UFABC

Roberto M. Serra

Federal University of ABC, Santo André, São Paulo, Brazil

E-mail: serra@ufabc.edu.br

Quantum Information & Quantum Thermodynamics

Web: quantum.ufabc.edu.br

Brazilian National Institute for Science and Technology of Quantum Information

UFABCQIS @ UFABCPEOPLERoberto M. Serra (Faculty) Fernando L. Semião (Faculty) Luciano Cruz (Faculty) Rafael Paiva (Faculty) Breno Marques (Faculty) Jonas Floriano (Postdoc) Saulo Moreira (Postdoc) Carlos Ivan Henao Osorio (PhD Student) Ivan Medina (PhD Student) Patrice Camati (PhD student) Wallace Santos Teixeira (PhD student) Jeferson Guimarães (MSc Student) Andrius (MSc student)

RESEARCH INTERESTS Theoretical and experimental

- Quantum information Science - Quantum thermodynamics - Experimental tests-of-principles in QIS - Entanglement and non-locality - Open quantum systems and decoherence - Quantum computation - Quantum coherence aspects in biology - Quantum metrology

Web: quantum.ufabc.edu.br

NMR spin qubits Quantum Optics twin-photons & squeezed light Trapped ions

Our quantum playground

UFABCQuantum Thermodynamics

Quantum Technology

Quantum Computation

Quantum key distribution (cryptograph)

Quantum Simulation

Quantum AI

Quantum Metrology

Quantum Info. Theory

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UFABCENIAC (1946)

vacuum

valves

Frist transistor

1947Single electron

transistor

1987

Frist quantum revolution

microelectronics

UFABCThermodynamics and information processing

M. P. Frank, The Physical Limits of Computing, Comput. Sci. Eng. 4 (3), 16 (2002)

According Landauer the limit for the irreversible

computational model is

per erased bit

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Single core performance

The ending of Moore Law# of transistors in chip doubles about ever two years (not even more!)

UFABC“....One never realizes experiments with a single electron or an atom or a small molecule. In thought experiments, one assumes that sometimes this is possible; invariably, this leads to ridiculous consequences....One may say that one does not realize experiments with single particles, more than one raises ichthyosaurs in the zoo.” E. Schrödinger (1952) Br. J. Philosophy Sci. 3 109 (1952)

Trapped Ions, D. Wineland group (Nobel prize, 2012)

Single photons, single atoms, S. Haroche group (Nobel prize, 2012)

Bolder, USA

Paris, France

UFABCQUANTUM COMPUTING Devices based on quantum systems (employing subatomic physics, photons, and/or nano-technology) could make calculation far faster than conventional machines if nothing spoils the quantum weirdness.

Quantum bits (qubits) - superposition logicBit A classical computer encodes information in strings of bits which can take 0 or 1 value

QubitQuantum Bits can be encoded in two-levelsystems (i.e. 1/2-spin, up and down state)

and can exist in a superposition of 0 and 1 simultaneously. It can be represented

as a vector in the Bloch sphere.

θ

φ

ψ

0

1

1

Quantum algorithms

superposition, interference , entanglement

Quantum advantage massive parallel processing w/ quantum logic

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“Technology Quarterly Here, There and Everywhere," The Economist (2017)

Brazilian National Institute for Science and Technology of Quantum Information

Huge investment on quantum technology - second quantum revolution

120 Principal investigators 29 research institutions 13 states e 25 cities Hundreds of PhD and MSc students Dozens of Postdoctoral researchers

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“Technology Quarterly Here, There and Everywhere," The Economist (2017)

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3

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IBM quantum ide

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3 or 4 qubits - Nuclear SpinUFABC CBPF

Liquid-state NMRUFABC UFRJ UFMG UFSC

Single photons

Linear optics

Braz

il

Hight fidelity universal gates

Entanglement

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Ground-to-satellite quantum teleportation & quantum cryptograph

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Quantum magnetometer

NV center in diamond

After a series of high profile GPS hacks and failures, WIRED reported, the U.S. military and several national labs are working on new quantum navigators that could revolutionize global positioning systems by cutting out the need for satellite.

UFABCEasy and difficult computational tasks

11245 + 33456 Adding n digits numbers requires n elementary operations

11245 x 33456 Adding n digits numbers requires n2 elementary operations

11245334 = p1 x p2 Factoring a n digit number requires

elementary operations

Computational complexity

travelling salesman is a NP problem

3-sat logical clauses satisfability is a NP problem

Let’s Back to computation

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( )zyxvB ,,=

cos 0 sin 12 2

ie ϕθ θψ = +

10

0! "

→ $ %& '

01

1! "

→ $ %& '

Representação matricial de um qubit

Qubit mais geral possível

cos 2

sin 2ie ϕθ

ψθ

$ %→' () *

.ˆ

,ˆ

,ˆ

ψσψ

ψσψ

ψσψ

z

y

x

z

y

x

=

=

=

{ }1,0

,0

0ˆ

,0

0ˆ

,0110

ˆ

Base

ii

ii

z

y

x

!!"

#$$%

&

−=

!!"

#$$%

&

−=

!!"

