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arXiv:0911.5465

Hierarchical Genetic Algorithm Approach to Determine Pulse Sequences in NMR

Ashok Ajoy, Anil Kumar

Published Nov 29, 2009• 1 citation
arXivHTMLPDF

Abstract

We develop a new class of genetic algorithm that computationally determines efficient pulse sequences to implement a quantum gate U in a three-qubit system. The method is shown to be quite general, and the same algorithm can be used to derive efficient sequences for a variety of target matrices. We demonstrate this by implementing the inversion-on-equality gate efficiently when the spin-spin coupling constants $J_{12}=J_{23}=J$ and $J_{13}=0$. We also propose new pulse sequences to implement the Parity gate and Fanout gate, which are about 50% more efficient than the previous best efforts. Moreover, these sequences are shown to require significantly less RF power for their implementation. The proposed algorithm introduces several new features in the conventional genetic algorithm framework. We use matrices instead of linear chains, and the columns of these matrices have a well defined hierarchy. The algorithm is a genetic algorithm coupled to a fast local optimizer, and is hence a hybrid GA. It shows fast convergence, and running on a MATLAB platform takes about 20 minutes on a standard personal computer to derive efficient pulse sequences for any target 8X8 matrix $U$.

DOI
10.48550/arxiv.0911.5465

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The experimental implementation of a quantum algorithm requires the decomposition of unitary operators. Here we treat unitary-operator decomposition as an optimization problem, and use a genetic algorithm---a global-optimization method inspired by nature's evolutionary process---for operator decomposition. We apply this method to NMR quantum information processing, and find a probabilistic way of performing universal quantum computation using global hard pulses. We also demonstrate the efficient creation of the singlet state (a special type of Bell state) directly from thermal equilibrium, using an optimum sequence of pulses.
Today, most superconducting quantum processors are based on transmons, the modifications of charge qubits. Traditional transmon control schemes for implementing high-fidelity quantum gates are based on the analog microwave signals. Current problems with this type of control are bulkiness, high cost, and unwanted feedback from the microwave equipment, which increases with the number of qubits involved. A promising breakthrough is the use of superconducting digital circuits operating with picosecond (single flux quantum or SFQ) pulses. In our previous work, we have shown how to use SFQ control sequences to implement the rotation of a qubit at rest on the Bloch sphere around the Y-axis by an angle π/2\pi/2π/2 with fidelity better than 99.99 %\%% . The next important step is to implement two-qubit operations. Here we present the Genetic Algorithm for SFQ Control Sequence Search, which implements the original control protocol using the ZX operation as an example. The algorithm also takes into account the leakage to the higher energy states of the system. Its parallel implementation can find the appropriate sequence for arbitrary system parameters from a practical range in a reasonable time. As a result of numerical experiments, control sequences were found that implement the ZX operation with 0.999 target level population.