Playing Quantum Games with Superconducting Circuits Quantum Computing with... · Bad Honnef Physics...

http://www.wmi.badw.de

Quantum Computing

with

Superconducting Circuits

Rudolf Gross

Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften

andTechnische Universität München

Bad Honnef Physics School onQuantum Technologies5 – 10 August 2018

http://www.we-heraeus-stiftung.de/index.html

09.08.2018/RG - 2www.wmi.badw.de Bad Honnef Physics School on Quantum Technologies, 5 – 10 August 2018, ©WMI

F. Deppe, K. Fedorov, H. Huebl, A. Marx

Michael FischerPhilip SchmidtPeter EderBehdad Ghaffari

Stephan PogorzalekDaniel SchwienbacherEdwar XieMinxing Xu

• U. Las Heras, M. Sanz, E. Solano, R. Di Candia• (Bilbao)• T. Ramos, J. J. Garcia-Ripoll (Madrid)• M. Hartmann (Edinburgh)• I. Cirac (MPQ Garching)

theory support

• M. Möttönen (Aalto)

• K. Inomata, T. Yamamoto, Y. Nakamura(NEC, Tokyo University)

• M. Aspelmeyer (U. Vienna)

• E. Weig, J.P. Kotthaus (U. Konstanz/LMU Munich)

experimental partners

former group members:Jan Goetz (Aalto University, Finland)Elisabeth Hoffmann (attocube)Matteo Mariantoni (Waterloo, Canada)Edwin P. Menzel (Rohde & Schwarz)Tomasz Niemczyk (BMW Group)Manuel Schwarz (IAV GmbH)Thomas Weißl (Inst. Néel, Grenoble)Karl-Friedrich Wulschner (Univ. of Vienna)Ling Zhong (Yale University)Christoph Zollitsch (UC London)

WMI Team & Partners


Intel Core i9 (14 nm)

Why Quantum Computing ?

What is next?

new architectures neuromorphic computing quantum computing

end of Moore‘s law


Quantum Advantage

• many problems in science and industrial applications/business are too complex for classical computing systems

• Quantum Computing may help to solve “hard” problems

algebraic algorithms e.g. factorization, cryptography, systems of equations, …

optimization problems e.g. logistics (traveling salesman), business processes, risk analysis, …

simulation of quantum systems e.g. quantum chemistry, material science, drug design, …


Simulation of Quantum SystemsHow much memory is needed to store a quantum state?How much time does it take to calculate dynamics of a quantum system?

by courtesy of S. Filipp (IBM Research)

Richard Feynman (1981):

“...trying to find a computer simulation of physics, ……, you'd better make it quantum mechanical, …..”


Information is inevitably tied to a physical representation and therefore to restrictions and possibilities related to the laws of physics and the parts available in the universe.

Quantum mechanical superpositions of information bearing states can be used, and the real utility of that needs to be understood. Quantum parallelism in computation is one possibility and will be assessed pessimistically.

Rolf Landauer, Physics Letters A 217, 188 - 193 (1996)

Information is Physical


M. H. Devoret, R. J. Schoelkopf, Science 339, 1169 – 1174 (2013)J. I. Cirac, H. J. Kimble, Nature Photonics 11, 18 – 20 (2017)

Roadmap to Quantum Computing

we do not go beyond this point in this tutorial

status in 2013


Jay M. Gambetta, Jerry M. Chow & Matthias Steffen npj Quantum Information 3, 2 (2017)

Roadmap to Quantum Computing


• Superconducting quantum circuits

• Trapped ion systems

• Optical lattices

• Quantum dot computer, spin-based

• Quantum dot computer, spatial-based

• Nuclear magnetic resonance on molecules in solution (liquid-state NMR)

• Solid-state NMR, Kane quantum computers

• Electrons-on-helium quantum computers

• Cavity quantum electrodynamics (c-QED)

• Molecular magnets

• Fullerene-based ESR quantum computer

• Linear optical quantum computer

• Diamond-based quantum computer (NV centers)

• …..

Hardware Platforms

….. many proposals, only some will be successful !!


Quantum Computing: Implementation Proposals

NMR Photons Atoms Solid State

linear optics cavity QED

trapped ions optical lattices

semiconductors superconductorsNV centerselectrons on LHe

flux charge phasenuclearspins

electronspins

orbitalstates

molecularmagnets


outline

• hype & hope: recent press releases

• solid state circuits go quantum

superconducting quantum electronics

advantages & drawbacks

• quantum computing

qubits, gates, readout, …

• experimental techniques

• outlook

Press Releases

Nov. 2017


An IBM cryostat wired for a 50 qubit system.

IBM scientists have successfully built and measured a processor prototype with 50 quantum bits. It is the first time any company has built a quantum computer at this scale

Nov. 2017

IBM reached milestone in quantum computing


Intel’s 17-qubit superconducting test chip for quantum computing has unique features for improved connectivity and better electrical and thermo-mechanical performance.

chip with advanced packaging delivered to QuTech

Intel Delivers 17-Qubit Superconducting Chip

Oct. 2017


Intel's new superconducting quantum chip called Tangle Lake has enough qubits to make things very interesting from a scientific standpoint

Intel Fabricates Quantum Chip “Tangle Lake”

Jan. 2018

Google has lifted the lid on its new quantum processor, Bristlecone. The project could play a key role in making quantum computers "functionally useful."

72 qubit processor


D-Wave 2000 Q:2 000 superconducting qubits,operating temperature: 30 mK

Quantum “Annealing” @ mK temperature


Superconducting Quantum Circuits

Quant


100 nm


Solid State CircuitsGo Quantum


multi

electron, spin, fluxon, photon

devices

single/few


devices

quantum


devices

today near future far future

quantifiable,but not quantum

classicaldescription

quantumdescription

65 nm process 2005 superconducting qubitsingle electron transistor

PTBIntel

• quantumconfinement

• tunneling• …

• superposition of states• entanglement• quantized em-fields

WMI 20062 µm

... solid state circuits go quantum

quantum1.0 quantum2.0


2nd Quantum Revolution

Quantum Information Theory

Solid-State Physics

Mathematics

…realization and full control of quantum systems !!


David J. WinelandSerge Haroche

The Nobel Prize in Physics 2012 was awarded jointly to Serge Haroche and David J. Wineland "for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems"

Nobel Prize in Physics 2002


http://web.physics.ucsb.edu/~martinisgroup/photos/BBCReZQu1103.jpg

quantumcomputing

http://research.physics.illinois.edu/QI/Photonics/research/

quantumcommunication

quantumsensing

Application fields

……. and more to come

quantummatter

https://www.mpq.mpg.de/4572004/profil

quantumsimulation

Credit: Francis Pratt / ISIS / STFC

quantummetrology

http://www.npl.co.uk/news/


Research Programs in QST @ Europe

• United Kingdom: £ 270 million for a five-year program

• Netherlands: € 146 million for a ten-year program

• ERANet program QUANTERA – Cofund Initiative in quantum science and technologies (launch: January 2018): € 30 million

• ….

