Related papers: Efficient Evaluation of Exponential and Gaussian F…
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…
This paper is concerned with exponential moments of integral-of-quadratic functions of quantum processes with canonical commutation relations of position-momentum type. Such quadratic-exponential functionals (QEFs) arise as robust…
We describe an array of quantum gates implementing Shor's algorithm for prime factorization in a quantum computer. The array includes a circuit for modular exponentiation with several subcomponents (such as controlled multipliers, adders,…
We show how to carry out quantum logical operations (controlled-not and Toffoli gates) on encoded qubits for several encodings which protect against various 1-bit errors. This improves the reliability of these operations by allowing one to…
We show a significant reduction of the number of quantum operations and the improvement of the circuit depth for the realization of the Toffoli gate by using qudits. This is done by establishing a general relation between the dimensionality…
We outline a proposal to test quantum mechanics in the high-complexity regime using noisy intermediate-scale quantum (NISQ) devices. The procedure involves simulating a non-Clifford random circuit, followed by its inverse, and then checking…
This article focuses on the development of scalable and quantum bit-efficient algorithms for computing power functions of random quantum states. Two algorithms, based on Hadamard testing and Gate Set Tomography, are proposed. We provide a…
It is imperative that useful quantum computers be very difficult to simulate classically; otherwise classical computers could be used for the applications envisioned for the quantum ones. Perfect quantum computers are unarguably…
In this paper, we introduce an efficient algorithm for the quantum amplitude estimation task which works in noisy intermediate-scale quantum(NISQ) devices. The quantum amplitude estimation is an important problem which has various…
Quantum search algorithm (also known as Grover's algorithm) lays the foundation for many other quantum algorithms. Although it is very simple, its implementation is limited on noisy intermediate-scale quantum (NISQ) processors. Grover's…
Quantum computing (QC) is a new paradigm offering the potential of exponential speedups over classical computing for certain computational problems. Each additional qubit doubles the size of the computational state space available to a QC…
Many quantum algorithms make use of oracles which evaluate classical functions on a superposition of inputs. In order to facilitate implementation, testing, and resource estimation of such algorithms, we present quantum circuits for…
In the era of Noisy Intermediate-Scale Quantum (NISQ) computers it is crucial to design quantum algorithms which do not require many qubits or deep circuits. Unfortunately, the most well-known quantum algorithms are too demanding to be run…
Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind…
Verifying the correct functioning of quantum gates is a crucial step towards reliable quantum information processing, but it becomes an overwhelming challenge as the system size grows due to the dimensionality curse. Recent theoretical…
Classical simulation of real-space quantum dynamics is challenging due to the exponential scaling of computational cost with system dimensions. Quantum computer offers the potential to simulate quantum dynamics with polynomial complexity;…
A massive gap exists between current quantum computing (QC) prototypes, and the size and scale required for many proposed QC algorithms. Current QC implementations are prone to noise and variability which affect their reliability, and yet…
Quantum computation offers the potential to solve fundamental yet otherwise intractable problems across a range of active fields of research. Recently, universal quantum-logic gate sets - the building blocks for a quantum computer - have…
Functions are a fundamental object in mathematics, with countless applications to different fields, and are usually classified based on certain properties, given their domains and images. An important property of a real-valued function is…
Quantum computing (QC) provides a promising avenue toward enabling quantum chemistry calculations, which are classically impossible due to a computational complexity that increases exponentially with system size. As fully fault-tolerant…