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arXiv:2202.09647 · Physical Review Applied

Experimental Demonstration of Composite Pulses on IBM’s Quantum Computer

Boyan T. Torosov, Nikolay V. Vitanov

Published Sep 23, 2022• 30 citations
arXivHTMLPDF

Abstract

We perform comprehensive experimental tests of various composite pulse sequences using one of the open-access IBM quantum processors, based on superconducting transmon qubits. We implement explicit pulse control of the qubit by making use of the opportunity of low-level access to the backend, provided by IBM Quantum. We obtain the excitation profiles for a huge variety of broadband, narrowband, and passband composite pulses, producing any prechosen target probabilities, ranging from zero to one. We also test universal composite pulses that compensate errors in any experimental parameter. In all experiments, we find excellent agreement between theoretical and experimental excitation profiles. This proves both the composite pulses as a very efficient and flexible quantum control tool and the high quality of the IBM quantum processor. As an extreme example, we test and observe a pronounced narrowband excitation profile for a composite sequence of as many as 1001 pulses.

DOI
10.1103/physrevapplied.18.034062

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We perform comprehensive experimental tests of various composite pulse sequences using one of the open-access IBM quantum processors, based on superconducting transmon qubits. We implement explicit pulse control of the qubit by making use of the opportunity of low-level access to the backend, provided by IBM Quantum. We obtain the excitation profiles for a huge variety of broadband, narrowband, and passband composite pulses, producing any prechosen target probabilities, ranging from zero to one. We also test universal composite pulses that compensate errors in any experimental parameter. In all experiments, we find excellent agreement between theoretical and experimental excitation profiles. This proves both the composite pulses as a very efficient and flexible quantum control tool and the high quality of the IBM quantum processor. As an extreme example, we test and observe a pronounced narrowband excitation profile for a composite sequence of as many as 1001 pulses.
We introduce a quantum control technique using polychromatic pulse trains, consisting of pulses with different carrier frequencies, i.e., different detunings with respect to the qubit transition frequency. We derive numerous polychromatic pulse trains, which generate broadband, narrowband, and passband excitation profiles for different target transition probabilities. This makes it possible to create high-fidelity excitation profiles which are either (i) robust to deviations in the experimental parameters, which is attractive for quantum computing, or (ii) more sensitive to such variations, which is attractive for crosstalk elimination and quantum sensing. The method is demonstrated experimentally using one of IBM's superconducting quantum processors, in a very good agreement between theory and experiment. These results demonstrate both the excellent coherence properties of the IBM qubits and the accuracy, robustness, and flexibility of the proposed quantum control technique. They also show that the detuning is a control parameter which is as efficient as the pulse phase that is commonly used in composite pulses. Hence the method opens a variety of perspectives for quantum control in areas where phase manipulation is difficult or inaccurate.
Composite pulses---sequences of pulses with well-defined relative phases---are an efficient, robust, and flexible technique for coherent control of quantum systems. Composite sequences can compensate for a variety of experimental errors in the driving field (e.g., in the pulse amplitude, duration, detuning, chirp, etc.) or in the quantum system and its environment (e.g., inhomogeneous broadening, stray electric or magnetic fields, unwanted couplings, etc.). The control parameters are the relative phases between the constituent pulses in the composite sequence, an accurate control over which is required in all composite sequences reported hitherto. In this paper, we introduce two types of composite pulse sequences which, in addition to error compensation in the basic experimental parameters, compensate for systematic errors in the composite phases. In the first type of such composite sequences, which compensate for pulse area errors, relative phase errors of over 10% can be tolerated with reasonably short sequences while maintaining the fidelity above the 99.99% quantum computing benchmark. In the second type of composite sequences, which compensate for simultaneous pulse area and detuning errors, relative phase errors of over 5% can be compensated.
We present a systematic SU(2) approach for construction of composite sequences of pulses with smooth temporal shapes that produce high-fidelity two-state excitation profiles. This makes possible the application of composite pulses to quantum control and quantum information processing with short and ultrashort laser pulses. We present an exact analytic formula for the composite phases for arbitrarily accurate broadband pulses and examples of narrowband, passband, and fractional-$\ensuremath{\pi}$ pulses as well as composite pulses with detuning compensation.
A number of composite pulse (CP) sequences for four basic quantum phase gates---the Z, S, T, and general phase gates---are presented. The CP sequences contain up to 18 pulses and can compensate up to eight orders of experimental errors in the pulse amplitude and duration. The short CP sequences (up to eight pulses) are calculated analytically and the longer ones numerically. The results demonstrate the remarkable flexibility of CPs accompanied by extreme accuracy and robustness to errors. These CP sequences, in particular the Z, S, and T gates, can be very useful quantum control tools in quantum information applications, because they provide a variety of options to find the optimal balance among ultrahigh fidelity, error range, and speed, which may be different in different physical applications.
Composite pulses are an efficient tool for robust quantum control. In this work, we derive the form of the composite pulse sequence to implement robust single-qubit gates in a three-level system, where two low-energy levels act as a qubit. The composite pulses can efficiently cancel the systematic errors up to a certain order. We find that the three-pulse sequence cannot completely eliminate the first order of systematic errors, but still availably makes the fidelity resistant to variations in a specific direction. When employing more pulses in the sequence (N>3N>3N>3), the fidelity can be insensitive to the variations in all directions and the robustness region becomes much wider. Finally we demonstrate the applications of composite pulses in quantum information processing, e.g., robust quantum information transfer between two qubits.