Planned Research Programs in QST

• QUTE Flagship: Call for Flagship ramp-up phase early in 2018: > € 1 000 million

• BMBF program QUTEGA: about € 300 million(Quantum Technology – Foundations & Applications)

starting in 2018

Public Funding of QST


Is China winning race with the US to develop quantum computers?Chinese funding to research the next generation in computing may be dwarfing American efforts, according to US experts

PUBLISHED : Monday, 09 April, 2018, 12:37pm

China is building the world’s largest quantum research facility to develop a quantum computer and other “revolutionary” forms of technology that can be used by the military for code-breaking

or on stealth submarines, according to scientists and authorities involved in the project.

World’s Biggest Quantum Research Facility in China

Hefei Evening News

350.000 m2

China Quantum Center in Hefei – 10 Billion Euro Funding

http://www.scmp.com/news/china/economy/article/2140860/china-winning-race-us-develop-quantum-computers


TUM gets new Center for Quantum Engineering


Industry starts to get interested in important future technology field of Quantum Science & Technology

already existing industry efforts

• Spin qubits in semiconductors: Intel, HRL Laboratories, NTT, …

• Superconducting quantum circuits: Google, IBM, Intel, Anyon Systems Inc., Quantum Circuits Inc., Raytheon BBN Technologies, Rigetti Computing, …

• Superconducting quantum annealer: D-Wave

• Topological qubits: Microsoft

• Trapped ions interfaced with photons: Lockheed Martin

• …..

Interest of Industry


The Belief in New Technologies


..... have a large probability to be wrong !!

“I think there is a world market for maybe five computers”

Thomas J. Watson, chairman of IBM, 1943

“Whereas a calculator on the Eniac is equipped with 18000 vacuumtubes and weighs 30 tons, computers in the future may have only 1000 tubes and weigh only 1½ tons”

Popular Mechanics, March 1949

“There is no reason anyone would want a computer in their home”

Ken Olson, president, chairman and founder of DEC, 1977

Long-term Predictions.....

SuperconductingQuantum Electronics


©WMI

Superconductivity in a Nutshell


Superconducting Quantum Electronics

key physical ingredients

𝑰𝒔 = 𝑰𝒄𝑱 𝐬𝐢𝐧𝝋 ,𝒅𝝋

𝒅𝒕=𝟐𝒆𝑽

ℏර

𝑪

.

𝚲𝐉𝐬 ⋅ 𝒅ℓ + න

𝑭

.

𝑩 ⋅ ෝ𝒏 𝑑𝐹 = 𝒏𝚽𝟎

𝚿 𝐫, 𝐭 = 𝚿𝟎𝒆𝒊𝜽 𝒓,𝒕

𝚿 𝐫, 𝐭 𝟐 = 𝒏𝒔 𝒓, 𝒕


Superconductivity in a Nutshell

http://www.wmi.badw.de/teaching/Lecturenotes/index.html

Lecture Notes on • Superconductivity & Low Temperature Physics I & II• Applied Superconductivity

Books • Festkörperphysik

R. Gross, A. Marx

Tutorials • Superconducting Quantum Circuits

• DPG-Frühjahrstagung Sektion Kondensierte Materie, Berlin, 11.03. – 16.03.2018• Summer School NanoQI 2017, 24.07. – 28.07.2017, San Sebastian, Spain

http://www.wmi.badw.de/teaching/Talks/index.html

http://www.wmi.badw.de/teaching/Lecturenotes/index.html

http://www.wmi.badw.de/teaching/Talks/index.html


conventional electronic circuits

• classical physics• no quantization of fields• no superposition of states• no entanglement

... from Conventional to Quantum Electronics

𝑯 =𝚽𝟐

𝟐𝑳+𝑸𝟐

𝟐𝑪

2

1

quantum electronic circuits

• quantum mechanics• quantization of fields• coherent superposition of states• entanglement

2

1

Y. Nakamura et al., Nature 398, 786 (1999)

𝑯 =𝚽𝟐

𝟐𝑳+𝑸𝟐

𝟐𝑪= ℏ𝝎 ෝ𝒂† ෝ𝒂 +

𝟏

𝟐

𝚽, 𝑸 = 𝒊ℏ

LC oscillator



capacitors

inductors

tunable, lossless, nonlinear inductor ≡ Josephson Junction

𝑰𝒔 = 𝑰𝒄𝑱 𝐬𝐢𝐧𝝋

𝝏𝝋

𝝏𝒕=𝟐𝒆𝑽

ℏ

𝑺𝟏

𝑺𝟐𝑰

𝜕𝐼𝑠𝜕𝑡

= 𝐼𝑐𝐽 cos𝜑𝜕𝜑

𝜕𝑡= 𝐼𝑐𝐽 cos𝜑

2𝑒𝑉

ℏ

𝑳𝑱 =𝑽

𝝏𝑰𝒔/𝝏𝒕=

ℏ

𝟐𝒆𝑰𝒄𝑱𝐜𝐨𝐬𝝋

𝑰𝒔𝟐 =𝑰𝒄𝑱 𝐬𝐢𝐧𝝋𝟐

𝑰𝒔𝟏 =𝑰𝒄𝑱 𝐬𝐢𝐧𝝋𝟏

𝐼𝑠 = 𝐼𝑐 cos 𝜋Φ

Φ0sin

𝜑1 + 𝜑22

𝚽 𝝋⋆𝑺𝟏

𝑺𝟐

𝑺𝟏

𝑺𝟐

𝑳𝑱(𝚽) =𝑽

𝝏𝑰𝒔/𝝏𝒕=

ℏ

𝟐𝒆𝑰𝒄(𝚽)𝐜𝐨𝐬𝝋⋆

𝑰𝒄(𝚽)

nonlinearity:

tunability:

𝑰𝒄 = 𝟐𝑰𝒄𝑱


𝑬𝐩𝐨𝐭 = 𝑬𝑱 𝟏 − 𝐜𝐨𝐬 𝝋𝑬𝐩𝐨𝐭 = 𝑬𝑱 𝟏 − 𝐜𝐨𝐬 𝝋 − 𝑰𝝋

0.0 0.5 1.0 1.5 2.0-8

-6

-4

-2

0

2

/ 2

Ep

ot /

EJ0

I = 0

I = 0.5 Ic

I = Ic

𝜑/2𝜋

Josephson Junction (JJ)

full quantum treatment (quantum2.0):

