Related papers: Distributed quantum algorithm for discrete logarit…
The assumed computationally difficulty of factoring large integers forms the basis of security for RSA public-key cryptography, which specifically relies on products of two large primes or semi-primes. The best-known factoring algorithms…
For quantum computers to successfully solve real-world problems, it is necessary to tackle the challenge of noise: the errors which occur in elementary physical components due to unwanted or imperfect interactions. The theory of quantum…
One of the most promising and versatile approaches to creating new quantum algorithms is based on the quantum hidden subgroup (QHS) paradigm, originally suggested by Alexei Kitaev. This class of quantum algorithms encompasses the…
Quantum computers will allow calculations beyond existing classical computers. However, current technology is still too noisy and imperfect to construct a universal digital quantum computer with quantum error correction. Inspired by the…
As we enter the era of useful quantum computers we need to better understand the limitations of classical support hardware, and develop mitigation techniques to ensure effective qubit utilisation. In this paper we discuss three key…
Quantum computing devices are inevitably subject to errors. To leverage quantum technologies for computational benefits in practical applications, quantum algorithms and protocols must be implemented reliably under noise and imperfections.…
In the era of noisy-intermediate-scale quantum computers, we expect to see quantum devices with increasing numbers of qubits emerge in the foreseeable future. To practically run quantum programs, logical qubits have to be mapped to the…
We present an algorithm to compute the number of solutions of the (constrained) number partitioning problem. A concrete implementation of the algorithm on an Ising-type quantum computer is given.
In the noisy intermediate-scale quantum (NISQ) era, quantum error mitigation (QEM) is essential for producing reliable outputs from quantum circuits. We present a statistical signal processing approach to QEM that estimates the most likely…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
Distributed computing seems to be a natural approach to overcome size limitations of quantum computers in terms of number of qubits. But one lacks an efficient distribution approach to deal systematically with potential algorithms. This…
Pollard's Rho is a method for solving the integer factorization problem. The strategy searches for a suitable pair of elements belonging to a sequence of natural numbers that given suitable conditions yields a nontrivial factor. In…
The next generation of distributed quantum processors combines single-location quantum computing and quantum networking techniques to permit large entangled qubit groups to be established through remote processors, and quantum algorithms…
We present a quantum-inspired tensor network algorithm for solving tridiagonal Quadratic Unconstrained Binary Optimization (QUBO) problems and quadratic unconstrained discrete optimization (QUDO) problems. We also solve the more general…
We provide a polynomial-time classical algorithm for noisy quantum circuits. The algorithm computes the expectation value of any observable for any circuit, with a small average error over input states drawn from an ensemble (e.g. the…
The noisy binary linear problem (NBLP) is known as a computationally hard problem, and therefore, it offers primitives for post-quantum cryptography. An efficient quantum NBLP algorithm that exhibits a polynomial quantum sample and time…
Previously, Bennet and Feynman asked if Heisenberg's uncertainty principle puts a limitation on a quantum computer (Quantum Mechanical Computers, Richard P. Feynman, Foundations of Physics, Vol. 16, No. 6, p597-531, 1986). Feynman's answer…
The development of large quantum computers will have dire consequences for cryptography. Most of the symmetric and asymmetric cryptographic algorithms are vulnerable to quantum algorithms. Grover's search algorithm gives a square root time…
Shor's quantum factoring algorithm finds the prime factors of a large number exponentially faster than any other known method a task that lies at the heart of modern information security, particularly on the internet. This algorithm…
In ensemble (or bulk) quantum computation, measurements of qubits in an individual computer cannot be performed. Instead, only expectation values can be measured. As a result of this limitation on the model of computation, various important…