, that are uniformly…
Quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given in a black box and the aim is to compute function value for arbitrary input using as few queries as possible. We concentrate on quantum…
We introduce a structured quantum search algorithm that leverages entanglement maps and a fixed-point method to minimize oracle query complexity in unsorted datasets. By partitioning qubits into rows based on their entanglement order, the…
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…
The problem of minimizing the maximum of $N$ convex, Lipschitz functions plays significant roles in optimization and machine learning. It has a series of results, with the most recent one requiring $O(N\epsilon^{-2/3} + \epsilon^{-8/3})$…
In his seminal work on recording quantum queries [Crypto 2019], Zhandry studied interactions between quantum query algorithms and the quantum oracle corresponding to random functions. Zhandry presented a framework for interpreting various…
We propose a class of randomized quantum algorithms for the task of sampling from matrix functions, without the use of quantum block encodings or any other coherent oracle access to the matrix elements. As such, our use of qubits is purely…
The evolution of quantum hardware is highlighting the need for advances in quantum software engineering that help developers create quantum software with good quality attributes. Specifically, reusability has been traditionally considered…
We propose quantum algorithms, purely quantum in nature, for calculating the determinant and inverse of an $(N-1)\times (N-1)$ matrix (depth is $O(N^2\log N)$) which is a simple modification of the algorithm for calculating the determinant…
The partial oracles framework is a quantum search algorithm that has the potential to exceed the quadratic speedup of Grover's algorithm, up to a theoretical maximum of an exponential speedup. Until now, however, the framework has lacked an…
Quantum algorithm is constructed which verifies the formulas of predicate calculus in time $O(\sqrt N)$ with bounded error probability, where $N$ is the time required for classical algorithms. This algorithm uses the polynomial number of…
We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…
This paper employs a powerful argument, called an algorithmic argument, to prove lower bounds of the quantum query complexity of a multiple-block ordered search problem in which, given a block number i, we are to find a location of a target…
Quantum algorithms claim significant speedup over their classical counterparts for solving many problems. An important aspect of many of these algorithms is the existence of a quantum oracle, which needs to be implemented efficiently in…
We describe a general-purpose framework to design quantum algorithms relying upon an efficient handling of arrays. The corner-stone of the framework is the direct embedding of information into quantum amplitudes, thus avoiding the need to…
Classical data encoding is usually treated as a black-box in the oracle-based quantum algorithms. On the other hand, their constructions are crucial for practical algorithm implementations. Here, we open the black-boxes of data encoding and…
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…
We define and study a new type of quantum oracle, the quantum conditional oracle, which provides oracle access to the conditional probabilities associated with an underlying distribution. Amongst other properties, we (a) obtain speed-ups…
Grover's algorithm is a primary algorithm offered as evidence that quantum computers can provide an advantage over classical computers. It involves an "oracle" specified for a given application whose structure is not part of the formal…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…