Related papers: Translation-Invariant Quantum Algorithms for Order…
We consider the problem of sorting $n$ items, given the outcomes of $m$ pre-existing comparisons. We present a simple and natural deterministic algorithm that runs in $O(m + \log T)$ time and does $O(\log T)$ comparisons, where $T$ is the…
Quantum query complexity plays an important role in studying quantum algorithms, which captures the most known quantum algorithms, such as search and period finding. A query algorithm applies $U_tO_x\cdots U_1O_xU_0$ to some input state,…
A scheme of universal quantum computation on a chain of qubits is described that does not require local control. All the required operations, an Ising-type interaction and spatially uniform simultaneous one-qubit gates, are…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
We present a simple $O(n^4)$-time algorithm for computing optimal search trees with two-way comparisons. The only previous solution to this problem, by Anderson et al., has the same running time, but is significantly more complicated and is…
The optimal runtime of a quantum computer searching a database is typically cited as the square root of the number of items in the database, which is famously achieved by Grover's algorithm. With parallel oracles, however, it is possible to…
We give an O(sqrt n log n)-query quantum algorithm for evaluating size-n AND-OR formulas. Its running time is poly-logarithmically greater after efficient preprocessing. Unlike previous approaches, the algorithm is based on a quantum walk…
It is known that quantum computers yield a speed-up for certain discrete problems. Here we want to know whether quantum computers are useful for continuous problems. We study the computation of the integral of functions from the classical…
Probabilistic language models, e.g. those based on an LSTM, often face the problem of finding a high probability prediction from a sequence of random variables over a set of tokens. This is commonly addressed using a form of greedy decoding…
Factoring large integers using a quantum computer is an outstanding research problem that can illustrate true quantum advantage over classical computers. Exponential time order is required in order to find the prime factors of an integer by…
Sorting is a fundamental computational process, which facilitates subsequent searching of a database. It can be thought of as factorisation of the search process. The location of a desired item in a sorted database can be found by classical…
This paper shows that a quantum mechanical algorithm that can query information relating to multiple items of the database, can search a database in a single query (a query is defined as any question to the database to which the database…
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 address the problem of learning an unknown unitary transformation from a finite number of examples. The problem consists in finding the learning machine that optimally emulates the examples, thus reproducing the unknown unitary maximum…
Quantum partial search algorithm is approximate search. It aims to find a target block (which has the target items). It runs a little faster than full Grover search. In this paper, we consider quantum partial search algorithm for multiple…
The continuous-time query model is a variant of the discrete query model in which queries can be interleaved with known operations (called "driving operations") continuously in time. Interesting algorithms have been discovered in this…
One of the significant breakthroughs in quantum computation is Grover's algorithm for unsorted database search. Recently, the applications of Grover's algorithm to solve global optimization problems have been demonstrated, where unknown…
This work proposes a computational procedure that uses a quantum walk in a complete graph to train classical artificial neural networks. The idea is to apply the quantum walk to search the weight set values. However, it is necessary to…
The task of finding an entry in an unsorted list of $N$ elements famously takes $O(N)$ queries to an oracle for a classical computer and $O(\sqrt{N})$ queries for a quantum computer using Grover's algorithm. Reformulated as a spatial search…
In this note we study the number of quantum queries required to identify an unknown multilinear polynomial of degree d in n variables over a finite field F_q. Any bounded-error classical algorithm for this task requires Omega(n^d) queries…