Hardware for universal quantum computers

Norbert M. Linke

TIQI group, Chris MonroeJQI, UMD

- a programmable trapped-ion machine -

Overview

Ion trap quantum computer modulehardware (5-7 qubits)modular gates and compiler

Quantum algorithms and applicationsBernstein Vaziraniarchitecture comparison

Outlook: current and future workquantum machine learningscaling up

Quantum computingwhat is a qubit?requirementswhy ions make good qubits

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Quantum computing

Classical bit Qubit

0

1

0 or 1superposition

n-bit register 2n states superposition of 2n states(entanglement)

bits

000 001 010 100011 101 110 111

0

0 1

1

a + b

000 + 111example:

000 001 010 100011 101 110 111

Quantum computing

Function evaluation – quantum parallel processing

000 001 010 100011 101 110 111

F(000) F(001) F(010) F(100)F(011) F(101) F(110) F(111)

Quantum Processor

F(x)

2n calculations at once

Quantum logic gates

OutputInput

Quantum computing

Example operation – the controlled-NOT (CNOT) gate

entangled state

phase kick-back

classical states

Many possible implementations – systems under investigation- super-conducting circuits- photonic networks- neutral atoms- NMR systems- NV centers- SINGLE IONS- ……

Building a quantum computer – requirements

Why is this so hard? – more requirements

- good qubits (quantum system with 2 levels, preparation, read-out)- universal set of gates (single qubit gate, 2-qubit entangling gate)

- long coherence times- many qubits - low gate errors

overhead for error correction

Quantum computing

Trapped ions

A good quantum computing candidate – why?

- Isolated quantum system, preparation and read-out with laser light- gate operations (using lasers/microwaves)

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The ion trap quantum computer (vision)

Ion trap Quantum computing – the big pic

quantum register

“accumulator”

segmented electrodes

D. J. Wineland et al. 1998 C. Monroe / J. Kim et al. 2013

Are we there yet…? – challenges

- Higher fidelity operations- Scalability: control over more qubits

+

+

+- -

Ion traps (reality)

Wolfgang Paul (Nobel Prize 1989)

The linear Paul trap – dynamic confinement in electric RF quadrupole + DC potential

Microfabricated versions – surface traps

MAT (Oxford)

D.P.L. Aude Craik et al., PRA 95 (2017)

Ion traps: state-of-the-art

Surface trap foundries – chips engineered by pros

trapped ion Coulomb crystals

Ion traps: hardware in current UMD module

S. Olmschenk, et al., PRA 76 (2007)

Trapped ion qubits: 171Yb+ level structure

atomic clock qubit -> B-field insensitivelong coherence times: ~1s

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+

1〉

0〉

12.6 GHz2S1/2

2P1/2

369 nm

F=0

F=1

F=0

F=1

Trapped ion qubits: State initialization

12.6 GHz2S1/2

2P1/2

F=0

F=1

F=0

F=1

369 nm

2.1 GHz

Trapped ion qubits: State detection

drive gates with pair of laser beams at 355nm

2S1/2

2P3/2

100 THz

D=33 THz

|0

|1

355 nm

2P1/2

GHz6.12HF

D=66 THz

171Yb+ as a qubit: coherent manipulation

Modular architecture

S. Debnath et al. Nature 536 (2016)

Grover, Hidden Shift, EC …

Hardware

2S1/2

2P3/2

D=33 THz

|0

|1

355 nm

2P1/2

GHz6.12HF

171Yb+

D=66 THz

Hardware: Read-out

Modular architecture

S. Debnath et al. Nature 536 (2016)

Grover, Hidden Shift, EC …

Quantum control: single qubit rotations (R-gates)

Raman beat note

Beatnote frequency

HFtr

ansi

tio

n p

rob

abili

ty

carrier

redsideband

bluesideband

x +HFx HF

Quantum control: entangling gates (XX-gates)

…

mode1

mode2

1 5 15

entangled state(EPR pair)

Quantum control: Full connectivity

not limited to local operations

NML et al. PNAS 114, 13 (2017)

Modular architecture

S. Debnath et al. Nature 536 (2016)

Grover, Hidden Shift, EC …

0100

1000

0010

0001

Quantum compiler: Modular CNOT gates

CNOT [1:2] F=96.4(6)%

CNOT [3:4] F=96.6(5)%1

0

0.2

0.4

0.6

0.8

CNOT [1:3] F=97.6(7)% CNOT [1:4] F=95.9(7)% CNOT [1:5] F=97.9(5)%

CNOT [2:3] F=95.6(6)% CNOT [2:4] F=98.4(7)% CNOT [2:5] F=96.8(7)%

CNOT [3:5] F=97.6(6)% CNOT [4:5] F=97.2(5)%

spam reduces this by ~2%

Quantum compiler: Modular CNOT gates

CNOT [1:2] F=96.4(6)%

CNOT [3:4] F=96.6(5)%1

0

0.2

0.4

0.6

0.8

CNOT [1:3] F=97.6(7)% CNOT [1:4] F=95.9(7)% CNOT [1:5] F=97.9(5)%

CNOT [2:3] F=95.6(6)% CNOT [2:4] F=98.4(7)% CNOT [2:5] F=96.8(7)%

CNOT [3:5] F=97.6(6)% CNOT [4:5] F=97.2(5)%

spam reduces this by ~2%

Quantum compiler: Modular CNOT gates

Modular architecture

Grover, Hidden Shift, EC …

S. Debnath et al. Nature 536 (2016)

Quantum algorithms: build it …and they will come!

