Related papers: A pseudo-simulation of Shor's quantum factoring al…
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically…
The road to computing on quantum devices has been accelerated by the promises that come from using Shor's algorithm to reduce the complexity of prime factorization. However, this promise hast not yet been realized due to noisy qubits and…
Quantum computation is a promising emerging technology which, compared to conventional computation, allows for substantial speed-ups e.g. for integer factorization or database search. However, since physical realizations of quantum…
We describe quantum-octave package of functions useful for simulations of quantum algorithms and protocols. Presented package allows to perform simulations with mixed states. We present numerical implementation of important quantum…
While quantum computers are capable of simulating many quantum systems efficiently, the simulation algorithms must begin with the preparation of an appropriate initial state. We present a method for generating physically relevant quantum…
Typical circuit implementations of Shor's algorithm involve controlled rotation gates of magnitude $\pi/2^{2L}$ where $L$ is the binary length of the integer N to be factored. Such gates cannot be implemented exactly using existing…
Quantum computers require quantum logic, something fundamentally different to classical Boolean logic. This difference leads to a greater efficiency of quantum computation over its classical counter-part. In this review we explain the basic…
These are the lecture notes of the master's course "Quantum Computing", taught at Chalmers University of Technology every fall since 2020, with participation of students from RWTH Aachen and Delft University of Technology. The aim of this…
We show how the execution time of algorithms on quantum computers depends on the architecture of the quantum computer, the choice of algorithms (including subroutines such as arithmetic), and the ``clock speed'' of the quantum computer. The…
Considering the large-scale quantum computer, it is important to know how much quantum computational resources is necessary precisely and quickly. Unfortunately the previous methods so far cannot support a large-scale quantum computing…
As quantum computing progresses steadily from theory into practice, programmers will face a common problem: How can they be sure that their code does what they intend it to do? This paper presents encouraging results in the application of…
Quantum simulations are designed to model quantum systems, and many compilation frameworks have been developed for executing such simulations on quantum computers. Most compilers leverage the capabilities of digital and analog quantum…
We determine the cost of performing Shor's algorithm for integer factorization on a ternary quantum computer, using two natural models of universal fault-tolerant computing: (i) a model based on magic state distillation that assumes the…
In this paper we discuss the problem of performing elementary finite field arithmetic on a quantum computer. Of particular interest, is the controlled-multiplication operation, which is the only group-specific operation in Shor's algorithms…
With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical…
Quantum Computers offer an intriguing challenge in modern Computer Science. With the inevitable physical limitations to Moore's Law, quantum hardware provides avenues to solve grander problems faster by utilizing Quantum Mechanical…
This paper shows a novel way of simulating a Markov process by a quantum computer. The main purpose of the paper is to show a particular application of quantum computing in the field of stochastic processes analysis. Using a Quantum…
Efficient realization of quantum algorithms is among main challenges on the way towards practical quantum computing. Various libraries and frameworks for quantum software engineering have been developed. Here we present a software package…
Quantum signal processing (QSP) is a powerful quantum algorithm to exactly implement matrix polynomials on quantum computers. Asymptotic analysis of quantum algorithms based on QSP has shown that asymptotically optimal results can in…
In a quantum computer any superposition of inputs evolves unitarily into the corresponding superposition of outputs. It has been recently demonstrated that such computers can dramatically speed up the task of finding factors of large…