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Scalable Quantum Information Processing with Trapped Ions Jungsang Kim1,2, Emily Mount1, So-Young Baek1, Stephen Crain1, Daniel Gaultney1, Rachel Noek1, Geert Vrijsen1, Andre van Rynbach1, Byeong-Hyeon Ahn1, Kai Hudek1, Louis Isabella2, and Peter Maunz3 1
Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA 2 Department of Physics, Duke University, Durham, NC 27708, USA 3 Sandia National Laboratories, Albuquerque, NM 87185, USA Email:
[email protected]
Abstract: We present a scalable approach to quantum information processing utilizing trapped ions and photons. Ions trapped in microfabricated surface traps provide a practical platform for realizing quantum networks of distributed computing nodes and quantum repeaters. OCIS codes: (270.5585) Quantum Information Processing; (270.5565) Quantum Communications
1. Introduction Trapped atomic ions provide an ideal physical system to implement high quality qubits with long coherence times, efficient initialization and readout schemes, and robust quantum logic gates (see, for example, [1]). The entangling operation is realized by the Coulomb interaction between the ions, that dictate the motional degrees-of-freedom of the ion chains in a single trapping zone [2-6]. System-level proposals for constructing large-scale quantum processors based on this physical platform has been proposed [7,8], in some cases utilizing photonic interconnect networks [9,10]. Experimental implementation of such architectures requires employing new technologies, such as microfabricated traps [11,12], optical multiplexing techniques [13], and integrated optics [14,15]. In this paper, we will describe the experimental progress towards the realization of modular universal scalable ion-trap quantum computer (MUSIQC) architecture [9,10], where a set of small quantum registers is connected using remote entanglement generation process over a photonic network [16]. Microfabricated surface traps are developed to effectively accommodate all qubit operations necessary to realize a functional quantum register with an optical interface. We describe the quality of qubit operations that can be realized in our experimental platform. This hardware platform can be extended to realize a quantum repeater, capable of distributing quantum entanglement over macroscopic distances that can be utilized for secure communication. 2.
171
Yb+ Hyperfine Qubits in Microfabricated Surface Traps
We trap individual 171Yb+ ions in a microfabricated surface trap made at Sandia National Laboratories [17]. The trap has a linear slot down the middle, between the RF rails over which the ions are trapped [Fig. 1(a)]. The simplified level structure for the 171Yb+ ion is shown in Fig. 1(b) [18]. 171Yb+ has a nuclear spin ½, and the 2S½ ground states and 2P½ excited states (separated by about 812 THz in frequency, or 369.5nm in wavelength) are split into singlet and triplet levels due to hyperfine interaction, separated by 12.6 GHz. The two mF=0 ground states are used as the qubit levels |0 and |1 . This energy separation is insensitive to the magnetic field fluctuations to first order at zero external field, and forms very stable state pair used in atomic clock applications. In our experiment, we apply a small (< 5G) external magnetic field to define the quantization axis and destabilize the coherent dark states that form when the ion is pumped with a resonant laser field. Using laser fields with appropriate frequency control, one can readily cool the ion’s motional degree of freedom by Doppler cooling, and prepare and detect the qubit state with high fidelity. The motional degree-of-freedom can be manipulated using Raman transitions driven with two laser beams whose frequency differs exactly by the hyperfine splitting [Fig. 1(b)], plus or minus the motional frequency of the ion. This can effectively be achieved using a mode-locked picosecond lasers in the UV, far detuned from the atomic resonance, if the repetition rate of the laser is stabilized. Using such a setup, we can further cool the transverse motional mode of the ion close to the ground state using sideband-resolved Raman cooling technique. By comparing the red- and the blue-sidebands of the ion, one can accurately extract the number of average motional quanta in the system, and therefore measure the heating rate of the trap. Figure 1(c) shows the measurement of the number of motional quanta after the ion is allowed to “heat up” for a finite duration. We measure that the heating rate of our trap is about one quanta per ms, adequate for demonstration of two-qubit gate operation. Figure 1d shows our ability to prepare and detect the qubits in this trap [19]. In this experiment, we first prepare the qubit in the |0 state by optically pumping. This process can be performed with a high fidelity exceeding 99.95%. When preparation of |1 state is necessary, we apply a microwave field for an adequate amount of time to
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flip the qubit. For state detection, a laser resonant with 0 ↔ 2 P1/2 F = 0, mF = 0 transition illuminates the ion. When excited, the 2 P1/2 F = 0, mF = 0 can only decay back into 2 S1/2 F = 1 states due to atomic selection rules, and the ion goes through a cycling transition scattering many photons if it started in the |1 state. If it started in the |0 state, the ion does not undergo photon scattering. By observing whether the photons are scattered or not, one can readily discriminate between the two qubit states. In practice, our ability to determine whether the ion scatters photons or not is limited by the detection efficiency of the scattered photons, and non-ideal processes such as background photon detection events and off-resonant scattering of qubit states to 2 P1/2 F = 1 states that inadvertently flips the qubit. Using a collection lens with a high numerical aperture (NA), we have been able to determine the qubit state with a fidelity approaching 99.9%, with an average detection times of ~30µs [19].
