CMSC 33001: Novel Computing Architectures and Technologies Lecturer: Kevin Gui Scribe: Kevin Gui Lecture 06: Trapped Ion Quantum Computing October 8, 2018 1 Introduction Trapped ion is one of the physical realizations of quantum bits. The general idea is to use ions as qubits. different quantum states can be represented by different level of spins, an intrinsic physical property held by atoms. Ions are stabilized using a specifically trapping technique. Theory - Cirac + Zoller in 1995 (1) Experimental Demonstration - Wineland (2) in 1995, Blatt (3) in 1994 1.1 Divincenzo Criteria 1. Ion = Qubit 2. Coherence - hyperfine qubit in atomic clock (very long) 3. Manipulation - spin-qubit interaction, optical manipulation, readout and initialize via coupling 4. Two-qubit gates - phonons (vibrational mode) 5. Scalable - ions are cheap 2 What is spin? Since spin is used to represent different quantum states in the trapped ion system, let s take a look at the fundamental property of spin first. It is a very intriguing physical property arise from nature that physicist are still striving to understand nowadays. We can think of spin as a magnetic property carried by atoms intrinsically. The related magnetic momentum (sometimes people may also refers as angular momentum) is quantized, thus can be used to represent discrete quantum states. The first experiment to proved that quantization is the Stern-Gerlach Experiment. 2.1 Stern-Gerlach Experiment The Stern Gerlach experiment was conceived by Otto Stern in 1921 and performed by him and Walther Gerlach in Frankfurt in 1922. In the original experiment, silver atoms were
sent through a spatially varying magnetic field, which deflected them before they struck a detector screen, such as a glass slide. Particles with non-zero magnetic moment are deflected, due to the magnetic field gradient, from a straight path. The screen reveals discrete points of accumulation, rather than a continuous distribution, owing to their quantized spin. We can mathematically described the quantization of spin angular momentum. Let s take a look at electron for an example. Electrons are spin 1 particles. This means their angular 2 momentum j can be quantized as + 1 or - 1 2. 2 ψj=+ ψj= the initial state of the particles is ψ = c 1 1 2 + c 2 1 2, with c 1 2 + c 2 2 = 1. 2.2 Fine Structure & Hyperfine Structure Fine structure refers to splitting of the spectral lines of atoms due to electron spin. Hyperfine structures refers to small shifts and splittings in the energy levels of atoms due to nucleus spin. The following picture is a depiction of fine structure and hyperfine structure splitting in a neutral hydrogen atom. (S and P are different atom orbitals) People are interested in using a combination of fine structure splitting and hyperfine structure splitting to manipulate different level of spin interactions in order to do the initialization & readout. 2
3 Initialization & Readout There are many ways to implement the initialization and readout in the trapped ion system. Here is an illustration of one particular implementation method. Trapped ion qubits can be initialized and detected (readout) with nearly perfect accuracy using conventional optical pumping and state-dependent fluorescence techniques.(4) Here we use 171 Y b +, which has a simple electronic structure (with single valence electron). The detailed implementation are the following: Picture a) shows a silicon chip-trap mounted on a ceramic pin grid array carrier with raised interposer, confining atomic ions that hover 75µm above the surface. The inset is an image of 7 atomic ytterbium ( 171 Y b + ) ions arranged in a linear crystal and laser-cooled to be nearly at rest. In picture (b) and (c), hyperfine levels and that represent the two quantum state of a qubit. The electronic excited states e and e are separated from the ground states by an energy corresponding to an optical wavelength of 369.53 nm. Picture (b) shows that applying laser radiation (blue arrows) drives these transitions for initialization to state. When laser beams resonant with both e and e transitions are applied, the ion rapidly falls into the state and no longer interacts with the light field. Picture (c) shows the fluorescence detection of the qubit state (, fluorescence,, no fluorescence). When a single laser resonant with the transition e is applied, the closed cycling optical transition causes an ion in the state to fluoresce strongly at a rate scaled by the excited state radiative linewidth γ 20πMHz, whereas an ion in the state stays dark, because the laser is far from its resonance. 3
CMSC 33001 (Autumn 2018) 4 Lecture 06 How to trap those ions? In order to perform spin manipulation and detection on those ions, we need to first make them stay in a relatively small space interval. Then we can make sure the optical or microwave signal we send to them will be completely absorbed at all time. The most commonly used technique is called quadrupole ion trap. 4.1 Quadrupole ion trap A quadrupole ion trap is a type of ion trap that uses dynamic electric fields to trap charged particles. They are also called radio frequency (RF) traps or Paul traps in honor of Wolfgang Paul, who invented the device and shared the Nobel Prize in Physics in 1989 for this work. A charged particle, such as an atomic or molecular ion, feels a force from an electric field. It is not possible to create a static configuration of electric fields that traps the charged particle in all three directions (this restriction is known as Earnshaw s theorem). It is possible, however, to create an average confining force in all three directions by use of electric fields that change in time. To do so, the confining and anti-confining directions are switched at a rate faster than it takes the particle to escape the trap. The traps are also called radio frequency traps because the switching rate is often at a radio frequency. The electric fields are generated from electric potentials on metal electrodes. A pure quadrupole is created from hyperbolic electrodes, though cylindrical electrodes are often used for ease of fabrication. Microfabricated ion traps exist where the electrodes lie in a plane with the trapping region above the plane. 4