𝑯 = 𝑬𝑱 𝟏 − 𝐜𝐨𝐬 ෝ𝝋 + 𝑬𝑪 𝑵𝟐

𝝓, 𝑸 = 𝒊ℏ𝝓 =

ෝ𝝋

𝟐𝝅𝚽𝟎

≡ position ≡ momentum

quasi-classical treatment (quantum1.0)

external force

nonlinear quantum harmonic oscillator

𝑸 = 𝑵 𝟐𝒆(𝟐𝒆)𝟐

𝟐𝑪

𝚽𝟎𝑰𝒄 𝚽

𝟐𝝅

classical motion of “phase particle”in tilt washboard potential


𝟐𝝅

𝟐𝑬𝑱


JJ: Classical vs. Quantum Treatment

𝑬𝑱

𝟐𝑬𝐉

classical treatment valid for 𝟐𝑬𝑱

ℏ𝝎𝒑≃

𝑬𝑱

𝑬𝑪

𝟏/𝟐≫ 𝟏 (level spacing ≪ 𝑘B𝑇, potential depth)

enter quantum regime by decreasing junction area 𝑨 and reducing 𝑻

harmonic oscillator potentialclose to minimum- level spacing: ℏ𝜔p- lowest energy: ℏ𝜔p/2

≃ ℏ𝝎𝐩/𝟐

≃ ℏ𝝎𝐩

𝑬𝑱 𝟏 − 𝐜𝐨𝐬𝝋

ℏ𝝎𝒑 =ℏ

𝑳𝑱𝑪= 𝟐𝑬𝑪𝑬𝑱

𝑬𝑱 =𝚽𝟎𝑰𝒄𝟐𝝅

∝ 𝑨

𝑬𝑪 =𝟐𝒆 𝟐

𝟐𝑪∝𝟏

𝑨

nanotechnology & low temperatures required


1E-4 1E-3 0.01 0.1 1 1010

-2

10-1

100

101

102

10-2

10-1

100

101

102

Ai (m

2)

Ec / k

B

EJ0 / k

B

𝑬𝑱 ∝ 𝑨

𝑬𝑪 ∝ 𝟏/𝑨

𝑬𝑪 > 𝑬𝑱

𝑬𝑪 < 𝑬𝑱

JJ: Classical vs. Quantum Treatment


harmonic LC oscillator

E

|0>|1>|2>|3>|4>|5>

|g>

|e>

„artificial solid-state atom“„artificial solid-state photon“

„quantum optics“ on a chip

quantum2-levelsystem

=qubit

Linear and Nonlinear Quantum Electronic Circuits

𝑯 = ℏ𝝎 ෝ𝒂†ෝ𝒂 +𝟏

𝟐𝑳𝑱 𝚽 =

𝚽𝟎

𝟐𝝅𝑰𝒄 𝐜𝐨𝐬 𝝅𝚽𝚽𝟎

tunable, anharmonic LC oscillator

E

tunable,lossless

Josephsoninductance

𝚽

𝑰tunable

Josephsonjunction

….

….


photon box:

microwave resonator

artificial atom:

solid state quantum circuit

A. Wallraff et al., Nature 431, 162 (2004).S. Girvin, R. Schoelkopf, Nature 451, 664-669 (2008) .

anharmonic level structure(quantum two-level system: qubit)

quantum coherence(coherence time: < 500 µs)

persistent current flux qubit

coplanar waveguide (CPW) resonator

small mode volume(Vmod/l3 10-5 – 10-6)

high quality factor(Q 104 – 106)

Circuit QED

Tunable Artificial Atoms & Photon Boxes

75 µm

many more: quantronium, fluxonium, transmon, x-mon, …


e.g. Kimble and Mabuchi groups at CaltechRempe group at MPQ Garching, ….

cavity QED natural atom in optical cavity

Rempe group

circuit QED solid state circuit in µ-wave cavity

e.g. Wallraff (ETH), Martinis (UCSB), Schoelkopf (Yale), Nakamura (Tokyo), ….

WMI

resonator QED

Cavity & Circuit QED

Gross group

MPQ


geometrical representation on Bloch sphere

𝟏 or 𝒆

𝟎 or 𝒈

Quantum Bit

𝜳 = 𝐜𝐨𝐬𝜽

𝟐𝟏 + 𝒆𝒊𝝋 𝐬𝐢𝐧

𝜽

𝟐𝟎

𝝋(𝒕) phase coherence

𝜽 𝒕 amplitude energy, population

Bloch angles:

𝜑 𝑡 =𝐸𝑒 − 𝐸𝑔

ℏ𝑡 = 𝜔ge𝑡


two qubit gate (C-NOT)Bloch sphere 𝟏

𝟎

𝟏

𝟎

U1

𝟎 𝟏

readout

𝟏

𝟎

U1

𝟏

𝟎

Qubit

single qubit gate

U1

M.A. Nielsen, I.L. Chuang, Quantum Computation andQuantum Information (Cambridge Univ. Press, 2000)

Quantum Processor

𝜳 = 𝐜𝐨𝐬𝚯

𝟐𝟏 + 𝒆𝒊𝝓 𝐬𝐢𝐧

𝚯

𝟐𝟎


superconductingquantum circuits

resonators qubits

couplers interferometers

switches JPAs

hybrid systems

qubits


resonators


• High-Q quantum harmonic oscillators

linear circuit, not a qubit, not directly useful for quantum computation!

quantumsimulation of

manybodyHamiltonians

L C

ancilla qubit/nonlinearity explore quantumphysics (Fock states,

squeezing etc.)

typically longcoherence times

quantum memory

mediate couplingbetween qubits quantum bus

qubit readout(„dispersivereadout“)

identifydecoherence sources in

superconductingquantum circuits

indirect use

Superconducting Resonators

SC Quantum Circuits

Advantages & Drawbacks


2D / h ≈ 10 GHz – 1 THz

ℏ𝝎𝐠𝐞 ≈ 1 – 10 GHz

normal metal superconductorEF

E E E

D >> kBT

|g>|e>co

ntinuum

of

exc

itations

ℏ𝝎𝐠𝐞


1. Macroscopic quantum nature of superconducting ground state 2. Energy gap in excitation spectrum

e.g. Al:2Δ

ℎ= 50 GHz


• exploit macroscopic quantum nature of sc ground state andgap in excitation spectrum long coherence time

M. H. Devoret and R. J. Schoelkopf, Science 339, 1169 (2013)

Moore‘s Law for QubitLifetime



Coherence Time

N. Ofek et al., Nature 536, 441–445 (2016)

Extending the lifetime of a quantum bit with error correction in superconducting circuits

Yale group:3D circuit QEDarchitecture


2000 2004 2008 2012 201610-9

10-8

10-7

10-6

10-5

10-4

10-3

coh

ere

nce

tim

e (s

)

year

best T2 times

reproducible T2 times

CPB

quantronium

cQED

transmon

3D transmon

fluxonium

Coherence Time of SC-Qubits


2 µm

flux qubit(Al)

transmon qubit(Al)

3D coplanarwaveguideresonator (Al)

coplanar waveguideresonator (Nb)

𝑻𝟐 ≲ 𝟏𝟎𝟎𝛍𝐬Megrant et al., APL 100, 113510 (2012)

𝑻𝟐 ≲ 𝟏𝟎𝐦𝐬M. Reagor et al., APL 102, 192604 (2013)

N. Ofek et al., Nature 536, 441 (2016)

𝑻𝟐 ≲ 𝟓𝟎𝟎𝛍𝐬

fabricate tailor-made quantum circuits

3. Established fabrication technology: thin film & nanotechnology

4. Superb design flexibility, tunability and scalability




quantum circuit with 8 resonators and 24 qubits (multiplexing readout)


