Nicolás Pulido

Christian OspelkausPhysikalisch-Technische Bundesanstalt, Braunschweig

Institut für Quantenoptik, Leibniz Universität Hannover

Towards a Small-Scale

Trapped-Ion Quantum

Processor Based on

Near-Field Microwave

Quantum Logic Gates

INTRODUCTION

2

Qubits

Classical unit of information

Quantum degree of freedom

Superposition principle

“0”+

- “1”

Logic gates

Reversible operations

Uȁ ↑, 0

ȁ ↓, 1

1

2ȁ ↑ + ȁ ↓

3

748 957 416 402 469 183 253 951 … …

x 593 165 415 037 541 213 576 874 … …

… … … … …=

890 589 346 128 763 258 109 854 … …

… x … x … x …=

Basis for public key cryptography

(RSA)…Basis for secure websites,

digital signatures,

encrypted email,…

Mare Nostrum, Barcelona

Quantum computers and cryptography

4

Quantum computers and cryptography

890 589 346 128 763 258 109 854 … …

… x … x … x …=

(well, it can be done in polynomial time…)

Peter Shor

𝒰⨂⨂⋯

5

Quantum simulation

n=128 spins: 2n ≈ 3.4∙1038 entries

2n+5 ≈ 1040 Bits (32 bits per complex number)

22n+10 Bits ≈ 1080 Bits

Feynman, 1982:

Quantum computers

(and simulators)

can do much better!

State vector for n spins

Compute evolution (matrix)

Number of protons in the universe: ≈ 1080Crab nebula

The challenge

6

State detection

2,2

1,1

1,1

1,2 0,2

1,2 2,2

0,1

Be9

2/1S

2/3P

Notation: FmF,

3,3

313 nm

0

1

a qubit!

7

Raman

laser beams

State initialization via optical pumping

Preparation of arbitrary one-ion states via Raman laser beams

“Single qubit gate”

State manipulation

GHz101

Raman process

e

313 n

m

GHz80

8

Coupling to the motion

+n=0

n=1

n=2

n=3

Motional

Degree of Freedom

Internal

Degree of Freedom

Sideband transitions Basis for:

Ground state cooling

Fock, “cat” and coherent

states of motion

Quantum logic

Aluminum ion clock

n=0

“red” sideband

“blue” sideband

carrier

n=1n=2n=3

n=0n=1n=2n=3

Diedrich et al., PRL 62, 403 (1989)

9

Raman

laser beams + +

Normal modes

Description of normal modes as harmonic oscillators

Sideband transitions for normal modes

10

Entangling quantum logic gates

ninn 2

1Entangled state!

Mølmer and Sørensen, PRL 82, 1835 (1999)

Solano et al., PRA 59, 2539 (1999)

Sackett et al., Nature 404, 256 (2000)

Raman

laser beams

n

n

1 n 1 n

n n

1 n 1 n

1 n

1 n

1 n

1 n

11

A scalable, solid-state based platform for ion qubits

D. Wineland et al., J. Res. NIST 103 (1998)

D. Kielpinski et al., Nature 417 (2002)

++++

++ ++++

Two-qubit gate

processing

storage

processing

detection

laser

read-outread-out

Single-qubit gate

DCRF

12

A SCALABLE PLATFORM FOR

TRAPPING AND MANIPULATION

13

Surface-electrode ion traps for scalability

DC electrodes

RF electrodes

Field lines:

Chiaverini et al., Quant. Inf. Comp. 5, 419 (2005)

Seidelin et al., Phys. Rev. Lett. 96, 253003 (2006)

14

Trap fabrication

PTB cleanroom center,

thanks to divisions 2 &4!

A. Bautista-Salvador et al., NJP 21, 043011 (2019); patent DE 2018 10 111 220

15

Growing of thick metal films

A. Bautista-Salvador et al., NJP 21, 043011 (2019); patent DE 2018 10 111 220

16

Multi-Layer Ion Trap

17A. Bautista-Salvador et al., NJP 21, 043011 (2019); patent DE 10 2018 111 220

17

Choice of metals for electrodes

Hide dielectrics as much as possible

Choice of substrate materials

Scalable multilayer method

Fabrication requirements

+

-

RF loss

Heatconductivity

4K vs. 300KMachineability

Silicon, Aluminum

Nitride, Quartz,

Sapphire, …

18

Layer thickness & supported current

( → also: „atom chips“)

Integration (electronics, optics)

Turnaround, yield

People

Fabrication requirements

Jonathan

Morgner

Amado

Bautista-

Salvador

Martina

Wahn-

schaffe

MAIUS-B launch,

Esrange

> 80%

1 day (SL)

4 weeks (ML)

A. Bautista-Salvador et al., NJP 21, 043011 (2019); patent DE 10 2018 111 220

19

Yes! I am an inventor!

20

Vision: trap foundry service!

