Perturbation theory and numerical modeling of quantum logic operations with a large number of qubits

Abstract

Abstract. The perturbation theory is developed based on small parameters which naturally appear in solid state quantum computation. We report the simulations of the dynamics of quantum logic operations with a large number of qubits (up to 1000). A nuclear spin chain is considered in which selective excitations of spins are provided by having a uniform gradient of the external magnetic field. Quantum logic operations are utilized by applying resonant electromagnetic pulses. The spins interact with their nearest neighbors. We simulate the creation of the long-distance entanglement between remote qubits in the spin chain. Our method enables us to minimize unwanted non-resonant effects in a controlled way. The method we use cannot simulate complicated quantum logic (a quantum computer is required to do this), but it can be useful to test the experimental performance of simple quantum logic operations. We show that: (a) the probability distribution of unwanted states has a "band" structure, (b) the directions of spins in typical unwanted states are highly correlated, and (c) many of the unwanted states are high-energy states of a quantum computer (a spin chain). Our approach can be applied to simple quantum logic gates and fragments of quantum algorithms involving a large number of qubits.

Study of Decoherence of Elementary Gates Implemented in a Chain of Few Nuclear Spins Quantum Computer Model

“…One of the used approaches for quantum discrete system is described in [30], where it was used for studying sudden death of entanglement of two qubits. We will use this approach for our study of decoherence of several quantum gates during operation in a quantum computer model made up of a linear chain of three paramagnetic atoms with nuclear spin one half [31,34,36]. In this work, we are interested in determine the decoherence of a single qubit rotation, quantum controlled-not (CNOT), and quantum controlled-controllednot (C 2 NOT) gates during their implementation on this quantum computer model.…”

Quasi non-Markovian Approach to the Study of Decoherence of a Controlled-Not Quantum Gate in a Chain of Few Nuclear Spins Quantum Computer

“…We use the weak coupling approximation for a system consisting of a linear chain of three paramagnetic atoms with nuclear spin one half [19], interacting with a thermal reservoir (not pure) consisting of a bosonic bath [20][21][22]. The temporal dependence in some terms, in the weak coupling approximation, is what we have considered as something beyond Markovian which is totally related to this type of system, and more specifically, to the Ising interaction between the nuclear spins.…”

“…Then by doing a successive change of variables and substituting in (19), up to second order terms, using Markov approximation and Equation (12), we obtain …”

Modeling Full Adder in Ising Spin Quantum Computer With 1000 Qubits Using Quantum Maps

“…(ii) Due to the nonlocality of interaction of the rf pulses with the qubits, the direct simulation of the dynamics requires either the solution of large system of coupled differential equations for a long period of time or the diagonalization of large matrices. In order to overcome these difficulties a perturbation theory was developed in our previous papers [1][2][3][4][5][6][7][8][9]. In this paper we apply our perturbation approach to simulate the dynamics of a full adder with 1000 qubits.…”