State preservation by repetitive error detection in a superconducting quantum circuit,J. Kelly et al., Nature 519, 66-69 (2015)

UCSB&

chip with9 X-mon qubits

Superconducting Quantum Circuit


interaction energy = dipole moment ⋅ respective field

ℏ𝒈 = 𝐩 ⋅ 𝐄𝐫𝐦𝐬

ℏ𝒈 = 𝛍 ⋅ 𝐁𝐫𝐦𝐬

make electric (𝒑) or magnetic dipolemoment (𝝁) as big as possible

„big atoms“µm-sized circuits

„small cavities“quasi 1D cavities

make mode volume of cavity as small aspossible

𝑬𝐫𝐦𝐬𝐯𝐚𝐜 =

ℏ𝝎

𝝐𝟎𝑽𝐦𝐨𝐝

𝑩𝐫𝐦𝐬𝐯𝐚𝐜 =

𝝁𝟎ℏ𝝎

𝑽𝐦𝐨𝐝

5. Strong and ultrastrong coupling due to large dipole moments6. Fast manipulation by control pulses


T. Niemczyk et al., Nature Phys. 6, 772 (2010)

strong coupling: 𝒈 ≫ 𝜿, 𝜸(loss rates)

ultrastrong coupling: 𝒈 ≃ 𝝎𝒒, 𝝎𝒓

(system frequencies)


superconducting resonator

T. Niemczyk et al., Nature Phys. 6, 772 (2010)

flux qubit

X. Zhou, et al., Nature Physics 9 , 179 (2013)

Si3N4 nanomechanical beam

Superconducting Quantum Circuits7. Realization of hybrid quantum systems by combination with

other degrees of freedom (e.g. spin, photonic, phononic, plasmonic, ….)

examples from WMI

Ch. Zollitsch et al., Appl. Phys. Lett. 107, 142105 (2015)

paramagnetic spins

phosphorousdonors in Si

H. Huebl et al., PRL 111, 127003 (2013)

ferrimagneticspin ensemble

YIG


interferometer

nano-electromechanical circuit

Si3N4 nanobeam coupled to CPW resonator




resonator atom

𝝎𝒓 𝝎𝐠𝐞

𝝎𝒓

𝟐𝝅≃

𝝎𝐠𝐞

𝟐𝝅≃ few GHz

1 GHz ↔ 50 mK

ℏ𝝎𝒓 ≃ 10-24 J

ultra-low temperatures

ultra-sensitive µ-wave experiments

challenges

nano-fabrication

1. Low energy scales



2. Strong coupling to environment

protection against thermal microwave fieldse.g. cold attenuators, circulators, „Purcell filtering“ by cavity, ….

reduction of two-level fluctuatorse.g. substrate cleaning, avoid oxide layers, ….

strategies

optimum choice of operation pointe.g. operation @ qubit „sweet spot“, …

Qubit Design


Qubit Design

Josephson Junction (JJ)≡

tunable, lossless nonlinear inductor+

parallel capacitor

Qubit Hamiltonian

𝑯 = 𝑬𝑱 𝟏 − 𝐜𝐨𝐬 ෝ𝝋 + 𝑬𝑪 𝑵𝟐+ 𝑬𝐞𝐱

𝝓, 𝑸 = 𝒊ℏ

𝝓 =ෝ𝝋

𝟐𝝅𝚽𝟎 ≡ position

≡ momentum𝑸 = 𝑵 𝟐𝒆

(𝟐𝒆)𝟐

𝟐𝑪


𝟐𝝅

𝑳𝑱

𝑪

bias circuit

Josephson Junction

externalcircuit

Qubit design ≡ engineering of the qubit Hamiltonian


phase qubit

(EJ >> EC)current biased JJ

flux qubit

(EJ > EC)fluxon boxes

charge qubit

(EJ < EC)Cooper pair boxes

I I

I

V

J. Martinis (NIST) H. Mooij (Delft) V. Bouchiat (Quantronics)

nowadays superconducting qubit zoo is larger

transmon, camel-back, capacitively shunted 3JJ-FQB, quantronium, fluxonium…

“traditional” classification via 𝑬𝑱/𝑬𝑪 is increasingly difficult

Flexibility in Qubit Design (@2003)


phase qubit

(EJ >> EC)current biased JJ

flux qubit

(EJ > EC)fluxon boxes

charge qubit

(EJ < EC)Cooper pair boxes

Qubit Design by Potential Engineering

engineered qubit potential

I

V

I


𝑳𝑱

𝑪

add inductance

𝑯 = 𝑬𝑱 𝟏 − 𝐜𝐨𝐬 ෝ𝝋 + 𝑬𝑪 𝑵𝟐+ 𝑬𝐞𝐱

unsuitable for TLS!

add junctions

• flux/phase engineering

add bias current

add gate capacitor

• charge engineering

𝐸J naturally induces

anticrossings

add shunt capacitor change curvature ofcharge parabola

(3JJ flux qubit)

(rf SQUID &phase qubit)

(phase qubit)

(charge qubit)

(transmon qubit)

𝑳𝑱

𝑪

𝑳𝑱 𝜶𝑳𝑱

𝑳𝑱

𝑪

𝑳

𝑳𝑱

𝑪𝑱

𝑰

𝑵

𝑬𝑱𝑪𝐠

𝑽𝐠

𝑪𝑱

Qubit Design by Potential Engineering

𝑵

𝑬𝑱𝑪𝐠

𝑽𝐠

𝑪𝑱

𝑪𝒔


𝑯𝐂𝐏𝐁 = 𝑬𝑪 𝑵 − 𝑵𝐠𝟐+ 𝑬𝐉 𝟏 − 𝐜𝐨𝐬 ෝ𝝋

• gate charge 𝑵𝐠 ≡𝑪𝐠𝑽𝐠

𝟐𝒆

induced by gate voltage 𝑽𝐠

adds/removes excess CP to/fromisland

classical quantity

may assume fractional values!

charge qubit – the Cooper pair box (CPB)

charge regime 𝑬𝑪 ≳ 𝑬𝐉 charge is good quantum number

Example: Cooper Pair Box (CPB)

𝑵−𝑵𝒈

𝑬𝑱𝑪𝐠

𝑽𝐠

𝑪𝑱

additional term due gate voltage small

𝑵 = −𝒊𝝏

𝝏𝝋

• charge energy: 𝑬𝑪 ≡(𝟐𝒆)𝟐

𝟐 𝑪𝒈+𝑪𝑱

superconductingisland


tunable JJ (dc SQUID)

