Overcoming Stark-Shift Constraints in Phase-Controlled Rydberg Two-Qubit Gates

TL;DR

This work addresses Stark-shift–induced dynamical phases that impede the realization of certain two-qubit gates in strong Rydberg blockade. By actively controlling the absolute phases and local amplitudes of non-independently addressed qubits during nonresonant two-photon excitation, the authors show that any entangling two-qubit gate can be implemented with a three-pulse sequence, provided new control schemes are employed. They introduce two robust protocols, the Symmetric Orthogonal Protocol (SOP) and the Symmetric Parallel Protocol (SPP), which exploit phase and geometry optimization to realize high-fidelity $\mathcal{C}^+$ and $\mathcal{C}^-$ gates across varying pulse lengths and blockade parameters. Numerical results demonstrate that, with phase optimization, fidelities exceeding 0.99 are achievable for a broad set of conditions, and even higher fidelities are possible with longer sequences, highlighting a path toward scalable, robust neutral-atom quantum gates grounded in two-photon Rydberg excitation.

Abstract

Stark shifts introduce additional phases that constrain the set of entangling gates that can be prepared via two-photon transitions in the strong Rydberg blockade limit. For non-independently addressed qubits, by controlling the absolute phases and the local amplitudes of the pulses at each qubit, we show that any two-qubit phase gate can be prepared with high fidelity using a three-pulse sequence. Based on these insights, we introduce two robust control schemes tailored to different phase gates that yield better results with pulse sequences of either even or odd length.

Figures (6)

• Figure 1: (a) Diagram of the energy levels as the qubits come close and we describe the two-photon interaction in the adiabatic approximation, with pulses overlapping both qubits with different factors $a_k$ and $b_k$. (b) Symmetrical $3$-(double)-pulse sequence where the pump and Stokes Rabi frequencies are always identical and the pulse area of the first and third pulses in the sequence are the same and half the pulse areas of the second pulses.
• Figure 2: (a) Fidelity of the JP for the ${\cal C}^+$ gate with independent qubits for two-photon processes, as a function of the pulse areas in units of $\pi$. (b) Fidelity for the ${\cal C}^-$ gate when $\beta = 0.10\pi$. In (c) and (d) we show how the fidelity for the previous cases can be improved when the phases of the pulses $\phi_k$ are optimized for each value of the pulse areas.
• Figure 3: Fidelity of the ${\cal C}^+$ gate as a function of the pulse areas for $3$-pulse sequences with (a) $\beta = 0.045\pi$ ($\tilde{b}^2 = 0.02$), (b) $\beta = 0.10\pi$ ($\tilde{b}^2 = 0.1$), (c) $\beta = 0.46\pi$ ($\tilde{b}^2 = 0.2$) and (d) $\beta = 0.79\pi$ ($\tilde{b}^2 = 0.5$). The pulse phases $\phi_k$ have been optimized for each value of the pulse areas.
• Figure 4: Fidelity of the ${\cal C}^-$ gate as a function of the pulse areas for pulse sequences with $\tilde{b}^2 = 0.1$ and (a) $M = 2$, (b) $3$, (c) $4$ and (d) $5$ pulses. The pulse phases $\phi_k$ have been optimized for each value of the pulse areas.
• Figure 5: Fidelity of the ${\cal C}^-$ gate as a function of the pulse areas implementing the SPP scheme for pulse sequences with $\tilde{b}^2 = 0.1$ and (a) $M = 2$, (b) $3$, (c) $4$ and (d) $5$ pulses. The pulse phases $\phi_k$ have been optimized for each value of the pulse areas.