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Journal of Experimental and Theoretical Physics

Tomography of Qubit States and Implementation of Quantum Algorithms by Unipolar Pulses

M. V. Bastrakova, N. V. Klenov, Сатанин Аркадий Михайлович

Published Oct 1, 2020• 17 citations
Publisher

Abstract

Abstract The conventional technique for controlling the states of individual qubits and quantum registers is based on the use of high-frequency modulated pulses whose carrier frequency is close to the transition frequency between the ground states of “artificial atoms” and “molecules” (the Rabi technique). In this paper, an alternative concept for controlling superconducting qubits is developed that is based on the idea of fast excitation of a quantum system by solitary unmodulated pulses. The formation of entangled Bell states in a two-qubit superconducting register under the action of field pulses obtained by rapid single flux quantum (RSFQ) devices is demonstrated by numerical simulation. The tomography of quantum states is performed by solving the density matrix equation. It is shown that the technique of “unipolar pulses” allows one to speed up the formation of entangled states (at picosecond times) with a fidelity of 95–98%. The execution of the basic quantum algorithms is demonstrated: the Deutsch–Jozsa algorithm with an accuracy of more than 98% and Grover’s algorithm with an accuracy of 93%.

DOI
10.1134/s1063776120090137

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Abstract Methods for controlling states of interacting superconducting flux qubits using power-efficient devices of fast single-quantum logic (Josephson nonlinearity cavities) are studied. One- and two-qubit quantum logical operations performed within the conventional control technique using Rabi pulses and using picosecond single unipolar magnetic field pulses are comparatively analyzed. It is shown that all main operations can be implemented with an accuracy of better than 97% due to optimization of the shape and parameters of unipolar control pulses (associated with, e.g., propagation of fluxons in transmission lines). The efficiency of the developed technique for programming a two-qubit quantum processor implementing the simplest Deutsch–Jozsa algorithm is demonstrated.
In this paper we discuss methods for controlling the states of interacting superconducting flux qubits using energy-efficient devices of rapid single flux quantum logic (the resonators with Josephson nonlinearity). A comparative analysis for one - and two-qubit quantum logical operations performed both within the traditional control technique using Rabi pulses and using picosecond single unipolar magnetic field pulses is carried out. It is shown that by optimizing the shape and parameters of unipolar control pulses (associated, for example, with the propagation of fluxons in the transmission lines) it is possible to implement all the basic operations with the fidelity of more than 97 %. The efficiency of the developed technique was demonstrated for programming a two-bit quantum processor that implements the simplest Deutsch-Joza algorithm.
The present study is devoted to development of a technique for numerical simulation of the wave function dynamics the single Josephson qubits and arrays of noninteracting qubits controlled by ultra-short pulses. We wish to demonstrate the feasibility of a new principle of basic logical operations on the picosecond timescale. The influence of the unipolar pulse (“fluxon”) form on the evolution of the state during the execution of the quantum one-qubit operations – “NOT”, “READ” and “ NOT ” – is investigated in the presence of decoherence. In the array of non interacting qubits, the question of the influence of the spread of their energy parameters (tunnel constants) is studied. It is shown that a single unipolar pulse can control a huge array of artificial atoms with 10% spread of geometric parameters in the array.
Abstract An ultrafast qubit control concept is proposed and analyzed theoretically to reduce the duration of operations with single and multiple superconducting qubits. It is based on the generation of Ramsey fringes due to unipolar sub-nanosecond control pulses. The interference of waves of qubit states population propagating forward and backward in time play a key role in the concept. The influence of the shape and duration of control pulses on the contrast of the interference pattern is revealed in the frame of Ramsey’s paradigm. Protocols for the observation of Ramsey oscillations and an implementation of various gate operations are developed for flux qubits. We also suggest a notional engineering solution for creating the required sub-nanosecond control pulses with the desired shape and amplitude. It is demonstrated that this makes it possible to control the quantum states of the system with a fidelity of more than 99%.
Abstract The development of quantum computers based on superconductors requires the improvement of the qubit state control approach aimed at the increase of the hardware energy efficiency. A promising solution to this problem is the use of superconducting digital circuits operating with single-flux-quantum (SFQ) pulses, moving the qubit control system into the cold chamber. However, the qubit gate time under SFQ control is still longer than under conventional microwave driving. Here we introduce the bipolar SFQ pulse control based on ternary pulse sequences. We also develop a robust optimization algorithm for finding a sequence structure that minimizes the leakage of the transmon qubit state from the computational subspace. We show that the appropriate sequence can be found for arbitrary system parameters from the practical range. The proposed bipolar SFQ control reduces a single qubit gate time by halve compared to nowadays unipolar SFQ technique, while maintaining the gate fidelity over 99.99%.