Related papers: A Generalization of Bernstein-Vazirani Algorithm t…
Quantum computers leverage the principles of quantum mechanics to do computation with a potential advantage over classical computers. While a single classical computer transforms one particular binary input into an output after applying one…
Classical branching programs are studied to understand the space complexity of computational problems. Prior to this work, Nakanishi and Ablayev had separately defined two different quantum versions of branching programs that we refer to as…
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…
Quantum computing with qudits, quantum systems with $d > 2$ levels, offers a powerful extension beyond qubits, expanding the computational possibilities of quantum systems, allowing the simplification of the implementation of several…
The ability to extract relevant information is critical to learning. An ingenious approach as such is the information bottleneck, an optimisation problem whose solution corresponds to a faithful and memory-efficient representation of…
We discuss quantum algorithms, based on the Bernstein-Vazirani algorithm, for finding which variables a Boolean function depends on. There are 2^n possible linear Boolean functions of n variables; given a linear Boolean function, the…
These notes discuss the quantum algorithms we know of that can solve problems significantly faster than the corresponding classical algorithms. So far, we have only discovered a few techniques which can produce speed up versus classical…
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…
We describe a new implementation of the Bernstein-Vazirani algorithm which relies on the fact that the polarization states of classical light beams can be cloned. We explore the possibility of computing with waves and discuss a classical…
This paper demonstrates the use of entanglement resources in quantum speedup by presenting an algorithm which is the generalization of an algorithm proposed by Goswami and Panigrahi [arXiv:1706.09489 (2017)]. We generalize the algorithm and…
A general quantum algorithm for solving a problem is discussed. The number of steps required to solve a problem using this method is independent of the number of cases that has to be considered classically. Hence, it is more efficient than…
Qudit is a multi-level computational unit alternative to the conventional 2-level qubit. Compared to qubit, qudit provides a larger state space to store and process information, and thus can provide reduction of the circuit complexity,…
Quantum computers are known to be qualitatively more powerful than classical computers, but so far only a small number of different algorithms have been discovered that actually use this potential. It would therefore be highly desirable to…
Quantum computing promises the ability to compute properties of quantum systems exponentially faster than classical computers. Quantum advantage is achieved when a practical problem is solved more efficiently on a quantum computer than on a…
Vector set orthogonal normalization and matrix QR decomposition are fundamental problems in matrix analysis with important applications in many fields. We know that Gram-Schmidt process is a widely used method to solve these two problems.…
We introduce parity quantum optimization with the aim of solving optimization problems consisting of arbitrary $k$-body interactions and side conditions using planar quantum chip architectures. The method introduces a decomposition of the…
Qubits, which are quantum counterparts of classical bits, are used as basic information units for quantum information processing, whereas underlying physical information carriers, e.g. (artificial) atoms or ions, admit encoding of more…
We obtain the strongest separation between quantum and classical query complexity known to date -- specifically, we define a black-box problem that requires exponentially many queries in the classical bounded-error case, but can be solved…
We propose the first near-optimal quantum algorithm for estimating in Euclidean norm the mean of a vector-valued random variable with finite mean and covariance. Our result aims at extending the theory of multivariate sub-Gaussian…
A quantum algorithm for an oracle problem can be understood as a quantum strategy for a player in a two-player zero-sum game in which the other player is constrained to play classically. I formalize this correspondence and give examples of…