1 S. Debnath et al. Nature 536 (2016) 2 NML et al., PNAS 114, 13 (2017)3 NML et al., Sci Adv. 3, 10 (2017) 4 C. Figgatt et al., Nat. Communs. 8, 1918 (2017)5 N. Solmeyer et al., accepted QST (2018) 6 NML et al., arxiv 1712.08581 (2017)7 K. A. Landsman et al., arxiv 1806.02807 8 M. Benedetti et al., arxiv 1801.07686 (2018)9 A. Seif et al., arxiv 1804.07718(2018) 10 in preparation

Fault-tolerant quantum error detection3 – K. Brown (Georgia Tech.)

Renyi entropy measurement of a Fermi-Hubbard model system6 – S. Johri (Intel)

Quantum game theory and Nash equilibria5 – N. Solmeyer (Army Research Lab)

Quantum machine learning8 – A. Ortiz (NASA)

Quantum scrambling and out-of-time-order correlators7 – N. Yao (UC Berkeley)

Hidden Shift algorithm2 – M. Roetteler (Microsoft)

Quantum Fourier Transform, Bernstein-Vazirani algorithm, Deutsch-Josza algorithm1

Grover’s algorithm4 – D. Maslov (NSF)

…

Bacon-Shor quantum error correction codes10 – T. Yoder (Harvard)

Deuteron VQE – R. Pooser (Oak Ridge)

Quantum machine learning8,10 – A. Ortiz (NASA)

Neural-network-based qubit readout9 – A. Seif (QuiCS/UMD)

Example algorithms 1

Bernstein-Vazirani algorithm: oracle implements

f(x)

oracle

E. Bernstein and U. Vazirani, SIAM J. Comput. 26 (1997)

INPUT

OUTPUT f(x)0

use all states

carries information

Example algorithms 1

Bernstein-Vazirani algorithm: oracle implements

information about the oracle- single shot

CNOT imprints a phase flip on the qubits

oracle

E. Bernstein and U. Vazirani, SIAM J. Comput. 26 (1997)

f(x)

Example algorithms 2

Hidden shift algorithm: oracle implements

example “known” function

circuit

e.g.

information about the oracle- single shot

oracle

A. M. Childs et al., in Proceedings of TQC 8 (2013)M. Roetteler, in Proceedings of 21st SODA (2010)

star-shaped (superconductor) fully connected (ion trap)

Bernstein-Vazirani algorithm

Hidden shift algorithm

NML et al. PNAS 114, 13 (2017)

Connectivity matters: architecture comparison (2016)

star-shaped (superconductor) fully connected (ion trap)

Bernstein-Vazirani algorithm

Hidden shift algorithm

≤4 ≤4

2-qubit gate count

NML et al. PNAS 114, 13 (2017)

Connectivity matters: architecture comparison

star-shaped (superconductor) fully connected (ion trap)

Bernstein-Vazirani algorithm

Hidden shift algorithm

4

≤4 ≤4

2-qubit gate count

10

NML et al. PNAS 114, 13 (2017)

QC architecture comparison: experimental results

star-shaped (superconductor) fully connected (ion trap)

Bernstein-Vazirani algorithm

Hidden shift algorithm

4

≤4 ≤4

2-qubit gate count

10

NML et al. PNAS 114, 13 (2017)

QC architecture comparison: experimental results

Quantum machine learning: Bars and Stripes

Quantum machine learning: Bars and Stripes

Benedetti, M. et al. arxiv 1801.07686 (2018)

Quantum machine learning: Bars and Stripes

2-Layer star connectivity

2-Layer all-to-all connectivity

Benedetti, M. et al. arxiv 1801.07686 (2018)

Quantum machine learning: Bars and Stripes

Benedetti, M. et al. arxiv 1801.07686 (2018)

Quantum machine learning: Bars and Stripes

Animation from Wikipedia by Ephramac

Use Particle Swarm Optimization (PSO)

Quantum machine learning: Bars and Stripes

Best particle out of 21

2-Layer star connectivity

no system will be fully connected for large N

the compilation challenge

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

C. Monroe et al., Phys. Rev. A 89 (2014)

Outlook 1: the future - scaling up

D. Hucul, et al., Nature Phys. 11 (2015)

Michael Goldman

Marko Cetina

Kristin Beck

Outlook 2: control over ~20 qubits

Laird Egan

Chris Monroe ShantanuDebnath

KevinLandsman

NML CarolineFiggatt

DaiweiZhu

Dmitri Maslov(NSF)

Martin Roetteler(Microsoft)

Ken Brown(Georgia Tech)

Sonika Johri(Intel)

Norman Yao(UC Berkeley)