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arXiv:2312.11594 · Annalen der Physik

Shortcut‐to‐Adiabatic Controlled‐Phase Gate in Rydberg Atoms

Luis S. Yagüe Bosch, Tim Ehret, Francesco Petiziol, E. Arimondo, Sandro Wimberger

Published Nov 8, 2023• 12 citations
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Abstract

Abstract A shortcut‐to‐adiabatic protocol for the realization of a fast and high‐fidelity controlled‐phase gate in Rydberg atoms is developed. The adiabatic state transfer, driven in the high‐blockade limit, is sped up by compensating nonadiabatic transitions via oscillating fields that mimic a counterdiabatic Hamiltonian. High fidelities are obtained in wide parameter regions. The implementation of the bare effective counterdiabatic field, without original adiabatic pulses, enables to bypass gate errors produced by the accumulation of blockade‐dependent dynamical phases, making the protocol efficient also at low blockade values. As an application toward quantum algorithms, how the fidelity of the gate impacts the efficiency of a minimal quantum‐error correction circuit is analyzed.

DOI
10.1002/andp.202300275

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Abstract A shortcut‐to‐adiabatic protocol for the realization of a fast and high‐fidelity controlled‐phase gate in Rydberg atoms is developed. The adiabatic state transfer, driven in the high‐blockade limit, is sped up by compensating nonadiabatic transitions via oscillating fields that mimic a counterdiabatic Hamiltonian. High fidelities are obtained in wide parameter regions. The implementation of the bare effective counterdiabatic field, without original adiabatic pulses, enables to bypass gate errors produced by the accumulation of blockade‐dependent dynamical phases, making the protocol efficient also at low blockade values. As an application toward quantum algorithms, how the fidelity of the gate impacts the efficiency of a minimal quantum‐error correction circuit is analyzed.
Rydberg Atoms Quantum gates are the backbone of digital quantum computing. In article number 2300275, Luis S. Yagüe Bosch, Sandro Wimberger, and colleagues present a shortcut-to-adiabatic protocol for the realization of a controlled-phase gate in Rydberg atoms. The adiabatic state transfer for the gate is accelerated by compensating nonadiabatic transitions via oscillating fields. High fidelities and fast operation times are obtained, and an application to a minimal quantum-error correction circuit is analyzed.
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.
A shortcut-to-adiabaticity is compared with a numerically optimized protocol for implementing a high-fidelity quantum gate on Rydberg atoms. The counterdiabatic method offers an analytical framework for accelerating high-fidelity gates by mimicking the time evolution of a counterdiabatic Hamiltonian using fast-oscillating fields. This approach is contrasted with a numerically optimized gate designed using the Boulder Opal platform. The numerically optimized gate achieves higher fidelities while demonstrating robustness against errors similar to that of the effective counterdiabatic gate. The study serves as an example of the performance of analytic shortcut-to-adiabatic-inspired protocols compared to brute-force numerical optimization techniques for state-of-the-art quantum computing platforms. It stresses the important role played by constraints on the optimized pulses in time and in amplitude that are crucial in determining the quality of the optimization method.
A shortcut-to-adiabaticity is compared with a numerically optimized protocol for implementing a high-fidelity quantum gate on Rydberg atoms. The counterdiabatic method offers an analytical framework for accelerating high-fidelity gates by mimicking the time evolution of a counterdiabatic Hamiltonian using fast-oscillating fields. This approach is contrasted with a numerically optimized gate designed using the Boulder Opal platform. The numerically optimized gate achieves higher fidelities while demonstrating robustness against errors similar to that of the effective counterdiabatic gate. The study serves as an example of the performance of analytic shortcut-to-adiabatic-inspired protocols compared to brute-force numerical optimization techniques for state-of-the-art quantum computing platforms. It stresses the important role played by constraints on the optimized pulses in time and in amplitude that are crucial in determining the quality of the optimization method.
We designed a scheme for a neutral atom Rydberg blockade CZC_ZCZ​ gate based on the double sequence of adiabatic pulses applied symmetrically to both atoms and using counterdiabatic driving for Rydberg excitation. This provides a substantial reduction in the quantum gate operation time compared to previously proposed double adiabatic schemes, and makes our scheme competitive with modern time-optimal protocols for high-fidelity entangling gates with neutral atoms. Our approach creates a bridge between fully adiabatic and time-optimal gate schemes. The use of adiabatic passage reduces the sensitivity of gate fidelity to variations in laser intensity, while counterdiabatic driving provides short gate times. The intensity and phase profiles of the laser pulse acting on the atoms are described analytically depending only on the gate duration. We demonstrated the applicability of this scheme for single-photon and two-photon schemes of Rydberg excitation in rubidium and cesium atoms, and, for the first time, discussed the implementation of a CZC_ZCZ​ gate using three-photon excitation of rubidium atoms. In contrast to many modern CZC_ZCZ​ gate protocols, our scheme does not generate intrinsic single-qubit phase shifts, although they still appear in two-photon configuration. We also designed a numerically optimized amplitude-robust gate with an analytically defined phase profile of the laser pulse and compared its performance with the counteradiabatic gate scheme.
We propose a controlled-PHASE gate for neutral atoms in which one of the qubit state components adiabatically evolves along the multiple-atom eigenstate formed by the chirped laser pulse coupling to Rydberg states and intrinsic dipole-dipole exchange interactions and, consequently, accumulates an interaction-induced geometric phase. The geometric Rydberg gate is not limited by an adiabatic condition, which is sped up by shortcuts to adiabaticity (STA). Analyses show that an STA scheme is more robust than a non-adiabatic case against the variations of control parameters and faster than an adiabatic case, which protects from the decay of Rydberg states. Furthermore, an intermediate value of dipole-dipole interaction strength is enough for our scheme.