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

TL;DR

This paper analyzes the fidelity of a Rydberg blockade quantum gate through detailed simulations and quantum process tomography, identifying error sources and proposing corrections to improve gate performance.

Contribution

It provides a comprehensive error analysis of Rydberg blockade gates, including simulations that match experiments and a new pulse sequence to reduce errors.

Findings

Intrinsic gate error can be below 0.002 for specific atomic states.

Trace distance effectively measures errors from finite Rydberg blockade shift.

Modified pulse sequences can correct linear errors in gate fidelity.

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.