Quantum Gates and Quantum Simulations with Atoms Enrique Goran Ferdinand Chris Christopher Monroe University of Maryland

Trapped Atomic Ions Yb+ crystal ~5 mm Aarhus MIT Amherst Munich Basel NIST-Boulder Berkeley Northwestern Bonn NPL-Teddington Citadel Osaka Clemson Oxford Denison Paris Duke Pretoria Erlangen PTB-Braunschweig ETH-Zurich Saarbrucken Freiburg Sandia Georgia Tech Siegen Griffith Simon Fraser Hannover Singapore Honeywell Sussex Indiana Sydney Innsbruck Tsinghua-Beijing Lincoln Labs UCLA Lockheed Washington-Seattle Maryland/JQI Weizmann Mainz Williams Yb+ crystal ~5 mm

Atomic Qubit (171Yb+) 2S1/2 | = |1,0 wHF/2p = 12.642 812 118 GHz | = |0,0

Atomic Qubit Detection # photons collected in 500 ms 5 10 15 20 25 1 Probability |z g/2p = 20 MHz 2P1/2 2.1 GHz 369 nm | 2S1/2 wHF/2p = 12.642 812 118 GHz |

Atomic Qubit Detection >99% detection efficiency # photons collected in 500 ms 5 10 15 20 25 1 Probability g/2p = 20 MHz 2P1/2 2.1 GHz |z |z 369 nm | 2S1/2 wHF/2p = 12.642 812 118 GHz |

Atomic Qubit Manipulation g/2p = 20 MHz 2P3/2 D = 33 THz 2P1/2 355 nm | 2S1/2 wHF/2p = 12.642 812 118 GHz |

Quantum Gates

Entangling Trapped Ion Qubits ~5 mm   d ~ 10 nm ed ~ 500 Debye “dipole-dipole coupling” ∆𝐸= 𝑒 2 𝑟 2 + 𝛿 2 − 𝑒 2 𝑟 ≈− 𝑒𝛿 2 2 𝑟 3 | ↓↓ → | ↓↓ | ↓↑ → 𝑒 −𝑖𝜑 | ↓↑ | ↑↓ → 𝑒 −𝑖𝜑 | ↑↓ | ↑↑ → | ↑↑ 𝜑= ∆𝐸𝑡 ℏ = 𝑒 2 𝛿 2 𝑡 2ℏ 𝑟 3 = 𝜋 2 for full entanglement Cirac and Zoller (1995) Mølmer & Sørensen (1999) Solano, de Matos Filho, Zagury (1999) Milburn, Schneider, James (2000)

Programmable Quantum Computer Module (5 qubits) S. Debnath, et al., arXiv:1603.04512 (to appear in Nature, 2016)

Programmable Quantum Computer… Physical Layer Harris Corp 32channel AOM 2μm pixels H7260 32-channel PMT Array Coherent 355nm laser Laser S. Debnath, et al., arXiv:1603.04512 (to appear in Nature, 2016)

Addressing crosstalk measurements (~1% nearest-neighbor) S. Debnath, et al., arXiv:1603.04512 (to appear in Nature, 2016)

Many ions: phonon modes N ions in a line transverse trap frequency wx = high as you can go 𝜔 𝑧 < 𝜔 𝑥 𝑁 0.86 axial trap frequency J. P. Schiffer, Phys. Rev. Lett. 70, 818 (1993) axial modes transverse modes 𝜔 𝑧 𝜔 𝑥 Ising XX gate: pulse-shape laser to decouple all modes of motion laser m ~ 𝜔 𝑥 𝑁 0.86 ~ 𝜔 𝑥 𝑁 1.72 frequency

Controlled-Phase Gate 𝛼=𝑠𝑖𝑔𝑛 𝐽 𝑖𝑗 𝛽=𝑠𝑖𝑔𝑛 𝜃 ± phase of Ising coupling S. Debnath, et al., arXiv:1603.04512 (to appear in Nature, 2016)

