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arXiv:1501.06294 · Journal of Applied Physics

Quantum logic gates from time-dependent global magnetic field in a system with constant exchange

A. V. Nenashev, A. F. Zinovieva, А. В. Двуреченский, A. Yu. Gornov, Tatiana Zarodnyuk

Published Mar 20, 2015• 9 citations
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Abstract

We propose a method that implements a universal set of one- and two-quantum-bit gates for quantum computation in a system of coupled electron pairs with constant non-diagonal exchange interaction. In our proposal, suppression of the exchange interaction is performed by the continual repetition of single-spin rotations. A small g-factor difference between the electrons allows for addressing qubits and avoiding strong magnetic field pulses. Numerical experiments were performed to show that, to implement the one- and two-qubit operations, it is sufficient to change the strength of the magnetic field by a few Gauss. This introduces one and then the other electron in a resonance. To determine the evolution of the two-qubit system, we use the algorithms of optimal control theory.

DOI
10.1063/1.4915347

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We propose a method that implements a universal set of one- and two-quantum-bit gates for quantum computation in a system of coupled electron pairs with constant non-diagonal exchange interaction. In our proposal, suppression of the exchange interaction is performed by the continual repetition of single-spin rotations. A small g-factor difference between the electrons allows for addressing qubits and avoiding strong magnetic field pulses. Numerical experiments were performed to show that, to implement the one- and two-qubit operations, it is sufficient to change the strength of the magnetic field by a few Gauss. This introduces one and then the other electron in a resonance. To determine the evolution of the two-qubit system, we use the algorithms of optimal control theory.
The construction of a solid-state quantum computer remains a coveted, yet elusive goal. Among the most promising scalable candidates are the spin-based approaches, where qubits are represented by electron spins in quantum dots, or by donor-atom nuclear or electron spins, or by combinations thereof. It has been widely assumed that one-qubit gates in these systems, which are based on single-spin addressing, suffer from severe technical difficulties, including slow speed of operation, heating, and device and materials complexity, such as g-factor engineering. For this reason a variety of approaches have been suggested to circumvent one-qubit gates, including encoding the state of a qubit into two or more spins. These approaches inevitably introduce substantial overhead. Here we show that one-qubit gates can in fact be generated using only modest and presently feasible technological requirements. Our solution uses only global magnetic fields and controllable Heisenberg exchange interactions, thus circumventing the need for single-spin addressing. We explicitly show how to build up one-qubit gates from these components using simple pulse sequences. This should substantially simplify the implemention of spin-based solid state quantum computers.
The physical basis of the method of implementing quantum logical operations in a continuous microwave field in a system of two electrons with different g-factors and a constant exchange interaction is developed. A small variable additive Δ B ( t ) to the magnetic field is proposed as a control action. It is obtained that a simple functional dependence Δ B ( t ), based on harmonic functions, allows us to perform elementary quantum logical operations and their sequences. This method is adapted to the experimental conditions.
Abstract We studied the dynamics of a pair of single-electron double quantum dots (DQDs) under longitudinal and transverse static magnetic fields and time-dependent harmonic modulation of their interaction couplings. We propose to modulate the tunnel coupling between the QDs to produce one-qubit gates and the exchange coupling between DQDs to generate entangling gates, the set of operations required for quantum computing. We developed analytical approximations to set the conditions to control the qubits and applied them to numerical calculations to test the accuracy and robustness of the analytical model. The results shows that the unitary evolution of the two-electron state performs the designed operations even under conditions shifted from the ideal ones.
We propose a method for quantum computation which uses control of spin-orbit coupling in a linear array of single electron quantum dots. Quantum gates are carried out by pulsing the exchange interaction between neighboring electron spins, including the anisotropic corrections due to spin-orbit coupling. Control over these corrections, even if limited, is sufficient for universal quantum computation over qubits encoded into pairs of electron spins. The number of voltage pulses required to carry out either single-qubit rotations or controlled-Not gates scales as the inverse of a dimensionless measure of the degree of control of spin-orbit coupling.
The universal quantum computation is obtained when there exists asymmetric anisotropic exchange between electron spins in coupled semiconductor quantum dots. The asymmetric Heisenberg model can be transformed into the isotropic model through the control of two local unitary rotations for the realization of essential quantum gates. The rotations on each qubit are symmetrical and depend on the strength and orientation of asymmetric exchange. The implementation of the axially symmetric local magnetic fields can assist the construction of quantum logic gates in anisotropic coupled quantum dots. This proposal can efficiently use each physical electron spin as a logical qubit in the universal quantum computation.