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arXiv:1811.08096 · Physical Review Applied

Experimental Realization of a Fast Controlled- Z Gate via a Shortcut to Adiabaticity

Tenghui Wang, Zhenxing Zhang, Liang Xiang, Zhi-Long Jia, Peng Duan, Zhiwen Zong, Zhenhai Sun, Zhangjingzi Dong, Jianlan Wu, Yi Yin, Guo‐Ping Guo

Published Mar 13, 2019• 49 citations
arXivHTMLPDF

Abstract

In quantum information processing, the shortcut-to-adiabaticity (STA) protocol has been proposed to accelerate a system's adiabatic evolution by introducing an additional, counterdiabatic Hamiltonian. This protocol is particularly suitable for realizing the controlled-$Z$ ($C\phantom{\rule{0}{0ex}}Z$) gate, but a counterdiabatic Hamiltonian requires a variable, complex coupling of qubits. By introducing a representation transformation and a rescaling method, this work uses the STA protocol to obtain a high-fidelity $C\phantom{\rule{0}{0ex}}Z$ gate with two coupled transmon qubits. This method affords high flexibility in the evolution time and control waveform, and is expected to be directly useful in other quantum systems as well.

DOI
10.1103/physrevapplied.11.034030

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In quantum information processing, the shortcut-to-adiabaticity (STA) protocol has been proposed to accelerate a system's adiabatic evolution by introducing an additional, counterdiabatic Hamiltonian. This protocol is particularly suitable for realizing the controlled-ZZZ (C\phantom{\rule{0}{0ex}}Z) gate, but a counterdiabatic Hamiltonian requires a variable, complex coupling of qubits. By introducing a representation transformation and a rescaling method, this work uses the STA protocol to obtain a high-fidelity C\phantom{\rule{0}{0ex}}Z gate with two coupled transmon qubits. This method affords high flexibility in the evolution time and control waveform, and is expected to be directly useful in other quantum systems as well.
Shortcuts to adiabaticity are powerful quantum control methods, allowing quick evolution into target states of otherwise slow adiabatic dynamics. Such methods have widespread applications in quantum technologies, and various shortcuts to adiabaticity protocols have been demonstrated in closed systems. However, realizing shortcuts to adiabaticity for open quantum systems has presented a challenge due to the complex controls in existing proposals. Here, we present the experimental demonstration of shortcuts to adiabaticity for open quantum systems, using a superconducting circuit quantum electrodynamics system. By applying a counterdiabatic driving pulse, we reduce the adiabatic evolution time of a single lossy mode from 800 ns to 100 ns. In addition, we propose and implement an optimal control protocol to achieve fast and qubit-unconditional equilibrium of multiple lossy modes. Our results pave the way for precise time-domain control of open quantum systems and have potential applications in designing fast open-system protocols of physical and interdisciplinary interest, such as accelerating bioengineering and chemical reaction dynamics.
Based on a 'shortcut-to-adiabaticity' (STA) scheme, we theoretically design and experimentally realize a set of high-fidelity single-qubit quantum gates in a superconducting Xmon qubit system. Through a precise microwave control, the qubit is driven to follow a fast 'adiabatic' trajectory with the assistance of a counter-diabatic field and the correction of derivative removal by adiabatic gates. The experimental measurements of quantum process tomography and interleaved randomized benchmarking show that the process fidelities of our STA quantum gates are higher than 94.9% and the gate fidelities are higher than 99.8%, very close to the state-of-art gate fidelity of 99.9%. An alternate of high-fidelity quantum gates is successfully achieved under the STA protocol.
Abstract We review a scheme for the systematic design of quantum control protocols based on shortcuts to adiabaticity in few-level quantum systems. The adiabatic dynamics is accelerated by introducing high-frequency modulations in the control Hamiltonian, which mimic a time-dependent counterdiabatic correction. We present a number of applications for the high-fidelity realization of quantum state transfers and quantum gates based on effective counterdiabatic driving, in platforms ranging from superconducting circuits to Rydberg atoms.
Shortcuts to adiabaticity (STA) is a common protocol to realize high-fidelity and robust quantum control in various quantum systems. To date, STA has been widely applied in two- and three-level systems, whereas designing feasible strategies to achieve perfect quantum state engineering in multi-level systems still remains a challenging task. Here, we propose to use counterdiabatic (CD) driving and time-rescaling (TR) methods to construct multi-state stimulated Raman shortcut-to-adiabatic passage protocols for realizing robust and fast population transfer in chainwise-connected five-state systems. The first protocol is implemented by initially reducing the original five-state system to an equivalent two-state counterpart, and then designing the corresponding driving field by combining CD driving and unitary transformation. Further, we introduce the TR method to optimize the first protocol and thus offers an alternative solution. Numerical calculations show that both protocols can achieve complete population transfer and effectively suppress transient populations of all intermediate states. Compared with the first protocol, the optimized second exhibits better performance within a shorter evolution time.
Abstract Time-rescaling (TR) has been recently proposed as a method to engineer fast processes, also known as shortcuts to adiabaticity (STA), which enables the coherent control of quantum systems beyond the adiabatic regime (Bernardo 2020 Phys. Rev. Res. 2 013133). In this work, we revisit the technique and show that the obtained fast dynamics are transitionless, similar to the ones designed via the famous counterdiabatic (CD) approach. However, contrary to the CD approach, the TR method has the advantage of providing the Hamiltonians that generate the fast processes without requiring information about the instantaneous eigenstates of a reference protocol, and the convenience that experimental implementations dismiss additional coupling fields when compared with the reference adiabatic protocol. Here, we also show that the time evolution of the STA found via TR relates to that of the reference adiabatic protocol by a simple reparametrization of time. To illustrate our findings, we studied the paradigmatic problem of speeding up the stimulated Raman adiabatic passage and found out that TR revealed quantum dynamics more robust to parameter variations than those provided by the CD technique. These results motivate the application of TR to the control of larger quantum systems.
Shortcuts to adiabaticity (STA) provide control protocols to guide the dynamics of a quantum system through an adiabatic reference trajectory in an arbitrary prescheduled time.Designing STA proves challenging in complex quantum systems when the dynamics of the degrees of freedom span different time scales.We introduce counterdiabatic Born-Oppenheimer dynamics (CBOD) as a framework to design STA in systems with a large separation of energy scales.CBOD exploits the Born-Oppenheimer approximation to separate the Hamiltonian into effective fast and slow degrees of freedom and calculate the corresponding counterdiabatic drivings for each sub-system.We show the validity of the CBOD technique via an example of coupled harmonic oscillators, which can be solved exactly for comparison, and further apply it to a system of two-charged particles.