Fidelity of a Rydberg-blockade quantum gate from simulated quantum process tomography

Abstract

We present a detailed error analysis of a Rydberg blockade mediated controlled-NOT quantum gate between two neutral atoms as demonstrated recently in Phys. Rev. Lett. 104, 010503 (2010) and Phys. Rev. A 82, 030306 (2010). Numerical solutions of a master equation for the gate dynamics, including all known sources of technical error, are shown to be in good agreement with experiments. The primary sources of gate error are identified and suggestions given for future improvements. We also present numerical simulations of quantum process tomography to find the intrinsic fidelity, neglecting technical errors, of a Rydberg blockade controlled phase gate. The gate fidelity is characterized using trace overlap and trace distance measures. We show that the trace distance is linearly sensitive to errors arising from the finite Rydberg blockade shift and introduce a modified pulse sequence which corrects the linear errors. Our analysis shows that the intrinsic gate error extracted from simulated quantum process tomography can be under 0.002 for specific states of 87 Rb or Cs atoms. The relation between the process fidelity and the gate error probability used in calculations of fault tolerance thresholds is discussed.

High-fidelity Rydberg quantum gate via a two-atom dark state

“…The performance of the Rydberg blockade gate has been extensively analyzed [21][22][23][24], taking into account various experimental imperfections and fundamental limitations of the scheme. Assuming that technical errors due to, e.g., laser phase and amplitude fluctuations and finite temperature atomic motion and Doppler shifts, can be eliminated, and that leakage errors to the unwanted Rydberg states can be suppressed by using, e.g., shaped laser pulses [24], the remaining limitations of the standard blockade gate stem from the finite lifetime τ = 1/Γ ∝ n 3 of the Rydberg states, duration T ≃ 2π/Ω of the gate performed by excitation lasers with Rabi frequency Ω ≫ Γ, and finite Rydberg-Rydberg interaction strength B ≫ Ω.…”

Annulled van der Waals interaction and fast Rydberg quantum gates

“…[42] (and references therein). To stabilize the superposition state | − − , we choose |δ| = 0.26 GHz before the gate sequence; this choice of δ is from an optimization of the gate fidelity when L = 4.4µ m. As discussed later on, ionization [51] does not happen with this choice.…”

“…4(a) we plot the resulting gate operation time T g , optimized Rabi frequency and gate error as a function of B. The minimum error shown, 3.1 × 10 −3 , is close to the gate error limit, 2 × 10 −3 , of a conventional Rydberg C Z gate [42,43], while the gate operation time of around 50 ns, compares favorably to a gate time of several microseconds of a conventional gate. In the proposed gate, one photon transitions which leak population during the gate operation, limit the speed of the protocol and as a consequence radiative decay bounds the achievable error.…”

Robustness of high-fidelity Rydberg gates with single-site addressability

“…For the nonindividually addressable implementation of the Rydberg gate protocol in [2], atomic motion can also play a significant role in limiting the fidelity [16,17]. The role of these and other factors limiting gate fidelities have been studied theoretically for Rydberg gate schemes involving both analytic pulse sequences [15,18] and, for the non-addressable protocol of [2], numerically optimized pulses [16,17]. These studies indicate that gates with errors of the order of 10 −3 might be achieved with suitable choice of atoms and qubit levels.…”

“…Twoqubit gates relying on controlled use of dipolar interactions between atoms in Rydberg states have the potential of being fast, but are subject to a number of intrinsic and technical sources of error that can restrict both the achieved fidelity and speed of operation. An important source of intrinsic error specific to Rydberg gates is the lifetime of the atoms in the Rydberg states while technical errors may derive from a number of experimental factors, as discussed recently in [15]. For the nonindividually addressable implementation of the Rydberg gate protocol in [2], atomic motion can also play a significant role in limiting the fidelity [16,17].…”