𝑪𝐉/𝟐

readout

• dc SQUID with 𝜷𝑳 ≪ 𝟏 tunable JJ with effective 𝑬𝑱(𝚽) and 𝑬𝑪

• gate voltage 𝑽𝐠 is control knob

• readout with additional JJ

detect number of excess Cooper pairs on island

• Josephson energy 𝑬𝑱 𝐜𝐨𝐬 ෝ𝝋

couples charge states/parabolas

avoided level crossings

island

𝑪𝐠

𝑽𝐠

typical prameters:𝐸𝐶/ℎ ≃ 5 GHz, 𝐸J/ℎ ≃ 5 GHz

𝑪𝐉/𝟐

charge qubit – the split Cooper pair box (CPB)

𝑯𝐂𝐏𝐁 = 𝑬𝑪 𝑵 − 𝑵𝐠𝟐+ 𝑬𝐉(𝚽) 𝟏 − 𝐜𝐨𝐬 ෝ𝝋

0.0 0.5 1.0 1.5 2.00.0

0.5

1.0

E / E

C

CVe / 2e

E

E+

E

𝑬𝐉

𝑬𝑪= 𝟎. 𝟎𝟔

𝑬𝐉(𝚽)

𝑵𝐠

𝐸/𝐸

𝐶

E+

𝑵=𝟎

𝑵=𝟏

𝑵=𝟐



from the Cooper pair box to the transmon qubit

advantages of the CPB:

• simple design (2JJ, 𝛽𝐿 ≪ 1)

• level splitting Δ = 𝐸J ∝ 𝐼c(flux qubit: 𝛥 ∝ exp − Τ𝐸𝐽 𝐸𝐶 )

• voltages convenient for coupling to other qubits coupling to readout circuitry coupling to control signals

• large anharmonicity (few GHz)

• in first order insensitive to charge fluctuations at „sweet spot“ 𝑁g = 𝑛 +1

2

disadvantages:

• coherence times short due to susceptibility to 1/𝑓 charge noise

• in practice: coherence times of only a few 10 ns even at the sweet spot!

• idea flatten energy dispersion



J. Koch et al., PRA 76, 042319 (2007).

take a CPB geometry andincrease Τ𝑬𝐉𝟎 𝑬𝑪 by shunt capacitor

charge dispersion decreases exponentially with Τ𝐸J 𝐸𝐶 less sensitive to charge noise

anharmonicity decreases only polynomially with Τ𝐸J 𝐸𝐶 optimum trade-off for Τ𝐸J 𝐸𝐶 ≈ 50

few hundreds of MHz anharmonicity left charge no longer good quantum number not tunable via gate voltage anymore tune via flux (dc SQUID)

transmission line shuntedplasma oscillation qubit

𝑵𝒈 = 𝑪𝒈𝑽𝒈/𝟐𝒆 𝑵𝒈 = 𝑪𝒈𝑽𝒈/𝟐𝒆

𝑵−𝑵𝒈

𝑬𝑱𝑪𝐠

𝑽𝐠

𝑪𝑱

𝑪𝒔superconductingisland

Example: Transmon Qubit


• embed into a resonator for readout filtering control

2D geometries: 𝟏𝟎 − 𝟒𝟎 𝛍𝐬3D geometries: up to 𝟓𝟎𝟎 𝛍𝐬

• the transmon is currentlymost successful qubit withrespect to coherence times

• coherence of transmonsmostly limited by spuriousTLS (defects) in substrateand metal-substrate interface

J. Koch et al., Phys. Rev. A 76, 042319 (2007).


Qubit Coherence


• interaction with environment for control purposes and readout

uncontrolled interactions (noise) also exist quantum effects (population oscillations, quantum interference,

superpositions, entanglement) unobservable after characteristic time after decoherence time quantum effects have decayed to Τ1 𝑒 of their original

level term “decoherence” originally only referred to phase nowadays sloppily comprises both phase and amplitude effects

𝜳 𝒕 = 𝐜𝐨𝐬𝜽(𝒕)

𝟐𝐞 + 𝒆𝒊𝝋(𝒕) 𝐬𝐢𝐧

𝜽(𝒕)

𝟐𝐠



• ideal quantum system

completely isolated in reality, however, …

Quantum Coherence


• population energy relaxation time 𝑻𝟏 decay from |e⟩ to |g⟩ nonadiabatic (irreversible) processes induced by high-frequency fluctuations (𝜔 ≈ 𝜔ge)

• phase pure dephasing time 𝑻𝝋 adiabatic (reversible) processes induced by low-frequency fluctuations (𝜔 → 0) often encountered: 1/f-noise real measurements always contain 𝑇1-effects

𝑻𝟐−𝟏 = 𝟐𝑻𝟏

−𝟏 + 𝑻𝝋−𝟏

nomenclature not very consistent in literature!

energy relaxation and dephasing

Qubit Lifetime



𝜽(𝒕)

𝟐𝐠



𝝋 𝒕 =𝑬𝒆 − 𝑬𝒈

ℏ𝒕 = 𝝎𝐠𝐞𝒕

𝜹𝝋 = 𝜹𝝎𝐠𝐞𝑻𝝋 ≃ 𝟐𝝅


Qubits strongly couple to electromagnetic fields decoherence due to environmental fluctuations

• place qubit in cavity: „Purcell filtering“

𝝎𝒓 𝝎𝝎𝒒

large detuning𝛿 = 𝜔𝑟 − 𝜔𝑞 ≫ 𝑔

strongly reduced „photon DOS“ @ 𝝎𝒒

𝜔𝑞/2𝜋

(GH

z)

𝜆 = 𝛿Φ/Φ0

𝜹𝝎𝒒

𝜹𝝎𝒒

• operate qubit @ sweet spot: 1st order coupling to noise vanishes

𝜹𝝎𝒒 =𝝏𝝎𝒒

𝝏𝝀𝜹𝝀 +

𝟏

𝟐

𝝏𝟐𝝎𝒒

𝝏𝝀𝟐𝜹𝝀𝟐 +⋯

1st ordercoupling

2nd ordercoupling

Qubit Lifetime


𝑵𝒈 = 𝑪𝒈𝑽𝒈/𝟐𝒆 𝑵𝒈 = 𝑪𝒈𝑽𝒈/𝟐𝒆


𝜹𝝎𝒒 =𝟏

𝟐

𝝏𝟐𝝎𝒒

𝝏𝑵𝒈𝟐 𝜹𝑵𝒈

𝟐 is large𝝎𝒒

𝜹𝝎𝒒 =𝟏

𝟐

𝝏𝟐𝝎𝒒

𝝏𝑵𝒈𝟐 𝜹𝑵𝒈

𝟐 is small𝝎𝒒

𝑻𝟐 < 𝟓𝟎𝟎 𝛍𝐬


Photon Statistics from Dephasing

𝑪 𝝉 ∝ 𝐕𝐚𝐫(𝒏)

𝜸𝝋𝒏 ∝ 𝐕𝐚𝐫(𝒏𝒓)