This is the cross section view of the quadrupole trapping system. The blue arrows in the four corners represent the oscillating electric field. In picture 1 the positively charged ions feel vertical electric forces and thus are squeezed in the vertical direction. In picture 1 the ions feel horizontal forces and thus are squeezed in the horizontal direction. 5 Cooling After we use the quadrupole trapping method to trap the ions in certain position, we still need sufficient cooling to make sure that the ions are staying in its position without too much intention to escape out. More technical speaking, cooling allows: 1. increases the time that the ions remain in the trap 2. lead to increased precision for measurements of masses, magnetic moments, and optical or microwave spectra 3. the formation of spatially ordered structures of ions, can be observed only at low temperatures 5.1 Laser (Doppler) Cooling Doppler cooling involves light with frequency tuned slightly below an electronic transition in an atom. Because the light is detuned to the red (i.e. at lower frequency) of the transition, the atoms will absorb more photons if they move towards the light source, due to the Doppler effect. (Does not require a big cold environment!) Thus, if one applies light from two opposite directions, the atoms will always absorb more photons from the laser beam pointing opposite to their direction of motion. In each absorption event, the atom loses a momentum equal to the momentum of the photon. The result of the absorption and emission process is a reduced speed of the atom, provided its initial speed is larger than the recoil velocity from scattering a single photon. If the absorption and emission are repeated many times, the mean velocity, and therefore the kinetic energy of the atom will be reduced. Since the temperature of an ensemble of atoms is a measure of the random internal kinetic energy, this is equivalent to cooling the 5
atoms. 6 Logic Gate Operation Implementation There are many physical ways we can implement gate operations between qubits. Here is an example of physical implementation(5), which demonstration of CNOT gate and SWAP gate. We know that a bell state can be created by first apply a Hadamard gate and then a CNOT gate. We also know that a SWAP gate can be done by apply the CNOT gate 3 times. Here the results of the bell state and the swap are experimentally verified. Here we start with the state for both Be and Mg, this pulse sequence generates a Bell state with GE (blue-dashed box) and single-qubit microwave (µwv) gates. The notation (θ, φ) represents the rotation angle and relative phase of each gate pulse. A parity oscillation is induced by applying analysis π/2 pulses with a variable phase to the created Bell state. The bell-state creation is verified by performing a CHSH-type Bell-inequality test on this state, achieving a sum of correlations of B = 2.70(2) > 2. This inequality, measured on an entangled system consisting of different elements, agrees with the predictions of quantum mechanics while eliminating the detection loophole but not the locality loophole. Now we can use the previous implemented CNOT gate to do the SWAP gate. Here the pulse sequence of a Ramsey experiment where a superposition state of a Be qubit is coherently transferred to a Mg qubit with a SWAP gate (black-dashed box). Given GE, either of the two qubits can be the target qubit of a CNOT gate (green-dashed boxes) by applying singlequbit I/2 pulses to it. Note: for a detailed implementation the MS interaction, please refer to the last page of the original paper(5). 6
CMSC 33001 (Autumn 2018) 7 Lecture 06 Potential Advantage vs Superconducting Circuit System One of the biggest advantage for ion trap qubits versus qubits made of superconduction circuits is that it is easier to entangle different ion particles to form universal gates. Picture A is the superconducting qubits connected by microwave resonators. The star shaped graph shows the connectivity between different entangled qubits. Picture B shows the linear chain of trapped ions connected by laser-mediated interactions. Since all qubits are entangled, it can be abstracted as a fully connected graph(6). Below is a comparison experiment(6) showing that the ion trap system requires less number of qubit gates (by counting Single- and 2-qubit gates) for some quantum gate operation and algorithms: References [1] J. I. Cirac and P. Zoller. Phys. Rev. Lett. 74, 4091 [2] C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland. Phys. Rev. Lett. 75, 4714 7
[3] I. Marzoli, J. I. Cirac, R. Blatt, and P. Zoller. Phys. Rev. A 49, 2771 [4] Brown, K., Kim, J. and Monroe, C. (2016). Co-designing a scalable quantum computer with trapped atomic ions. [5] T. R. Tan, J. P. Gaebler, Y. Lin, Y. Wan, R. Bowler, D. Leibfried D. J. Wineland. Nature volume 528, pages 380 383. Multi-element logic gates for trapped-ion qubits [6] arxiv:1702.01852 8