Are you interested in a surfacetrap? Let us know! We canpossibly make it for you…

NEAR-FIELD MICROWAVE

QUANTUM GATES

21

Ion-trap multi-qubit quantum logic

Internal states

as qubits

Motion as a

quantum buse

Raman process

+ +

(Two-level atom) (Harmonic oscillator)

Sideband

transitions

n=0n=1n=2n=3

n=0n=1n=2n=3

Entangling gates,

clocks, …

Raman lasers?

Why not usemicrowaves?≈ GHz

200−800nm

22

MAGIC

Mintert and Wunderlich, PRL 87, 257904 (2001)

23

Near-field idea

Free-space laser field

Basic near-field idea

Ideal near-field

geometry

𝐸

𝐸

𝐼𝑀𝑊

𝐼𝑀𝑊𝐼𝑀𝑊

200 − 800 nm

𝑥0 = ℏ/(2𝑚𝜔trap) ≈ 10 nm

𝑥0

𝐵𝐵 − ∆𝐵

Ospelkaus et al., PRL 101, 090502 (2008)

See also: Mintert and Wunderlich, PRL 87, 257904 (2001)

24

No

spontaneous

emission

J. Amini

"Integrated"

quantum

control

Temperature

insensitivity

Potentially

easier to

control

Nature 476, 181 (2011)

PRL 101, 090502 (2008)

Near-field idea

25

Simultaneous blue and red

sideband drive

Analysis π pulse phase scan

yields fidelities

Fidelity 0.76(3)

Entangling two-qubit gate

𝑃ȁ ↑↑

𝑃ȁ ↓↓

𝑃ȁ ↓↑ + 𝑃ȁ ↑↓

Π = 𝑃ȁ ↑↑ + 𝑃ȁ ↓↓ − 𝑃ȁ ↓↑ + 𝑃ȁ ↑↓

Nature 476, 181 (2011)

Further results

• Sideband cooling

• Micromotion nulling

• Field mapping

• Individual-ion

addressing (4x)

U. Warring et al., PRA 87,

013437 (2013).

U. Warring et al., PRL 110,

173002 (2013).

See also: Oxford!

26

Meander Design

U. Warring et al., PRA, 87, 013437 (2013)

Skin effect and inductive couplings

Full-Wave numerical simulations (Ansys HFSS)

M. Carsjens et al., Appl. Phys. B 114, 243 (2014)

27

Characterization of Microwave Near-Fields

𝐵 ∝ ℜ 𝑒𝑖𝜔𝑡𝜅 Ԧ𝑒𝛼 sin𝜓 − 𝑖 Ԧ𝑒𝛼−𝜋/2 cos𝜓

+ 𝑄𝛽 cos𝜓 + 𝑖𝑄𝛽−𝜋/2 sin𝜓 ∙𝑥 − 𝑥0𝑧 − 𝑧0

+⋯

ȁ

2,0

↔

1,0

ȁ

2,1

↔

1,1

𝛽 99,9° 109(12)°

𝛼 24,3° 31.1(3)°

𝜓 6,4° 4,3(1,2)°

𝜅 8,5 μm 8,7(1,0) μm

𝑥0 45,5 μm 45,3(1) μm

𝑧0 −0,8 μm −0,8(2) μm

M. Wahnschaffe et al., Appl. Phys. Lett. 110, 034103 (2017)

28

Flange assembly

30

9Be+ Ion Qubits

Ablation

1064 nm

Photoionization

235 nm

Cooling, Detection

313 nm

31

9Be+ Ion Qubits

Ablation

1064 nm

Photoionization

235 nm

Cooling, Detection

313 nm

33

Field-independent qubit

9Be+ at 223 G

-1,000

+1,000

0

𝑓 [MHz]

𝐵 [G]400 800

-1

+1

0 𝐵 [G]400

𝜕𝐸/𝜕𝐵

𝜇𝐵

ȁ2, +2

ȁ2, −2ȁ2, −1

ȁ2, 0

ȁ2, +1

ȁ1, +1

ȁ1,0

ȁ1, −1

ȁ1, −1

ȁ2, +2

ȁ1,0

ȁ1, +1

ȁ2, −2ȁ2, −1

ȁ2, 0

ȁ2, +1NIST Quantum II

PTB / LUH

→ NIST, Oxford

34

Controlling the motion

Motional mode ሶ𝒏 [ph/ms]

HF-Rocking 0.028±0.001

1-ion-HF 0.122±0.01

1-ion-LF 0.116±0.01

ത𝑛 = 0.12 (3)𝜏𝜋 = 400 µ𝑠

𝜔 = 2𝜋 7.2 MHz

35

Mølmer-Sørensen gate

n

n

1 n 1 n

n n

1 n 1 n

1 n

1 n

1 n

1 n

Mølmer and Sørensen, PRL 82, 1835 (1999)

ninn 2

1Entangled state!