𝜸𝝋𝒏𝐭𝐡 𝒏𝒓 ∝ 𝒏𝒓

𝟐 + 𝒏𝒓𝜸𝝋𝒏𝐜𝐨𝐡 𝒏𝒓 ∝ 𝟐𝒏𝒓

𝜸𝝋𝒏𝐬𝐡𝐨𝐭 𝒏𝒓 ∝ 𝒏𝒓

thermal field

classicallimit

Poissonian

𝐕𝐚𝐫(𝐧) 𝒏𝟐 + 𝐧 𝒏𝟐 𝐧

J. Goetz et al., Phys. Rev. Lett. 118, 103602 (2017)


• superconducting resonators

can be fabricated in various geometries with high quality factors

thin film based resonators: 𝑻𝟐 ≤ 𝟐𝟎 𝛍𝐬 (Nb on Si)

𝑻𝟐 ≤ 𝟏𝟎𝟎 𝛍𝐬 (Al on sapphire)

3D (bulk based) resonators: 𝑻𝟐 ≤ 𝟏𝟎𝐦𝐬 (Al)

• superconducting qubits

large variety of different qubits due to flexible potential engineering

transmon qubits presently show best coherence times: 𝑻𝟐 ≤ 𝟓𝟎𝟎 𝛍𝐬

𝑻𝟐 Times of Resonators & Qubits

reduction of two-level fluctuators is important taske.g. substrate cleaning, avoid oxide layers, remove surface spins….


𝑻𝟐 > 𝟐𝟎 µs

https://quantumexperience.ng.bluemix.net/qx/devices

𝑻𝟐 Times of Qubits



𝑻𝟐 Times of Qubits

Qubit

Connectivity𝑻𝟏 (µsec) 𝑻𝟐/𝑻𝟐

∗ (µsec)

Computer Qubit # Min Max Ave Min Max Ave Min Max Ave

IBM QX2 5 2 4 2.4 44.9 63.1 53.2 27.7 61.4 44.5

IBM QX4 5 2 4 2.4 36.2 54.8 48.1 14.9 55.7 31.1

IBM QX5 16 2 3 2.75 28.3 69.9 42.8 14.5 127.3 59.0

IBM QS1_1 20 2 6 3.9 47.5 173.5 80.1 15.6 94.2 41.3

Rigetti 19Q 19 1 3 2.21 8.2 31.0 20.3 4.9 26.8 10.9

Google indicated that their 𝑻𝟏 times are roughly 2-4x worse than IBM’s, but that their single and two qubit gate fidelities are 2-10x better, and their measurement fidelities are roughly 10x better.

https://quantumcomputingreport.com/scorecards/qubit-quality/


Single Qubit Gates


important states on the Bloch sphere

𝒙

𝒚

𝒛

|𝐠⟩

|𝐞⟩

𝐞 + 𝐠

𝟐

𝐞 − 𝒊 𝐠

𝟐

𝐞 − 𝐠

𝟐

𝐞 + 𝒊 𝐠

𝟐

𝒙

𝒚

𝒛

|𝟏⟩

|𝟎⟩

𝟎 + 𝟏

𝟐

𝟎 − 𝒊 𝟏

𝟐

𝟎 − 𝟏

𝟐

𝟎 + 𝒊|𝟏⟩

𝟐

𝚿 𝒕 = 𝐜𝐨𝐬𝜽

𝟐𝐞 + 𝒆𝒊𝝋 𝐬𝐢𝐧

𝜽

𝟐𝐠 𝚿 𝒕 = 𝐜𝐨𝐬

𝜽

𝟐𝟎 + 𝒆𝒊𝝋 𝐬𝐢𝐧

𝜽

𝟐𝟏

ITphysics

Single Qubit Gates


• single qubit gate

unitary operation 𝑈 on state |𝛹⟩ described by rotations on Bloch sphere + global phase technical implementation by microwave pulses

• rotation matrices

about x-axis 𝑅𝑥 𝛼 ≡ e−𝑖𝛼ෝ𝜎𝑥2 =

cos𝛼

2−𝑖 sin

𝛼

2

−𝑖 sin𝛼

2cos

𝛼

2

about y-axis 𝑅𝑦 𝛼 ≡ e−𝑖𝛼ෝ𝜎𝑦

2 =cos

𝛼

2−sin

𝛼

2

sin𝛼

2cos

𝛼

2

about z-axis 𝑅𝑧 𝛼 ≡ e−𝑖𝛼ෝ𝜎𝑧2 = 𝑒−𝑖 Τ𝛼 2 0

0 𝑒𝑖 Τ𝛼 2

In general unitary expressed by rotations

𝑈 = 𝑒𝑖𝛼 𝑅𝑧 𝛽 𝑅𝑦 𝛾 𝑅𝑧 𝛿 with 𝛼, 𝛽, 𝛾, 𝛿 ∈ ℝ

Z-Y decomposition (others possible) 𝛼 is a global phase (unobservable)

Single Qubit Gates


examples for 1-qubit gates

NOT

graphical representation example

matrix representation (taken from QI theroy books) typically follow IT convention!

Single Qubit Gates


unitary operations

𝑼|𝜳⟩ expressed via the Hermitian Pauli spin matrices 𝟏, ෝ𝝈𝒙, ෝ𝝈𝒚, ෝ𝝈𝒛

ෝ𝝈𝒙 ≡𝟎 𝟏𝟏 𝟎

ෝ𝝈𝒚 ≡𝟎 −𝒊𝒊 𝟎

ෝ𝝈𝒛 ≡𝟏 𝟎𝟎 −𝟏

𝟏 ≡𝟏 𝟎𝟎 𝟏

|𝐠⟩ and |𝐞⟩ are the eigenvectors of ෝ𝝈𝒛

pseudo spin

|𝜳⟩ is equivalent to spin wave function in external magnetic field

pseudo spin and Pauli matrices



𝜽(𝒕)

𝟐𝐠

Single Qubit Gatessu

pp

lem

enta

rym

ater

ial


ෝ𝝈𝒙 ≡𝟎 𝟏𝟏 𝟎


ෝ𝝈𝒛 ≡𝟏 𝟎𝟎 −𝟏

𝟏 ≡𝟏 𝟎𝟎 𝟏

conventions: Pauli matrices and Bloch sphere

these definitons contain several conventions, such as

the global scaling factor the positon of the minus sign in 𝜎𝑧 here, we show two examples with fixed 𝜎𝑧

physics convention 𝐠 ≡𝟎𝟏

, 𝐞 ≡𝟏𝟎

ground state energy negative (more „physical“)



𝜽(𝒕)

𝟐𝐠


𝟐𝟎 + 𝒆𝒊𝝋(𝒕) 𝐬𝐢𝐧

𝜽(𝒕)

𝟐𝟏

information theory (IT) convention

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press

𝟎 ≡𝟏𝟎

, 𝟏 ≡𝟎𝟏

ground state energy positive („unphysical“) easily generalized (more „logical”)

unless otherwise mentioned physics convention! formal resolution equate g to 1 and e to 0 used in this lecture!


