Related papers: Quantum hashing with the icosahedral group
Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian…
In this paper we present a new method of coding/decoding algorithms using Fibonacci $Q$-matrices. This method is based on the blocked message matrices. The main advantage of our model is the encryption of each message matrix with different…
Quantum computation offers a promising alternative to classical computing methods in many areas of numerical science, with algorithms that make use of the unique way in which quantum computers store and manipulate data often achieving…
The Variational Quantum Eigensolver approach to the electronic structure problem on a quantum computer involves measurement of the Hamiltonian expectation value. Formally, quantum mechanics allows one to measure all mutually commuting or…
Given a system of equations in a "random" finitely generated subgroup of the braid group, we show how to find a small ordered list of elements in the subgroup, which contains a solution to the equations with a significant probability.…
Near-term quantum computers are primarily limited by errors in quantum operations (or gates) between two quantum bits (or qubits). A physical machine typically provides a set of basis gates that include primitive 2-qubit (2Q) and 1-qubit…
Compiling quantum algorithms for near-term quantum computers (accounting for connectivity and native gate alphabets) is a major challenge that has received significant attention both by industry and academia. Avoiding the exponential…
In the paper we develop a method for constructing quantum algorithms for computing Boolean functions by quantum ordered read-once branching programs (quantum OBDDs). Our method is based on fingerprinting technique and representation of…
We present a novel quantum algorithm for solving the unstructured search problem with one marked element. Our algorithm allows generating quantum circuits that use asymptotically fewer additional quantum gates than the famous Grover's…
Braided groups and braided matrices are novel algebraic structures living in braided or quasitensor categories. As such they are a generalization of super-groups and super-matrices to the case of braid statistics. Here we construct braided…
We describe an efficient quantum algorithm for the quantum Schur transform. The Schur transform is an operation on a quantum computer that maps the standard computational basis to a basis composed of irreducible representations of the…
In this paper, a quantum algorithm based on gaussian process regression model is proposed. The proposed quantum algorithm consists of three sub-algorithms. One is the first quantum subalgorithm to efficiently generate mean predictor. The…
Atom-like emitters in solids are promising platforms for quantum sensing and information processing, but inhomogeneities in the emitter fine structure complicate quantum control. We present a framework that leverages this diversity to…
In this paper, we develop a Lie group theoretic approach for parametric representation of unitary matrices. This leads to develop a quantum neural network framework for quantum circuit approximation of multi-qubit unitary gates. Layers of…
What makes a class of quantum circuits efficiently classically simulable on average? I present a framework that applies harmonic analysis of groups to circuits with a structure encoded by group parameters. Expanding the circuits in a…
The compiling of quantum gates is crucial for the successful quantum algorithm implementations. The environmental noise as well as the bandwidth of control pulses pose a challenge to precise and fast qubit control, especially in a weakly…
Variational quantum algorithms are promising applications of noisy intermediate-scale quantum (NISQ) computers. These algorithms consist of a number of separate prepare-and-measure experiments that estimate terms in a Hamiltonian. The…
Rig groupoids provide a semantic model of \PiLang, a universal classical reversible programming language over finite types. We prove that extending rig groupoids with just two maps and three equations about them results in a model of…
This study presents a roadmap towards utilizing a single arbitrary gate for universal quantum computing. Since two decades ago, it has been widely accepted that almost any single arbitrary gate with qubit number $>2$ is universal. Utilizing…
We propose and analyze an approach to realize quantum computation and simulation using fermionic particles under quantum gas microscopes. Our work is inspired by a recent experimental demonstration of large-scale quantum registers, where…