Related papers: Pitfalls of the sublinear QAOA-based factorization…
We perform logical and physical resource estimation for computing binary elliptic curve discrete logarithms using Shor's algorithm on fault-tolerant quantum computers. We adopt a windowed approach to design our circuit implementation of the…
Major obstacles remain to the implementation of macroscopic quantum computing: hardware problems of noise, decoherence, and scaling; software problems of error correction; and, most important, algorithm construction. Finding truly quantum…
Quantum Approximation Optimization Algorithm (QAOA) is a highly advocated variational algorithm for solving the combinatorial optimization problem. One critical feature in the quantum circuit of QAOA algorithm is that it consists of…
Quantum devices use qubits to represent information, which allows them to exploit important properties from quantum physics, specifically superposition and entanglement. As a result, quantum computers have the potential to outperform the…
QAOA is a hybrid quantum-classical algorithm to solve optimization problems in gate-based quantum computers. It is based on a variational quantum circuit that can be interpreted as a discretization of the annealing process that 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 approximate optimization algorithm (QAOA) is one of the popular quantum algorithms that are used to solve combinatorial optimization problems via approximations. QAOA is able to be evaluated on both physical and virtual quantum…
NP-hard problems are not believed to be exactly solvable through general polynomial time algorithms. Hybrid quantum-classical algorithms to address such combinatorial problems have been of great interest in the past few years. Such…
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…
Shor and Grover demonstrated that a quantum computer can outperform any classical computer in factoring numbers and in searching a database by exploiting the parallelism of quantum mechanics. Whereas Shor's algorithm requires both…
We show that $n$-bit integers can be factorized by independently running a quantum circuit with $\tilde{O}(n^{3/2})$ gates for $\sqrt{n}+4$ times, and then using polynomial-time classical post-processing. The correctness of the algorithm…
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…
Quantum computer hardware is predicted to scale over hundreds of thousands of qubits coming online in the next decade. Despite significant theoretical and experimental QEC progress, quantum computer architecture has suffered a significant…
Protein folding processes are a vital aspect of molecular biology that is hard to simulate with conventional computers. Quantum algorithms have been proven superior for certain problems and may help tackle this complex life science…
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…
The availability of working quantum computers has led to several proposals and claims of quantum advantage. In 2023, this has included claims that quantum computers can successfully factor large integers, by optimizing the search for nearby…
Very recently, Monz, et al. [arXiv:1507.08852] have reported the demonstration of factoring 15 using a scalable Shor algorithm with an ion-trap quantum computer. In this note, we remark that the report is somewhat misleading because there…
Integer factorization is a fundamental problem in algorithmic number theory and computer science. It is considered as a one way or trapdoor function in the (RSA) cryptosystem. To date, from elementary trial division to sophisticated methods…
Most quantum algorithms that give an exponential speedup over classical algorithms exploit the Fourier transform in some way. In Shor's algorithm, sampling from the quantum Fourier spectrum is used to discover periodicity of the modular…
The Quantum Approximate Optimization Algorithm (QAOA) by Farhi et al. is a quantum computational framework for solving quantum or classical optimization tasks. Here, we explore using QAOA for Binary Linear Least Squares (BLLS); a problem…