High-fidelity readout scheme for rare-earth solid-state quantum computing

A. Walther, L. Rippe, Y. Yan, J. Karlsson, D. Serrano, A. N. Nilsson, S. Bengtsson, and S. Kröll

Phys. Rev. A 92, 022319 – Published 10 August 2015

Abstract

We propose and analyze a high-fidelity readout scheme for a single-instance approach to quantum computing in rare-earth-ion-doped crystals. The scheme is based on using different elements as qubit and readout ions, where the readout ions are doped into the material at a much lower concentration than the qubit ions. It is shown that by allowing the qubit ion sitting closest to a readout ion to act as a readout buffer, the readout error can be reduced by more than an order of magnitude. The scheme is shown to be robust against certain experimental variations, such as varying detection efficiencies, and we use the scheme to predict the attainable quantum fidelity of a controlled not (cnot) gate in these solid-state systems. In addition, we discuss the potential scalability of the protocol to larger qubit systems. The results are based on parameters which we believe are experimentally feasible with current technology and which can be simultaneously realized.

Received 31 March 2015

DOI:https://doi.org/10.1103/PhysRevA.92.022319

Authors & Affiliations

A. Walther^*, L. Rippe, Y. Yan^†, J. Karlsson, D. Serrano, A. N. Nilsson, S. Bengtsson, and S. Kröll

Department of Physics, Lund University, 221 00 Lund, Sweden

^*andreas.walther@fysik.lth.se
^†Present address: College of Physics, Optoelectronics and Energy and Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006, China, and Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province and Key Lab of Modern Optical Technologies of Education Ministry of China, Soochow University, Suzhou 215006, China.

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Vol. 92, Iss. 2 — August 2015

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Images

Figure 1
A chain consisting of one readout ion in the vicinity of several qubit ions (e.g., Eu), where the closest qubit ion is being used as a buffer stage (the bright one); see the text for more details. The lines between the ions show which of them can interact directly via frequency shifts caused by changes to the permanent dipole moments. With a 4% doping concentration, it is expected that each Eu ion can, on average, interact with about five other Eu ions surrounding it.
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Figure 2
Pulse sequence for reading out the state of one qubit via one buffer ion and the readout ion (note that the buffer is just the closest qubit ion). In the instance shown the qubit is in the $| 0 〉$ state, and the first pulse, (1), resonant with the $| 1 〉 \to | e 〉$ qubit transition, does not excite it. The buffer ion is now unshifted, and a pulse, (2), resonant with the $| 0 〉 \to | e 〉$ buffer transition will cause an excitation of the buffer ion. At this stage, the qubit ion is coherently returned to the ground state by pulse (3), such that it spends a minimum amount of time in the excited state. Finally, the readout ion is continuously excited and light is detected, (4). In the current example, the readout ion was shifted due to an excited buffer ion, and there is no fluorescence. However, if the qubit were originally in the $| 1 〉$ state, pulse (2) would be off resonant, and the buffer would not get excited, and thus the readout ion would instead fluoresce.
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Figure 3
Histograms of simulated photon statistics for detection of a single Nd ion in a cavity. In (a), the readout ion Nd is directly controlled by the qubit ion. In (b) and (c) the cumulative statistics is shown from 10 and 3 repeated readouts, respectively, using one buffer step. The vertical axis shows the probability of receiving $n$ photons during the optimal photon collection time, and the corresponding probabilities of correctly distinguishing the states are (a) 93%, (b) 99.7%, and (c) 99.85%. For (b) and (c), detection efficiencies of 1% and 10%, respectively, have been used, which also makes it possible to obtain good distinguishability with fewer buffer transfers in (c).
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Figure 4
The (real) elements of the density matrix of a prepared Bell state, including all error sources as described in the text. The total fidelity is 99.4% without readout and 99.1% with readout.
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Figure 5
Predicted fidelity of $n$ -qubit GHZ states with and without readout. The fidelity includes pulses for tomography but assumes that all ions can interact with each other, which is reasonable at least up to five qubits with 4% doping concentration.
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