Related papers: Exact quantum algorithms have advantage for almost…
The nature of quantum computation is discussed. It is argued that, in terms of the amount of information manipulated in a given time, quantum and classical computation are equally efficient. Quantum superposition does not permit quantum…
This paper studies the important problem of quantum classification of Boolean functions from a entirely novel perspective. Typically, quantum classification algorithms allow us to classify functions with a probability of $1.0$, if we are…
The quantum query complexity of Boolean matrix multiplication is typically studied as a function of the matrix dimension, n, as well as the number of 1s in the output, \ell. We prove an upper bound of O (n\sqrt{\ell}) for all values of…
In this paper, we consider a quantum algorithm for solving the following problem: ``Suppose $f$ is a function given as a black box (that is also called an oracle) and $f$ is invariant under some AND-mask. Examine a property of $f$ by…
We show an equivalence between 1-query quantum algorithms and representations by degree-2 polynomials. Namely, a partial Boolean function $f$ is computable by a 1-query quantum algorithm with error bounded by $\epsilon<1/2$ iff $f$ can be…
We present an exact quantum algorithm for solving the Exact Satisfiability (XSAT) problem, which belongs to the important NP-complete complexity class. The algorithm is based on an intuitive approach that can be divided into two parts:…
We give a new upper bound on the quantum query complexity of deciding $st$-connectivity on certain classes of planar graphs, and show the bound is sometimes exponentially better than previous results. We then show Boolean formula evaluation…
It is generally believed that entanglement is essential for quantum computing. We present here a few simple examples in which quantum computing without entanglement is better than anything classically achievable, in terms of the reliability…
The quantum hybrid algorithm has become a very promising and speedily method today for solving the larger-scale optimization in the noisy intermediate-scale quantum (NISQ) era. The unit commitment (UC) problem is a fundamental problem in…
Mapping functions on bits to Hamiltonians acting on qubits has many applications in quantum computing. In particular, Hamiltonians representing Boolean functions are required for applications of quantum annealing or the quantum approximate…
Quantum simulation has emerged as a key application of quantum computing, with significant progress made in algorithms for simulating both closed and open quantum systems. The simulation of open quantum systems, particularly those governed…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
Quantum computing is seeking to realize hardware-optimized algorithms for application-related computational tasks. NP (nondeterministic-polynomial-time) is a complexity class containing many important but intractable problems like the…
While efficient algorithms are known for solving many important problems related to groups, no efficient algorithm is known for determining whether two arbitrary groups are isomorphic. The particular case of 2-nilpotent groups, a special…
Quantum algorithms require less operations than classical algorithms. The exact reason of this has not been pinpointed until now. Our explanation is that quantum algorithms know in advance 50% of the solution of the problem they will find…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
Noise is often regarded as anathema to quantum computation, but in some settings it can be an unlikely ally. We consider the problem of learning the class of $n$-bit parity functions by making queries to a quantum example oracle. In the…
Quantum machine learning promises great speedups over classical algorithms, but it often requires repeated computations to achieve a desired level of accuracy for its point estimates. Bayesian learning focuses more on sampling from…
In this paper we propose a new approach to quantum neural networks. Our multi-layer architecture avoids the use of measurements that usually emulate the non-linear activation functions which are characteristic of the classical neural…
We present two new results about exact learning by quantum computers. First, we show how to exactly learn a $k$-Fourier-sparse $n$-bit Boolean function from $O(k^{1.5}(\log k)^2)$ uniform quantum examples for that function. This improves…