Dynamical fidelity of a solid-state quantum computation

Abstract

In this paper we analyze the dynamics in a spin-model of quantum computer. Main attention is paid to the dynamical fidelity (associated with dynamical errors) of an algorithm that allows to create an entangled state for remote qubits. We show that in the regime of selective resonant excitations of qubits there is no any danger of quantum chaos. Moreover, in this regime a modified perturbation theory gives an adequate description of the dynamics of the system. Our approach allows to explicitly describe all peculiarities of the evolution of the system under time-dependent pulses corresponding to a quantum protocol. Specifically, we analyze, both analytically and numerically, how the fidelity decreases in dependence on the model parameters.

Stability of the Quantum Fourier Transformation on the Ising Quantum Computer

“…If only intrinsic errors in the generalized 2πk method are concerned QFT is always more stable than IQFT. Note that the intrinsic errors due to non-resonant transitions for QFT grow as ∼ T 2 (∼ n 6 ) whereas in previously studied "simple" algorithms, for instance entanglement protocol [4], they grow only as the first power of the number of gates ∼ T . This means that QFT is much more sensitive to intrinsic errors.…”

“…The second reason is that it is a complex algorithm, where by complex we mean it has more than O(n) number of quantum gates as opposed to previously studied more simple algorithms where the number of gates scales only linearly with the size of the computer (e.g. entanglement protocol [4]). Previous study of Shor's algorithm in IQC [5] did not use recently introduced generalized 2πk method [6] which is the best known procedure for inducing transitions on IQC.…”

Entropy production and fidelity for quantum many-body systems with noise

“…One should expect that in this situation the perturbation theory works well (see Ref. [35]). Let us see what the perturbation theory gives for our model (32) describing the system within a single pulse.…”

“…According to the quantum protocol, many such resonant transitions take place for different p pulses, with different values of ν p = ω k . The detailed analytical analysis [35] has revealed that in this regime the perturbation theory works very well for many pulses, thus, indicating that there is no any effect of the quantum chaos. Therefore, the implementation of the constant gradient magnetic field is very effective in reducing any kind of decoherence.…”

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.…”