Figure 1: Performance of single qubit manipulation in a surface trap. (a) Schematic layout of the surface trap fabricated at Sandia National Labs. (b) Atomic level structure of 171Yb+ ions. The two hyperfine ground states with mF=0 are used as the qubit. (c) Measurement of the heating rate of the ions for a transverse mode in the trap using Raman transitions configured to be sensitive to the ion motion. (d) High performance single qubit detection using a high NA optical lens, achieving ~99.9% fidelity. (e) Rabi oscillations driven by a microwave field resonant with the hyperfine qubit. (f) Ramsey interferometry is used to measure the coherence time of the qubit, which exceeds 1s when spin echo is used. (d) is from Ref. [19], and the rest are from Ref. [18].
With the ability to prepare and detect the qubit with such a high fidelity, we can characterize our ability to manipulate single ion qubits in the trap. Between the qubit preparation (in the |0 state) and detection, one can change the qubit state by applying a sequence of either microwave or optical Raman pulses over a controlled duration with controlled phase among them. Figure 1(e) shows an example where a microwave pulse with varying duration is applied to measure Rabi oscillations of the qubit. Similarly, one can break up a π-pulse into two halves with a variable delay and phase shift between them, to measure the coherence time of the qubit. In this method (Ramsey interferometry), the visibility of the oscillation observed when the phase of the second pulse is swept indicates the coherence of the qubit. By plotting this coherence (or visibility) as a function of delay time, one can determine how long the qubit stays coherent with respect to the commercial Rb-based frequency reference used to run our experiments. Figure 1(f) shows a qubit coherence time exceeding one second when simple spin-echo pulses are used to cancel out the effect of time-varying magnetic field over many experiments. Manipulation of qubits can be extended to more than one in a single trap. We have successfully trapped 2-5 ions in a chain in these microfabricated surface traps. Multiple ions are simultaneously initialized by illuminating the entire ion chain with an optical pumping beam, and individual qubits can be measured by directing the scattered photons from each ion onto separate photon detector. We utilize micromirror-based beam steering system to direct focused Raman beams to individual ions in the chain [13], and perform individual single qubit operations. Multi-qubit gate operations can be performed using a carefully tailored Raman pulse profiles [20]. Using these techniques, arbitrary quantum logic operations can be implemented on the ion chain.
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3. Scaling with Photonic Networks and Applications Quantum logic operations between qubits trapped in two different traps can be realized by a photonic interface. In this approach, one ion from each chain (interface ion) is excited so that a single photon is emitted, where the qubit of the ion is entangled with an internal degree of freedom of the photon (e.g., the frequency). When the two photons interfere at a beamsplitter, one can realize a Bell-state measurement that leads to entanglement swapping that leaves the two interface ions entangled with each other [16]. When combined with local entangling operations within each chain, such shared entanglement can be used to carry out a two-qubit operation between qubits in two different chains. Figure 2(a) shows a schematic approach to constructing a large-scale, modular quantum information processors using this approach (MUSIQC). Each elementary logic unit (ELU) consists of an ion chain capable of arbitrary quantum gate operation among them and an interface ion. The photons from each ELU go through an optical switch before the Bell-state detector, which allows generation of entangled pairs between arbitrary pairs of ELUs in the system, to construct a scalable quantum processor. Figure 2(b) shows the schematic of a quantum repeater using similar hardware capabilities. In this example, the emitted photons propagate over a long distance, generating entangled ion pairs at a distance. The photons should undergo a frequency conversion to a wavelength favorable for long-distance propagation (telecom wavelength) in order for this scheme to be practical, which can be realized using conventional nonlinear optics techniques. Each quantum repeater node consists of two optical interfaces to generate entangled pairs with neighboring nodes on either side, and a local gate operation can further swap entanglement once the remote entanglement generation process is successful.
