Proposal for High-Fidelity Quantum Simulation Using a Hybrid Dressed State

Jianming Cai, Itsik Cohen, Alex Retzker, and Martin B. Plenio

Phys. Rev. Lett. 115, 160504 – Published 16 October 2015

Abstract

A fundamental goal of quantum technologies concerns the exploitation of quantum coherent dynamics for the realization of novel quantum applications such as quantum computing, quantum simulation, and quantum metrology. A key challenge on the way towards these goals remains the protection of quantum coherent dynamics from environmental noise. Here, we propose a concept of a hybrid dressed state from a pair of continuously driven systems. It allows sufficiently strong driving fields to suppress the effect of environmental noise while at the same time being insusceptible to both the amplitude and phase noise in the continuous driving fields. This combination of robust features significantly enhances coherence times under realistic conditions and at the same time provides new flexibility in Hamiltonian engineering that otherwise is not achievable. We demonstrate theoretically applications of our scheme for a noise-resistant analog quantum simulation in the well-studied physical systems of nitrogen-vacancy centers in diamond and of trapped ions. The scheme may also be exploited for quantum computation and quantum metrology.

Received 21 May 2015

DOI:https://doi.org/10.1103/PhysRevLett.115.160504

Authors & Affiliations

Jianming Cai^1,2,3,*, Itsik Cohen⁴, Alex Retzker⁴, and Martin B. Plenio^2,3

¹School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
²Institut für Theoretische Physik, Albert-Einstein Allee 11, Universität Ulm, 89069 Ulm, Germany
³Center for Integrated Quantum Science and Technology, Universität Ulm, 89069 Ulm, Germany
⁴Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Givat Ram, Israel

^*jianmingcai@hust.edu.cn

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Vol. 115, Iss. 16 — 16 October 2015

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Images

Figure 1
Hybrid dressed states from a pair of continuously driven quantum systems. (a) The effective spin- $\frac{1}{2}$ system is carried by a pair of two-level systems (with Ising-like coupling strength $a$ ) under continuous driving (with a Rabi frequency $Ω$ ). (b) The corresponding energy structure of hybrid dressed states.
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Figure 2
Stability of hybrid dressed states. (a) The decay of coherence as a function of time $t$ for the cases of no dynamical decoupling and for a simple dressed spin (simple DS) with a driving fluctuation of $δ_{Ω} / Ω = 0.02, 0.04$ . (b) The coherence time of a hybrid dressed spin (hybrid DS) as a function of the driving fluctuation as compared with a simple dressed spin. The other parameters are the noise amplitude $δ = 0.2 MHz$ , the correlation time $τ_{c} = 20 μ s$ , and the driving amplitude $Ω = 3.5 MHz$ , and the phase fluctuates in $[- 2 °, 2 °]$ .
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Figure 3
The robustness of coherent coupling between two hybrid dressed spins (hybrid DS). (a) The state fidelity based on hybrid DS with resonant driving (namely, $θ_{1} = θ_{2} = π / 2$ ) under realistic noise and driving fluctuation, with respect to the ideal entangling evolution, remains high for the time while the coherence of an individual simple dressed spin (simple DS) decays rapidly. (b) The coherent oscillation of state population during the entangling evolution. The maximally entangled hybrid dressed state is generated at time $t = π / 2 g_{k, k + 1}$ (green star). The relevant parameters are the noise amplitude $δ = 0.04 MHz$ , the driving amplitudes $Ω_{1} = 1 MHz$ , $Ω_{2} = 3 MHz$ with a relative fluctuation $δ_{Ω_{1}} / Ω_{1} = δ_{Ω_{2}} / Ω_{2} = 0.02$ ; and the nearest-neighbor coupling is $a = (2 π) 20 kHz$ (corresponding to a distance of $\sim 15 nm$ ). The noise and fluctuation correlation time is $τ_{c} = 20 μ s$ .
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Figure 4
Quantum simulation using a hybrid dressed state. (a) A two-dimensional lattice quantum simulator for the simulation of an interacting spin model. The hybrid dressed spin- $\frac{1}{2}$ of the index $(k, l)$ is represented by driven two-level systems $(k, l)_{a}$ and $(k, l)_{b}$ . (b) The effective spin-spin interaction range $α_{e}$ as a function of the original interaction range $α$ . (c) The spin structure factor $S_{x x} = \sum_{k, l > k} \exp [- i q (l - k)] ⟨ σ_{x}^{(k)} σ_{x}^{(l)} ⟩$ with $q = 0$ achieved via adiabatic preparation for a one-dimensional eight-site Ising chain using hybrid dressed spins (hybrid DS) and simple two-level systems (simple TLS). The parameters are $g (t) = a_{0} (t / T)$ , $h (t) = a_{0} - g (t)$ with $a_{0} = (2 π) 40 kHz$ , and $T = 80 μ s$ .
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