pp

lem

enta

rym

ater

ial


ෝ𝝈𝒙 ≡𝟎 𝟏𝟏 𝟎


ෝ𝝈𝒛 ≡𝟏 𝟎𝟎 −𝟏

𝟏 ≡𝟏 𝟎𝟎 𝟏

interpretation of the Pauli matrices

1 = |g⟩⟨g| + e e

ො𝜎𝑥 = ො𝜎− + ො𝜎+

ො𝜎𝑧 = |e⟩⟨e| − g g

ො𝜎𝑦 = 𝑖 ො𝜎− − ො𝜎+

• Pauli matrices can expressed in terms of projection operators

ො𝜎− = g e

ො𝜎+ = e g

induce transitions between |g⟩ and |e⟩

puts an excitation into the qubit

removes an excitation from the qubit

⟨ ො𝜎𝑧⟩ gives the qubit population

reflects normalization

• combination of basis definition and operator description in terms of projection operators matrix form of operators

• in this lecture, we fix the matrix definitions of the Pauli matrices “physical” intuition in g , e -notation notation consistent with Nielsen & Chuang and most physics papers!

g

e

g

e

g

e

g

e? ?


pp

lem

enta

rym

ater

ial


Hadamard gate 𝑯 is of particular importance

𝑯 𝐠 =𝟏

𝟐( 𝐞 − |𝐠⟩)

𝑯 𝐞 =𝟏

𝟐(|𝐞⟩ + |𝐠⟩)

𝑯 ≡𝟏

𝟐

𝟏 𝟏𝟏 −𝟏

=𝟏

𝟐ෝ𝝈𝒙 + ෝ𝝈𝒛

𝒙

𝒚

𝒛

|𝐠⟩

|𝐞⟩

𝐞 + 𝐠

𝟐

𝐞 − 𝐠

𝟐

• physics convention

• applied to one of the basis states |g⟩ or |e⟩, it results in a superposition state ofthe basis states

𝑯 =𝟏

𝟐𝒆 𝒆 − 𝒈 𝒈 + 𝒆 𝒈 + 𝒈 𝒆

Single Qubit Gates


https://quantumexperience.ng.bluemix.net/qx/editor

Single Qubit Gate Errors

gate fidelity > 99.7%


Single Qubit Gate Errors




Two-Qubit Gates


Two-Qubit Gates

• for quantum processor we need gates that perform conditional logic between qubits

state of one qubit depends on the state of another

• most relevant: Controlled-NOT or CNOT gate control

target

flips the target qubit only if the control qubit is |1⟩, otherwise it does nothing

controltarget


• mitigate frequency crowding• optimal pulse control• flux-noise mitigation

Two-Qubit Gates

Idea: Parametric frequency modulation of a coupling element (flux tunable qubit)

realization by tunable coupler:

Bertet et al., Phys. Rev. B 73, 064512 (2006); Tian et al., NJP 10, 115001 (2008); Kapit et al., Phys. Rev. A 87, 062336 (2013); Roushan et al., Nat. Phys 13 146 (2017); McKay et al., Phys. Rev. Applied 6, 064007 (2016); Roth et al, arXiv:1708.02090 (2017)


Two-Qubit Gates

tunable coupler

Bertet et al., Phys. Rev. B 73, 064512 (2006); Tian et al., NJP 10, 115001 (2008); Kapit et al., Phys. Rev. A 87, 062336 (2013); Roushan et al., Nat. Phys 13 146 (2017); McKay et al., Phys. Rev. Applied 6, 064007 (2016); Roth et al, arXiv:1708.02090 (2017)

𝑯𝐂 =ℏ𝝎𝟏

𝟐ෝ𝝈𝒛,𝟏 +

ℏ𝝎𝟐

𝟐ෝ𝝈𝒛,𝟐 +

ℏ𝑱(𝒕)

𝟐ෝ𝝈𝒙,𝟏ෝ𝝈𝒙,𝟐

𝑱 𝒕 =𝒈𝟏𝒈𝟐𝟐

𝟏

𝚫𝟏 𝒕+

𝟏

𝚫𝟐 𝒕

𝚫𝟏,𝟐 𝒕 = 𝝎𝟏,𝟐 −𝝎𝑪 𝚽 𝒕


Two-Qubit Gates

• iSWAP operation between states |𝟎𝟏⟩ and 𝟎𝟏𝜔𝑑 = 𝜔2 − 𝜔1 (qubits’ difference frequency)

∼ ෝ𝝈+𝟏 ෝ𝝈−

𝟐 + ෝ𝝈−𝟏 ෝ𝝈+

𝟐= 𝐗𝟏𝐗𝟐 + 𝐘𝟏𝐘𝟐

• 2-photon transition (bSWAP): 𝟎𝟎 ↔ 𝟏𝟏𝜔𝑑 = 𝜔2 +𝜔1 (qubits’ difference frequency)

∼ ෝ𝝈+𝟏 ෝ𝝈+

𝟐+ ෝ𝝈−

𝟏 ෝ𝝈−𝟐 = 𝐗𝟏𝐗𝟐 − 𝐘𝟏𝐘𝟐

• Phase gate: shift of 𝟏𝟏𝜔𝑑 = 𝜔2 − 𝜔1 + 𝛼 (difference + anharmonicity)

∼ ෝ𝝈𝒛𝟏 ෝ𝝈𝒛

𝟐= 𝐙𝟏𝐙𝟐

tunable coupler can create XX, YY & ZZ interactions

𝟎𝟎

𝟏𝟏

𝟐𝟎

𝟏𝟎

𝟎𝟐

𝟎𝟏

𝜔2−𝜔1

𝜔2+𝜔1

𝜔2−𝜔1+𝛼


https://quantumexperience.ng.bluemix.net/qx/editor

Two-Qubit Gate Errors



Two-Qubit Gate Errors





1-Qubit Gate Fidelity 2-Qubit Gate Fidelity Read Out Fidelity

Computer Min Max Ave Min Max Ave Min Max Ave

IBM QX2 99.71% 99.88% 99.79% 94.22% 97.12% 95.33% 92.20% 98.20% 96.24%

IBM QX4 99.83% 99.96% 99.88% 95.11% 98.39% 97.11% 94.80% 97.10% 95.60%

IBM QX5 99.59% 99.87% 99.77% 91.98% 97.29% 95.70% 88.53% 96.66% 93.32%

IBM QS1_1 96.93% 99.92% 99.48% 82.28% 98.87% 95.68% 69.05% 93.55% 83.95%

Rigetti 19Q 94.96% 99.42% 98.63% 79.00% 93.60% 87.50% 84.00% 97.00% 93.30%

Single and Two-Qubit Gate Fidelity

Google indicated that their 𝑇1 times are roughly 2-4x worse than IBM’s, but that their single and two qubit gate fidelities are 2-10x better, and their measurement fidelities are roughly 10x better.




