Related papers: Distributed quantum algorithm for discrete logarit…
Integer factorization is a significant problem, with implications for the security of widely-used cryptographic schemes. No efficient classical algorithm for polynomial-time integer factorization has been found despite extensive research.…
Quantum computing not only holds the potential to solve long-standing problems in quantum physics, but also to offer speed-ups across a broad spectrum of other fields. However, due to the noise and the limited scale of current quantum…
Properties of Shor's algorithm and the related period-finding algorithm could serve as benchmarks for the operation of a quantum computer. Distinctive universal behaviour is expected for the probability for success of the period-finding…
Experimental groups are now fabricating quantum processors powerful enough to execute small instances of quantum algorithms and definitively demonstrate quantum error correction that extends the lifetime of quantum data, adding urgency to…
The quantum computer algorithm by Peter Shor for factorization of integers is studied. The quantum nature of a QC makes its outcome random. The output probability distribution is investigated and the chances of a successful operation is…
Variational quantum algorithms have found success in the NISQ era owing to their hybrid quantum-classical approach which mitigate the problems of noise in quantum computers. In our study we introduce the dynamic ansatz in the Variational…
Distributed quantum computation is often proposed to increase the scalability of quantum hardware, as it reduces cooperative noise and requisite connectivity by sharing quantum information between distant quantum devices. However, such…
Nonlinear equations are challenging to solve due to their inherently nonlinear nature. As analytical solutions typically do not exist, numerical methods have been developed to tackle their solutions. In this article, we give a quantum…
Universal fault-tolerant quantum computers require millions of qubits with low error rates. Since this technology is years ahead, noisy intermediate-scale quantum (NISQ) computation is receiving tremendous interest. In this setup, quantum…
Distributed quantum computing can give substantial noise reduction due to shallower circuits. An experiment illustrates the advantages in the case of Grover search. This motivates studying the quantum advantage of the distributed version of…
This paper introduces a noise-aware distributed Quantum Approximate Optimization Algorithm (QAOA) tailored for execution on near-term quantum hardware. Leveraging a distributed framework, we address the limitations of current Noisy…
Quantum algorithms for factoring and discrete logarithm have previously been generalized to finding hidden subgroups of finite Abelian groups. This paper explores the possibility of extending this general viewpoint to finding hidden…
Integer programming (IP) is an NP-hard combinatorial optimization problem that is widely used to represent a diverse set of real-world problems spanning multiple fields, such as finance, engineering, logistics, and operations research. It…
Rapid advancements in cloud based platforms providing access to quantum computing capabilities have opened up several challenges for efficient usage of these highly delicate and costly devices. Although most of the current systems use a…
We consider a recently proposed generalisation of the abelian hidden subgroup problem: the shifted subset problem. The problem is to determine a subset S of some abelian group, given access to quantum states of the form |S+x>, for some…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
Quantum algorithms offer an exponential speedup over classical algorithms for a range of computational problems. The fundamental mechanisms underlying quantum computation required the development and construction of quantum computers. These…
We evaluate the performance of quantum arithmetic algorithms run on a distributed quantum computer (a quantum multicomputer). We vary the node capacity and I/O capabilities, and the network topology. The tradeoff of choosing between gates…
Distributed quantum systems and especially the Quantum Internet have the ever-increasing potential to fully demonstrate the power of quantum computation. This is particularly true given that developing a general-purpose quantum computer is…
We consider a version of Shor's quantum factoring algorithm such that the quantum Fourier transform is replaced by an extremely simple one where decomposition coefficients take only the values of $1,i,-1,-i$. In numerous calculations which…