Related papers: Quantum circuits for solving one-dimensional Schr\…
The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other…
A number of quantum algorithms have been performed on small quantum computers; these include Shor's prime factorization algorithm, error correction, Grover's search algorithm and a number of analog and digital quantum simulations. Because…
Quantum computers are the promising candidates for simulation of large quantum systems, which is a daunting task to perform in a classical computer. Here, we report the experimental realization of quantum tunneling of a single particle…
This work presents a quantum algorithm for solving linear systems of equations of the form $\mathbf{A}{\frac{\mathbf{\partial f}}{\mathbf{\partial x}}} = \mathbf{B}\mathbf{f}$, based on the Quantum Singular Value Transformation (QSVT). The…
Although quantum circuits have been ubiquitous for decades in quantum computing, the first complete equational theory for quantum circuits has only recently been introduced. Completeness guarantees that any true equation on quantum circuits…
Quantum algorithms are known for providing more efficient solutions to certain computational tasks than any corresponding classical algorithm. Here we show that a single qudit is sufficient to implement an oracle based quantum algorithm,…
Quantum computers are expected to give major speed-ups for the simulation of quantum systems. In these conference proceedings, we discuss quantum algorithms for the simulation of perturbative Quantum Chromodynamics (QCD) processes. In…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…
We explicitly construct a quantum circuit which exactly generates random three-qubit states. The optimal circuit consists of three CNOT gates and fifteen single qubit elementary rotations, parametrized by fourteen independent angles. The…
Understanding the capacity of quantum circuits through the lens of approximation theory is essential for evaluating the complexity of quantum circuits required to solve various problems in scientific computation. We design quantum circuits…
We present a method that outputs a sequence of simple unitary operations to prepare a given quantum state that is a generalized coherent state. Our method takes as inputs the expectation values of some relevant observables on the state to…
Quantum computing promises exponential improvements in solving large systems of partial differential equations (PDE), which forms a bottleneck in high-resolution computational fluid dynamics (CFD) simulations, in, among others, aerospace…
In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schr\"odinger equation, which is solved for the wave function, bound…
Using the tensor product representation in the density matrix renormalization group, we show that a quantum circuit of Grover's algorithm, which has one-qubit unitary gates, generalized Toffoli gates, and projective measurements, can be…
Classical simulators play a major role in the development and benchmark of quantum algorithms and practically any software framework for quantum computation provides the option of running the algorithms on simulators. However, the…
Spins based in silicon provide one of the most promising architectures for quantum computing. A scalable design for silicon-germanium quantum dot qubits is presented. The design incorporates vertical and lateral tunneling. Simulations of a…
We give quantum circuits that simulate an arbitrary two-qubit unitary operator up to global phase. For several quantum gate libraries we prove that gate counts are optimal in worst and average cases. Our lower and upper bounds compare…
The commonly used circuit model of quantum computing leaves out the problems of imprecision in the initial state preparation, particle statistics (indistinguishability of particles belonging to the same quantum state), and error correction…
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 this paper, we present efficient quantum algorithms that are exponentially faster than classical algorithms for solving the quantum optimal control problem. This problem involves finding the control variable that maximizes a physical…