Technical Roadmap for Fault-Tolerant Quantum ComputingAmir Fruchtman, Iris Choi, University of Oxford (2016)

Two-Qubit Gate Fidelity

Qubit Readout


Qubit Readout

𝝎 ≠ 𝝎𝐠𝐞

rf signal in

qubit𝒈 or 𝒆

dispersive readout strategy

qubit state is encoded into phase of outgoing rf-signal no energy is dissipated on chip repeat with enough photons to beat noise, use low-noise amplifiers

already demonstrated

multiplexed readout of several qubits, 80 ns readout pulse, fidelity >97%

resonator

or

tran

smis

sio

n

frequency (GHz)

Blais et al. PRA 2004, Walraff et al., Nature 2004


Qubit Readout

courtesy: Olivier Buisson

𝑻𝐑𝐎 = 𝟓𝟐𝟎 ns

single shot readout


1-Qubit Gate Fidelity 2-Qubit Gate Fidelity Read Out Fidelity

Computer Min Max Ave Min Max Ave Min Max Ave

IBM QX2 99.71% 99.88% 99.79% 94.22% 97.12% 95.33% 92.20% 98.20% 96.24%

IBM QX4 99.83% 99.96% 99.88% 95.11% 98.39% 97.11% 94.80% 97.10% 95.60%

IBM QX5 99.59% 99.87% 99.77% 91.98% 97.29% 95.70% 88.53% 96.66% 93.32%

IBM QS1_1 96.93% 99.92% 99.48% 82.28% 98.87% 95.68% 69.05% 93.55% 83.95%

Rigetti 19Q 94.96% 99.42% 98.63% 79.00% 93.60% 87.50% 84.00% 97.00% 93.30%

Qubit Readout Fidelity




Qubit Readoutsystem/technique fidelity 𝑻𝐑𝐎 (ns)

JC nonlinearity of a superconducting cavityReed et al., Phys. Rev. Lett. 105, 173601 (2010)

87% 500

Internal Josephson Bifurcation AmplifierSchmitt et al., Phys. Rev. A 90, 062333 (2014)

96% 50-500

Josephson phase-locked parametric oscillatorLin et al., Nat. Commun. 5, 4480 (2014)

89% 100

External Josephson Parametric AmplifierJeffrey et al., Phys. Rev. Lett. 112, 190504 (2014)

98.7% 140

Internal Josephson Parametric OscillatorKrantz et al., Nat. Commun. 7, 11417(2016)

81.5% 600

External Josephson Parametric Dimer AmplifierWalter et al., Phys. Rev. Appl. 7, 054020 (2017)

99.2% 88

Multiplexed readout with TWPAHeinsoo et al., arXiv:1801.07904

97% 250

Longitudinal coupling + bifurcation amplifierBuisson group, unpublished (2018)

97% 50

External Josephson TWPABultink et al., APL 112, 092601 (2018)

99.8% 1100

ExperimentalTechniques


resonator atom

𝝎𝒓 𝝎𝐠𝐞

𝝎𝒓

𝟐𝝅≃

𝝎𝐠𝐞

𝟐𝝅≃ few GHz

1 GHz 50 mK

ℏ𝝎𝒓 ≃ 10-24 J

ultra-low temperatures

ultra-sensitive µ-wave experiments

energy scales

Drawbacks of sc quantum circuits

experimentalchallenges

nano-fabrication

sup

ple

men

tary

mat

eria

l


Experimental Techniques

ultra-low Ttechniques

microwavetechnology

nano-technology

key physical ingredients and technological challenges


Optical “table” @ mK temperature

1 GHz ≃ 50 mK

ħωr ≃ 10-24 J

mK

tech

no

logy

fo

r sc

qu

antu

m c

ircu

its


mK technology for circuit QED


IBM cryostat wired for a 50 qubit system

µ-wave Technology + mK temperature


• materials for superconducting circuits

• Typical superconductors Nb

type-II superconductor, 𝑇c ≈ 9K fast measurements at 4K possible shadow evaporation for nanoscale junction not possible (without hard mask)

Al type-I superconductor, 𝑇c ≈ 1.2 K measurements require millikelvin temperatures shadow evaporation possible (stable oxide)

• Normal metals mainly Au (no natural oxide layer) for on-chip resistors and passivation layers

• Dielectric substrates silicon, sapphire contribute to dielectric losses (𝑇1)



• micro- and nanopatterning of superconducting circuits

• Lithography define pattern optical lithography (UV) electron beam lithography (EBL)

• Thin-film deposition deposit materials DC sputtering (metals, e.g. Nb) RF sputtering (insulators) electron beam evaporation (metals, e.g. Al) epitaxial growth (molecular beam epitaxy, higher substrate temperatures)

• Processing positive pattern Lift-off

deposit material only where you want it negative pattern Etching

deposit material everywhere remove what you don‘t want



WMI EBL system

• Nanobeam nb5• up to 100 kV acceleration voltage

strongly reduced „natural“ undercut frombackscattered electrons

undercut now deliberately designedduring the process

• large beam current fast• few nm resolution (in practice mostly resist

limited)• heavily automated (operated „from the office“)

advantage: fewer user-dependentparameers in the process

better reproducibility


electron beam lithography (EBL)


resist mask first layer second layer tunnel junction

ghost

structures

small

junctions

large

junction

J. Schuler, PhD ThesisTU Munich (2005)

key fabrication technique for Al/AlOx/Al Josephson junctions with submicron lateral dimensions


qubit fabrication by shadow evaporation technique



qubit fabrication by shadow evaporation technique


500 μm

ground

center

20 μm

1 μm

Nb Si3N4 Si

Fredrik Hocke et al., New J. Phys. 14 , 123037 (2012)

Xiaoqing Zhou, et al., Nature Physics 9 , 179 (2013)

Matthias Perpeintner, et al., APL 105, 123106 (2014)

Fredrik Hocke, et al., APL 105, 133102 (2014)

M. Abdi et al., PRL 114, 173602 (2015)


CPW resonator coupled to nanomechanical beam


CPW resonator with inductively coupled beam


Challenges&

Problems


100

101

102

103

104

105

106

107

108

102

101

100

10-1

102

101

100

10-1

erro

r co

rre

ctio

n g

ain

wo

rst

qu

bit

err

or

number of qubits

10−1

10−2

10−3

10−4

Quantum Computing: Quantity & Quality

logical qubit 𝟏𝟎−𝟏𝟐 quantum computer

increase quantity ??

error correction threshold

Google 9

GoogleSupremacy Device


Major Challenges

• increase number of qubits while at the same time improving gate and readout fidelities as well as qubit coherence

• reduce crosstalk, frequency collision

• improve materials:density of two-level fluctuators and surface spins, dielectric losses, …

• develop system architecture e.g. 3D integration and packaging of multi-qubit chips, circuits with small footprint, …

• develop control circuitrye.g. scalable classical control electronics, cryogenic (microwave) components (switches, circulators, etc), optimal control pulses, ….

• develop alternative types of qubits with better performance

• develop new types of gatese.g. geometric gates, single-step multi-qubit entanglement generation, multi-qubit interactions based on n-body terms, …


The WMI team

Thank you !

Playing Quantum Games with Superconducting Circuits Quantum Computing with... · Bad Honnef Physics...

Documents

Transcript of Playing Quantum Games with Superconducting Circuits Quantum Computing with... · Bad Honnef Physics...