Related papers: Enhanced Scalability in Assessing Quantum Integer …
Since simulating quantum computers requires exponentially more classical resources, efficient algorithms are extremely helpful. We analyze algorithms that create single qubit and specific controlled qubit matrix representations of gates.…
We identify a sub-class of BQP that captures certain structural commonalities among many quantum algorithms including Shor's algorithms. This class does not contain all of BQP (e.g. Grover's algorithm does not fall into this class). Our…
Current technological advancements of quantum computers highlight the need for application-driven, practical and well-defined methods of benchmarking their performance. As the existing NISQ device's quality of two-qubit gate errors rate is…
Quantum computers promise to solve certain problems more efficiently than their digital counterparts. A major challenge towards practically useful quantum computing is characterizing and reducing the various errors that accumulate during an…
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…
Current asymmetric cryptography is based on the principle that while classical computers can efficiently multiply large integers, the inverse operation, factorization, is significantly more complex. For sufficiently large integers, this…
As the field of quantum computing grows, novel algorithms which take advantage of quantum phenomena need to be developed. As we are currently in the NISQ (noisy intermediate scale quantum) era, quantum algorithm researchers cannot reliably…
Quantum computers require quantum arithmetic. We provide an explicit construction of quantum networks effecting basic arithmetic operations: from addition to modular exponentiation. Quantum modular exponentiation seems to be the most…
The accurate implementation of quantum gates is essential for the realisation of quantum algorithms and digital quantum simulations. This accuracy may be increased on noisy hardware through the variational optimisation of gates, however the…
Numerous methods have been considered to create a fast integer factorization algorithm. Despite its apparent simplicity, the difficulty to find such an algorithm plays a crucial role in modern cryptography, notably, in the security of RSA…
Characterization of quantum processes is a preliminary step necessary in the development of quantum technology. The conventional method uses standard quantum process tomography, which requires $d^2$ input states and $d^4$ quantum…
Quantum information processing offers promising advances for a wide range of fields and applications, provided that we can efficiently assess the performance of the control applied in candidate systems. That is, we must be able to determine…
A Quantum Computer is a new type of computer which can efficiently solve complex problems such as prime factorization. A quantum computer threatens the security of public key encryption systems because these systems rely on the fact that…
With the advent of large-scale quantum annealing devices, several challenges have emerged. For example, it has been shown that the performance of a device can be significantly affected by several degrees of freedom when programming the…
As far as we know, a useful quantum computer will require fault-tolerant gates, and existing schemes demand a prohibitively large space and time overhead. We argue that a first generation quantum computer will be very valuable to design,…
Quantum computing has garnered attention for its potential to solve complex computational problems with considerable speedup. Despite notable advancements in the field, achieving meaningful scalability and noise control in quantum hardware…
Amongst the most remarkable successes of quantum computation are Shor's efficient quantum algorithms for the computational tasks of integer factorisation and the evaluation of discrete logarithms. In this article we review the essential…
We propose two algorithms to factor numbers using Gauss sums and entanglement: (i) in a Shor-like algorithm we encode the standard Gauss sum in one of two entangled states and (ii) in an interference algorithm we create a superposition of…
The implementation and practicality of quantum algorithms highly hinge on the quality of operations within a quantum processor. Therefore, including realistic error models in quantum computing simulation platforms is crucial for testing…
The hope of the quantum computing field is that quantum architectures are able to scale up and realize fault-tolerant quantum computing. Due to engineering challenges, such ''cheap'' error correction may be decades away. In the meantime, we…