Qubits, Quantum Registers, and Quantum Gates

Paul Isaac Hagouel, Ioannis G. Karafyllidis

Quantum computing is a process that incorporates interacting physical systems that represent quantum bits and quantum gates. We present the quantum bit (qubit), the quantum register and the quantum gates. The qubit is described as a vector in a two-dimensional Hilbert space and the quantum register, which comprises a number of qubits, as a vector in a multidimensional Hilbert space. Quantum gates are Hilbert space operators that rotate the qubit or the quantum register vectors. Quantum computations are modeled and described using a quantum circuit model. We also present a quantum computer simulator based on the circuit model of quantum computation. In this model quantum computations and quantum algorithms are represented by circuits, which comprise quantum gates and quantum registers. The well-known Deutsch's algorithm is described and the corresponding quantum circuit is presented. Possible applications of quantum computers are be presented and discussed.

Bettina Just

Fedor Pavlovich Meshchaninov, Alikhan Magomedrasulov, Leonid Evgenevich Fedichkin

A two-qubit register is simulated using a graph of four quantum dots, each of which has a point contact. One-qubit Pauli gates and two-qubit gates CNOT CZ and CP(π) were implemented, the effect of dephasing created by point contacts on the accuracy of two-qubit gates was calculated numerically, and this system was calculated using the model potential.

Margriet van Riggelen, Jiwon Yun, H. Benjamin van Ommen +1 more

Quantum networks based on optically active solid-state spins may enable quantum technologies including long-range quantum communication and distributed quantum computing. Network nodes containing multiple high-fidelity qubits can facilitate large-scale fault-tolerant operation. However, the stringent error thresholds remain out of reach for multi-qubit registers. In this work, we demonstrate high-fidelity two-qubit gates in a 7-qubit register, based on nuclear spins coupled to a nitrogen-vacancy (NV) center in diamond. We analyze crosstalk in highly connected spin systems, develop an efficient optimization procedure, and characterize the gates using gate set tomography. The two-qubit gate fidelities (best: 99.61(5)%, average: 99.18(2)%) demonstrate a multi-qubit register at the threshold for distributed quantum computation. Finally, as an example application, we perform a variational quantum eigensolver (VQE) simulation of the ground-state energy of H2 and LiH molecules. These results demonstrate one of the key prerequisites for scalable quantum networks based on solid-state spins.

Belal Ehsan Baaquie, L. C. Kwek