Quantum Fourier Transform (QFT) 𝑦 𝑘 = 1 𝑁 𝑗=0 𝑁−1 𝑒 2𝜋𝑖 𝑗𝑘 𝑁 𝑥 𝑗 𝑁= 2 𝑛 output amplitudes input amplitudes QFT circuit (n=5 qubits) controlled phase gate S. Debnath, et al., arXiv:1603.04512 (to appear in Nature, 2016)

QFT: Period Finding state preparation 7 15 23 31 results e.g. state with period 8 = 7 15 23 31 results S. Debnath, et al., arXiv:1603.04512 (to appear in Nature, 2016)

Toffoli gate fidelity 83% (excl. spam ~1.4%)

Quantum Simulation

weak/slow global spin-dependent force F = F0|↑↑| - F0|↓↓|

global spin-dependent force | | ADD: Independent spin flips B ↑ ↓ ↑ ↓ F = F0|↑↑| - F0|↓↓| F = F0|↑↑| - F0|↓↓|

Adiabatic Quantum Simulation from S. Lloyd, Science 319, 1209 (2008) H= 𝑖<𝑗 𝐽 0 𝑖−𝑗 𝛼 𝜎 𝑥 𝑖 𝜎 𝑥 𝑗 +𝐵 𝑖 𝜎 𝑦 𝑖 0<𝛼<3 Initialization: spins along y Detection: measure spins along x Time (<10 msec)

Antiferromagnetic Néel order of N=10 spins 2600 runs, a=1.12 All in state  All in state  AFM ground state order 222 events 441 events out of 2600 = 17% Prob of any state at random =2 x (1/210) = 0.2% 219 events R. Islam et al., Science 340, 583 (2013) Since we are able to image each ion individually using the camera, we can directly observe an increase in the number of excitations as we move to long-range afm interactions. For instance, with 10 spins, we can easily see the difference between when each of our spins is up and when each is down. If we turn on our antiferromagnetic hamiltonian, we can then image our degenerate Neel ordered ground state. If we perform 2600 simulations of our AFM hamiltonian with a range of interaction parameterized by this alpha, we find About 220 events for each of the ground states, or 17 percent probability of landing in the ground state. Compared to the probability of falling into these states at random, it’s clear that we’re still recovering some ground state character. 1:00 – 16:00

First Excited States (Pop. ~2% each) Of course we can also look at the first excited states, that have a single defect like having two down spins next to each other, or two up spins, and find that they are not nearly as prevalent as the ground state, but still more populated than random chance would give.

Second Excited States (Pop. ~1% each)

Distribution of all 210 = 1024 states Probability Initial paramagnetic state B >> J0 0 341 682 1023 0 341 682 1023 Nominal AFM state B << J0 0101010101 1010101010 Probability 0.10 0.08 0.06 0.04 0.02 In fact, using the camera we can look at the distribution of all 1024 possible states in the system. In the initial paramagnetic state, all possible spin configurations are roughly equally populated, save for a few detection errors. When we ramp down the Hamiltonian, we see the two ground states popping out very clearly, each with about 9% probability, and the rest of the states suppressed. :30 – 16:30 R. Islam et al., Science 340, 583 (2013)

AFM order of N=14 spins (16,384 configurations)

etc… Propagation of correlations and entanglement with long-range interactions P. Richerme et. al., Nature 511, 198 (2014) P. Jurcevic et al., Nature 511, 202 (2014) Many-Body Spectroscopy C. Senko et. al., Science 345, 430 (2014) Spin-1 Dynamics C. Senko, et al., Phys. Rev. X 5, 021026 (2015) Many-body Localization J. Smith, et al., arXiv 1508.07026 (2015)

Dynamics of N=22 spins initial state at t=0 state measured at J0t = 36 𝐻 𝑋𝑌 = 𝑖<𝑗 𝐽 0 𝑖−𝑗 𝛼 𝜎 𝑥 𝑖 𝜎 𝑥 𝑗 + 𝜎 𝑦 𝑖 𝜎 𝑦 𝑗 a = 0.6 state measured at J0t = 36 initial state at t=0 B. Neyenhuis et al., in preparation (2015)

