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arXiv:1201.6370 · Physical Review A

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

X. L. Zhang, Alexander Gill, L. Isenhower, Thad G Walker, Mark E. Saffman

Published Apr 10, 2012• 94 citations
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Abstract

We present a detailed error analysis of a Rydberg blockade mediated controlled-not quantum gate between two neutral atoms as demonstrated recently in Isenhower et al. [Phys. Rev. Lett. 104, 010503 (2010)] and Zhang et al. [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.

DOI
10.1103/physreva.85.042310

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We present a detailed error analysis of a Rydberg blockade mediated controlled-not quantum gate between two neutral atoms as demonstrated recently in Isenhower et al. [Phys. Rev. Lett. 104, 010503 (2010)] and Zhang et al. [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{}^{87}87Rb or Cs atoms. The relation between the process fidelity and the gate error probability used in calculations of fault tolerance thresholds is discussed.
We propose and analyze the implementation of a two-qubit quantum gate using circular Rydberg states with maximum orbital angular momentum. The intrinsic quantum gate error is limited by the finite Rydberg lifetime and finite Rydberg blockade shift. Circular states have much longer radiative lifetimes than low orbital angular momentum states and are therefore candidates for high-fidelity gate operations. We analyze the dipole-dipole interaction of two circular state Rydberg atoms and present numerical simulations of quantum process tomography to find the intrinsic fidelity of a Rydberg blockade-controlled phase gate. Our analysis shows that the intrinsic gate error can be less than $9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ for circular Cs atoms in a cryogenic environment.
For neutral-atom qubits, two-qubit gates are typically realized via the Rydberg-blockade effect, which hints at the special status of Rydberg levels compared with regular qubit register states. However, the experimental and theoretical studies that have been done to reveal how the ground-Rydberg coherence of the control-qubit atom affects the fidelity of a two-qubit gate are not yet adequate, especially when all experimental two-qubit gates feature a single atom that stays in the Rydberg state for a certain time. Here, we perform a careful investigation of decoherence in ground-Rydberg transitions in a single atom with various pulse sequences. In particular, based on the commonly used controlled-ZZZ (CZ{C}_{Z}CZ​) gate sequence proposed by D. Jaksch et al., Phys. Rev. Lett. 85, 2208 (2000), we observe that a control-qubit atom subject to a two-qubit entangling process with the HHH-CZ{C}_{Z}CZ​ controlled-not gate scheme experiences a process that is essentially similar to ground-Rydberg Ramsey interference. Then, we build a straightforward theoretical model to link the decoherence time ${\ensuremath{\tau}}_{\mathrm{gr}}$ of the control qubit (extracted from Ramsey fringes of the ground-Rydberg transition) to this CZ{C}_{Z}CZ​ pulse sequence, and also analyze the typical origins of decoherence effects. Finally, we discuss the loss of fidelity of the CZ{C}_{Z}CZ​ gate due to the limits imposed by the ground-Rydberg coherence properties, and the prospect of improving fidelity with refined gate protocols.
Abstract For the quantum error correction and noisy intermediate-scale quantum algorithms to function with high efficiency, the raw fidelity of quantum logic gates on physical qubits needs to satisfy strict requirements. The neutral atom quantum computing equipped with Rydberg blockade gates has made impressive progress recently, which makes it worthwhile to explore its potential in the two-qubit entangling gates, including the controlled-phase gate, and in particular, the CZ gate. Provided the quantum coherence is well preserved, improving the fidelity of Rydberg blockade gates calls for special mechanisms to deal with adverse effects caused by realistic experimental conditions. Here, the heralded very-high-fidelity Rydberg blockade controlled-phase gate is designed to address these issues, which contains self-correction and projection as the key steps. This trailblazing method builds upon the previously established buffer-atom-mediated gate framework, with a special form of symmetry under parity–time transformation playing a crucial role in the process. We further analyze the performance with respect to a few typical sources of imperfections. This procedure can also be regarded as quantum hardware error correction or mitigation. While this paper by itself does not cover every single subtle issue and still contains many oversimplifications, we find it reasonable to anticipate a very-high-fidelity two-qubit quantum logic gate operated in the sense of heralded but probabilistic, whose gate error can be reduced to the level of 10−4–10−6 or even lower with reasonably high possibilities.
We study the spatial performance of the entangling gate proposed by H. Levine et al. (Phys. Rev. Lett. 123, 170503 (2019)). This gate is based on a Rydberg blockade technique and consists of just two global laser pulses which drive nearby atoms. We analyze the multilevel Zeeman structure of interacting 87^{87}87Rb Rydberg atoms and model two experimentally available excitation schemes using specific driving beams geometry and polarization. In particular, we estimate the blockade shift dependence on inter-atomic distance and angle with respect to the quantization axis. In addition, we show that using Rydberg ddd-states, in contrast to sss-states, leads to a pronounced angular dependence of the blockade shift and gate fidelity.
We demonstrate the deterministic entanglement of two individually addressed neutral atoms using a Rydberg blockade mediated controlled-not gate. Parity oscillation measurements reveal a Bell state fidelity of $F=0.58\ifmmode\pm\else\textpm\fi{}0.04$, which is above the entanglement threshold of F=0.5F=0.5F=0.5, without any correction for atom loss, and $F=0.71\ifmmode\pm\else\textpm\fi{}0.05$ after correcting for background collisional losses. The fidelity results are shown to be in good agreement with a detailed error model.
We demonstrate high fidelity two-qubit Rydberg blockade and entanglement on a pair of sites in a large two-dimensional qubit array. The qubit array is defined by a grid of blue detuned lines of light with 121 sites for trapping atomic qubits. Improved experimental methods have increased the observed Bell state fidelity to F_{Bell}=0.86(2). Accounting for errors in state preparation and measurement we infer a fidelity of F_{Bell}^{-SPAM}=0.88. Accounting for errors in single qubit operations we infer that a Bell state created with the Rydberg mediated C_{Z} gate has a fidelity of F_{Bell}^{C_{Z}}=0.89. Comparison with a detailed error model based on quantum process matrices indicates that finite atom temperature and laser noise are the dominant error sources contributing to the observed gate infidelity.