Shor’s algorithm solves the integer factoring and discrete logarithm problems in polynomial time. Therefore, the evaluation of Shor’s algorithm is essential for evaluating the security of currently used public-key cryptosystems because the integer factoring and discrete logarithm problems are crucial for the security of these cryptosystems. In this article, a new approximate quantum Fourier transform […]
Large-scale quantum information processing requires the use of quantum error-correcting codes to mitigate the effects of noise in quantum devices. Topological error-correcting codes, such as surface codes, are promising candidates, as they can be implemented using only local interactions in a 2-D array of physical qubits. Procedures, such as defect braiding and lattice surgery, can […]
The well-known 3-bit Hermitian gate (a Toffoli gate) has been implemented using Clifford+T circuits. Compared with the Peres gate, its implementation circuit requires more controlled- not (cnot) gates. However, the Peres gate is not Hermitian. This article reports four 3-bit Hermitian gates named LI gates, whose realized circuits have the same T-count, T-depth, and cnot […]
Quantum random-access lookup of a string of classical bits is a necessary ingredient in several important quantum algorithms. In some cases, the cost of such quantum random-access memory (qRAM) is the limiting factor in the implementation of the algorithm. In this article, we study the cost of fault-tolerantly implementing a qRAM. We construct and analyze […]