Scaling Up

Qubit economics Cost per Qubit # qubits in a module 2 100 $100M $10M

Scaling through Modularity

Quantum CCD Multiplexer a (C.O.M.) b (stretch) c (Egyptian) Mode competition – example: axial modes, N = 4 ions d (stretch-2) 60 mode amplitudes b+c d c b 2b,a+c a+b c-a b-a 2a b-a c-a b+c cooling beam a a+b 2b,a+c Fluorescence counts 40 2a d carrier a b axial modes only c 20 -15 -10 -5 5 10 15 Raman Detuning dR (MHz) Nature 417, 709 (2002)

Univ. of Maryland Boulder

(to 1,000,000 qubits?) N collection fibers N/2 beam splitters N × N optical crossconnect switch N trapped ion quantum registers OPTICAL!!! CCD camera C. Monroe, J. Kim, et al., Phys. Rev. A 89, 022317 (2014)

Linking remote atoms with photons Heralded coincident events (psuc=1/2): (H1 & V2) or (V1 & H2) → |↓↑ - |↓↑ (H1 & V1) or (V2 & H2) → |↓↑ + |↓↑ (H1 & H1) or (H2 & H2) → |↓↓ (V1 & V1) or (V2 & V2) → |↑↑ 50/50 PBS 50/50 PBS H1 V1 V2 H2 50/50 BS l/4 l/4 optical fiber Current: 171Yb+ ion 171Yb+ ion NA=0.6 Simon & Irvine, PRL 91, 110405 (2003) L.-M. Duan, et. al., QIC 4, 165 (2004) Y. L. Lim, et al., PRL 95, 030505 (2005) D. Moehring et al., Nature 449, 68 (2007) D. Hucul, et al., Nature Phys. 11, 37 (2015)

Large scale quantum network? 1947: first transistor 2000: integrated circuit 2015: qubit collection Large scale quantum network? single module N ion trap modules

Single Module ~100 spins on two 19” Racks

Leading Quantum Computer Hardware Candidates Trapped Atomic Ions FEATURES & STATE-OF-ART very long (>>1 sec) memory 5-20 qubits demonstrated atomic qubits all identical connections reconfigurable CHALLENGES lasers & optics slow gates high vacuum engineering needed individual atoms lasers photon Investments: IARPA Lockheed GTRI UK Gov’t Sandia LARGE Google/UCSB IBM Lincoln Labs Intel/Delft Atomic qubits connected through laser forces on motion or photons Superconducting Circuits FEATURES & STATE-OF-ART connected with wires fast gates 5-10 qubits demonstrated printable 2D circuits and VLSI CHALLENGES short (10-6 sec) memory 0.05K cryogenics all qubits different not reconfigurable Superconducting qubit: “right or left current”

Trapped Ion Quantum Information www.iontrap.umd.edu Postdocs Kristi Beck Paul Hess Marty Lichtman Norbert Linke Steven Moses Brian Neyenhuis ( Lockheed) Guido Pagano Phil Richerme ( Indiana) Grahame Vittorini ( Honeywell) Jiehang Zhang Res. Scientists Jonathan Mizrahi Kai Hudek Marko Cetina Jason Amini Grad Students David Campos Clay Crocker Shantanu Debnath Caroline Figgatt David Hucul (UCLA) Volkan Inlek Kevn Landsman Aaron Lee Kale Johnson Harvey Kaplan Antonis Kyprianidis Ksenia Sosnova Jake Smith Ken Wright Collaborators Luming Duan (Michigan) Philip Hauke (Innsbruck) David Huse (Princeton) Alexey Gorshkov (JQI/NIST) Alex Retzker (Hebrew U) LPS/NSA ARO Undergrads Eric Birckelbaw Kate Collins Akshay Grewal Micah Hernandez Hannah Ruth