Related papers: Exact quantum Fourier transforms and discrete loga…
An exact, one-to-one transform is presented that not only allows digital circular convolutions, but is free from multiplications and quantisation errors for transform lengths of arbitrary powers of two. The transform is analogous to the…
Quantum walks (QWs) are of interest as examples of uniquely quantum behavior and are applicable in a variety of quantum search and simulation models. Implementing QWs on quantum devices is useful from both points of view. We describe a…
Due to the great difficulty in scalability, quantum computers are limited in the number of qubits during the early stages of the quantum computing regime. In addition to the required qubits for storing the corresponding eigenvector, suppose…
Quantum algorithm is constructed which verifies the formulas of predicate calculus in time $O(\sqrt N)$ with bounded error probability, where $N$ is the time required for classical algorithms. This algorithm uses the polynomial number of…
One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log_2 N queries to the list, a quantum computer can solve the problem…
The quantum permutation algorithm provides computational speed-up over classical algorithms in determining the parity of a given cyclic permutation. For its $n$-qubit implementations, the number of required quantum gates scales…
Quantum state preparation is an important ingredient for other higher-level quantum algorithms, such as Hamiltonian simulation, or for loading distributions into a quantum device to be used e.g. in the context of optimization tasks such as…
The standard circuit model for quantum computation presumes the ability to directly perform gates between arbitrary pairs of qubits, which is unlikely to be practical for large-scale experiments. Power-law interactions with strength…
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,…
We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…
Shor's factorisation algorithm is a combination of classical pre- and post-processing and a quantum period finding (QPF) subroutine which allows an exponential speed up over classical factoring algorithms. We consider the stability of this…
Monte Carlo integration is a widely used numerical method for approximating integrals, which is often computationally expensive. In recent years, quantum computing has shown promise for speeding up Monte Carlo integration, and several…
Quantum computers are able to outperform classical algorithms. This was long recognized by the visionary Richard Feynman who pointed out in the 1980s that quantum mechanical problems were better solved with quantum machines. It was only in…
In this work, we show the characterization of quantum iterations that would generally construct quantum amplitude amplification algorithms with a quadratic speedup, namely, quantum amplitude amplification operators (QAAOs). Exact quantum…
A common starting point of traditional quantum algorithm design is the notion of a universal quantum computer with a scalable number of qubits. This convenient abstraction mirrors classical computations manipulating finite sets of symbols,…
Effective quantum computation relies upon making good use of the exponential information capacity of a quantum machine. A large barrier to designing quantum algorithms for execution on real quantum machines is that, in general, it is…
Hamiltonian simulation is known to be one of the fundamental building blocks of a variety of quantum algorithms such as its most immediate application, that of simulating many-body systems to extract their physical properties. In this work,…
We present a general method for the implementation of quantum algorithms that optimizes both gate count and circuit depth. Our approach introduces connectivity-adapted CNOT-based building blocks called Parity Twine chains. It outperforms…
Shor's algorithm for factoring in polynomial time on a quantum computer\cite{Shor} gives an enormous advantage over all known classical factoring algorithm. We demonstrate how to factor products of large prime numbers using a compiled…
The quantum Fourier transform (QFT) is a ubiquitous quantum operation that is used in numerous quantum computing applications. The major obstacle to constructing a QFT circuit is that numerous elementary gates are required. Among the…