Figure 2: (a) Scalable quantum computation using a modular approach. (b) Realization of a quantum repeater for long-distance distribution of quantum entanglement. Figures are from [9].
We demonstrate successful single-qubit manipulation of 171Yb+ ions in a microfabricated surface trap. When combined with local entangling gates and optical interfaces, both of which have been demonstrated in macroscopic traps, this experimental hardware can be utilized to realize both scalable quantum information processors and quantum repeaters for long-distance quantum communication. 4. References [1] R. Blatt and D. Wineland, “Entangled states of trapped atomic ions,” Nature 453, 1008-1015 (2008). [2] J. I. Cirac and P. Zoller, “Quantum computation with cold trapped ions,” Phys. Rev. Lett. 74, 4091-4094 (1995). [3] A. Sørensen and K. Mølmer, “Quantum computation with ions in thermal motion,” Phys. Rev. Lett. 82, 1971-1974 (1999). [4] C. Monroe et al., "Demonstration of a fundamental quantum logic gate," Phys. Rev. Lett. 75, 4714-4717 (1995). [5] F. Schmidt-Kaler et al., "Realization of the Cirac-Zoller controlled-NOT quantum gate," Nature 422, 408-411 (2003). [6] D. Leibfried et al., “Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate,” Nature 422, 412-415 (2003). [7] D. Kielpinski et al., “Architecture for a large-scale ion-trap quantum computer,” Nature 417, 709-711 (2002). [8] S.-L. Zhu et al., “Trapped ion quantum computation with transverse phonon modes,” Phys. Rev. Lett. 97, 050505 (2006). [9] C. Monroe and J. Kim, “Scaling the ion trap quantum processor,” Science 339, 1164 (2013). [10] C. Monroe et al, “Large-scale modular quantum-computer architecture with atomic memory and photonic interconnects,” arXiv:1208.0391 (2012); Phys. Rev. A, in press (2014). [11] J. Chiaverini et al., “Surface-electrode architecture for ion-trap quantum information processing,” Quantum Inf. Comput. 5, 419 (2005). [12] D. L. Moehring et al., “Design, fabrication and experimental demonstration of junction surface ion traps,” New J. Phys. 13, 075018 (2011). [13] C. Knoernschild et al., “Independent individual addressing of multiple neutral atom qubits with a micromirror-based beam steering system,” Appl. Phys. Lett. 97, 134101 (2010). [14] J. Kim and C. Kim, “Integrated optical approach to trapped ion quantum computation,” Quantum Inf. Comput. 9, 181 (2009). [15] J. T. Merrill et al., “Demonstration of integrated microscale optics in surface-electrode ion traps,” New J. Phys. 13, 103005 (2011). [16] D. L. Moehring et al., “Entanglement of single-atom quantum bits at a distance,” Nature 449, 68 (2007). [17] D. Stick et al., “Demonstration of a microfabricated surface electrode ion trap,” arXiv:1008.0990 (2010). [18] E. Mount et al., “Single qubit manipulation in a microfabricated surface electrode ion trap,” New J. Phys. 15, 093018 (2013). [19] R. Noek et al., “High speed, high fidelity detection of an atomic hyperfine qubit,” Opt. Lett. 38, 4735 (2013). [20] T. Choi et al., “Optimal quantum control of multi-mode couplings between trapped ion qubits for scalable entanglement,” arXiv:1401.1575.