36

Mølmer-Sørensen gate

(With K. Hammerer, M. Schulte)

H. Hahn et al., npj Quant. Inf. 5, 1 (2019)

ℱ = 98.2 1.2 %

38

Pulse shaping

“not so square pulse”

avoid microwave

pseudopotential kicks

39

Pulse shaping

Square

1st order sin2

2nd order sin2

𝑥

𝑝

Square

1st order sin2

2nd order sin2

G. Zarantonello et al., arXiv:1911.03954 [quant-ph] (2019)

(With K. Hammerer, M. Schulte, R. F. Werner) 40

Order 17 shaped pulse

vs. 7-loop square pulse

Same pulse energy per

gate

Noise injection on radial

mode frequency

Pulse shaping

G. Zarantonello et al., Phys. Rev. Lett. 123, 260503 (2019)

41

Histogram fitting

ℱ = 99.5 % 99.3%…99.7%

Threshold detection (SPAM corr)

ℱ = 99.7 % 99.6%…99.8%

Maximum likelihood method

ℱ = 99.2 % 99.1%…99.7%

for gate without injected noise

No dynamic decoupling yet(!)

Encouraging results on

higher energy pulses

Integrated high-fidelity logic operations

G. Zarantonello et al., Phys. Rev. Lett. 123, 260503 (2019)

(With K. Hammerer, M. Schulte, R. F. Werner) 42

Where does that take us?

43

Time-varyingAC Zeeman

shifts

SPAM erroraffects gate

characterization

Anomalousmotionalheating

Frequentreloading

Repetitive

gates

Dynamic

decoupling

Cryo trap &

Automation

Cryo trap or

Surface cleaning

Small-scalequantumprocessor

MULTI-ZONE TRAPS

44

Next Fabrication Step: Connectivity

Laser Ions

Ion Trap

Interposer

Standard chip carrier

Wire bond

Through-Substrate Via

45

The future: scaling

Multi site operation

Laser zone

Single qubit op. zone

Entanglement zone

Requires:

Linear transport

X junction

Sympathetic cooling?

46

CRYOGENIC TRAP

47

Cryogenic trap

48

Low vibration interface

49

Cryogenic trap

50(T. Dubielzig, S. Halama)

Cold base plate

Objective

XYZ stage

Surface trap

Cryogenic trap

51(T. Dubielzig, M. Cabero-Müller)

NA = 0,5 (obscuration ~40%)

Magnification = 40x

8mm

180mm

Collaboration with NIST Boulder,

Precision Photonics, X.-P. Huang,

PTB (A. Linkogel, M. Sommerfeld,

A. Wiegmann, M.Schulz),

AEI (M. Dehne, J. Bogenstahl),

Sandia National Laboratories

Interferometric alignment @PTB

Ultra-low vibration (<8 nm RMS), analysis limited

by interferometer performance

Cooling power 1.2 W @4.2 K

Low motional heating expected

Should exhibit high-fidelity multi-qubit gates

Cyogenic trap

He (gas)

9Be+, 11/22/2019

52

Where does that take us?

53

User-ready single-ion

optical clock

opticlock has already demonstrated thepower of integration and automation

opticlock shares many components andtechnologies with our challenge

Apply to QC!

The integrated ion trap quantum device

Integrated

light source

Optical

waveguide

and coupler

Microwave

control

54

RT ion trap @ PTB

Micro trap fabrication

Cryo trap @ LUH

Cryogenic 5 T Penning Trap

Group activities

Ultra-low vibration

cryogenic setup

(< 8 nm RMS)

THANK YOU!

Labs and

offices

ERC Stg

„QLEDS“

SFB 1227 DQ-mat

Undergrads

Jonathan Morgner

Chris Nguyen

Julian Pick

Simon Roßmann

Jan Schaper

Florian Ungerechts

Jan Sebastian Warncke

PhD students

Matthias Borchert

Julia-Aileen Coenders

Timko Dubielzig

Sebastian Halama

Johannes Mielke

Malte Niemann

Teresa Meiners

Nicolás Pulido

Giorgio Zarantonello

Postdocs

Juan-Manuel Cornejo

Henning Hahn

Amado Bautista-Salvador

Humboldt / Mercator fellow

Ralf Lehnert (Indiana University, Bloomington)

Collaborators

NIST Ion Storage Group

M. Marangoni and G. Cerullo (Milan)

S. Ulmer (CERN) and the BASE collaboration

Piet Schmidt and Tanja Mehlstäubler (PTB)

J. Schöbel and A. Waag (TU Braunschweig)

K. Hammerer, M. Schulte, R. F. Werner (ITP, LUH)

MicroQC consortium

Osaka U and NICT (K. Hayazaka, K. Toyoda, U. Tanaka, T. Mukaiyama)

Daniel Rodríguez (Granada)

QUARTIQ

Funding

Quantum

Frontiers

56

Vacuum Setup

Imaging

o Significant less volume than

previous vacuum setup

o Revised and more flexible rf setup

o Single feedthrough-flange for

easy access

o Permanent magnets

57