#$$%

&=

σ

σ

σ

BvM →ψ:

3ℜ→ε

The most general state of a quantum bit (qubit)

Quantum Computation

UFABCClassical computational model

UFABCPortas lógicas de 1 qubit

a not a0 11 0

Porta convencional de 1 bit 0 1ψ α β= + 1 0ψ α β= +

0 11 0

X ! "≡ $ %

& 'X

α β

β α# $ # $

=% & % &' ( ' (

Porta de Hadamard 1 111 12

H! "

≡ $ %−' (

12

Hα α β

β α β

+# $ # $=% & % &−( ) ( )

NOTx x

X

Z

H

0 1α β+ 0 1β α+

0 1α β+

0 1α β+

0 1α β−

0 12 2

α β α β+ −+

X Portas lógicas de 1 qubit

Hadamard 0 12+

0

Classical 1 bit logic gate

Hadamard quantum logic gate

UFABCQubit rotations

cos sin2 2ˆ ˆ( ) cos 1 sin

2 2sin cos

2 2

X

iR i X

i

q qq qq

q q

é ùæ ö æ ö-ç ÷ ç ÷ê úè ø è øæ ö æ ö ê úº - =ç ÷ ç ÷ ê úè ø è ø æ ö æ ö-ê úç ÷ ç ÷è ø è øë û

cos sin2 2ˆ ˆ( ) cos 1 sin

2 2sin cos

2 2

YR i Y

q qq qq

q q

é ùæ ö æ ö-ç ÷ ç ÷ê úè ø è øæ ö æ ö ê úº - =ç ÷ ç ÷ ê úè ø è ø æ ö æ öê úç ÷ ç ÷

è ø è øë û

/ 2

/ 2

0ˆ ˆ( ) cos 1 sin2 2 0

i

Z i

eR i Z

e

q

q

q qq-é ùæ ö æ öº - = ê úç ÷ ç ÷

è ø è ø ë û

( ) ˆ ˆˆˆ exp cos 1 sin2 2 2nR i n i nq q qq s sæ ö æ ö æ ö= - × = - ×ç ÷ ç ÷ ç ÷

è ø è ø è ø!

! ! ! !

HXH Z= HYH Y= - HZH X=

( )122 YH X Z R pæ ö= + = ç ÷

è ø

Some identities

UFABCIt is impossible to copy unknown quantum information

No-cloning theorem

W. K. Wootters and W. H. Zurek, Nature 299, 802 (1982); D. Dieks, Phys. Lett. A 92,. 271 (1982).

.S M

By Ä

( )ˆ .U

S M S M S MB U By y y yÄ ® Ä = Ä

( )( )ˆ ,

ˆ .S M S M

S M S M

U B

U B

y y y

j j j

Ä = Ä

Ä = Ä

( ) ( ) ( )

( ) ( )

ˆ ˆ ˆS S M S M S M

S M S M

S S M M

U B U B U By j y j

y y j j

y j y j

é ù+ Ä = Ä + Äë û= Ä + Ä

¹ + Ä +

Suppose that, we want to copy the state psi to a blank state of an auxiliary system

A unitary operation can produce the copy as

A universal copy machine should work for a different state, let us say phi

What happens when we apply this unitary to a superposition state?

This is not a copy It is in fact an entangled state

UFABCTwo qubit logic gates

The control not gate (equivalent to the XOR)

control qubit

target qubit

Input state Output state

1 0 0 0

0 1 0 0

0 0 0 1

0 0 1 0

Computacional basis

Example: Input state Cnot gate Output state

UFABCSome quantum gates identities

=

Ay

Bf

By

Af

=

0A

Bf 0

B

Af H H

Z

Z

H H

H

H

H

H

=

UFABCOne qubit operations and Cnot gates are universal

†VV V

@

†V

UFABCDeutsch Algorithmquantum parallelism

D. Deutsch, Proc. R. Soc. London A 400, 97 (1985).

Let us consider the 1-bit function ( ) { } { }: 0,1 0,1f x ®

ax

by

( )f x

ax

( )b

y f xÅ

The function f (x) is computed by a oracle that you have no access

Ex.

( )1, 00, 1if x

f x xif x

=ì= = í =î

X

( )1 0 12 a a

+

0b

( )f x ( ) ( )( )1 0 0 1 12 a ab b

f f+

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1b

( )f x

0a

0 aby 1 ab

y 2 aby 3 ab

y

0 0 0 1ab a b

y =

1 ( ) ( )21

10 1 0 1 0 12ab a b a a b b

Hy Ä= = + Ä - 2 ( ) ( )a bH H HÄ = Ä

2 ( ) ( )

( ) ( ) ( ) ( )

2 ( )

(0) (1)

1 ˆ 0 0 1 1 0 121 1 0 0 1 1 1 0 12

abf x aab a b b a b b

f faa b b a b b

Uy é ù= - + -ë û

é ù= - - + - -ë û

( ) ( )( )

( ) ( )( )

(0)

2(0)

1 1 0 1 0 1 , (0) (1)21 1 0 1 0 1 , (0) (1)2

faa a b b

abf

aa a b b

if f f

if f fy

ì - + - =ïï= íï - - - ¹ïî

HH

H

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( )( ) ( )

( ) ( )

(0)

3 2(0)

1 1 0 0 1 , (0) (1)21 1 1 0 1 , (0) (1)2

faa b b

aab ab

faa b b

if f fH

if f fy y

ì - - =ïï= = íï - - ¹ïî

1b

( )f x

0a

0 aby 1 ab

y 2 aby 3 ab

y

3

( ) ( )(0)3

11 (0) (1) 0 12

f

ab a b bf fy = - Å -

0, (0) (1)(0) (1)

1, (0) (1)if f f

f fif f f

=ìÅ = í ¹î

H

H

H

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Quantum algorithms

superposition, interference , entanglement

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{{

1o Registrot qubits

2o Registron qubits

10

0t

10

0n

H

HVx

TFQ-1

0 1 2 3 4 5

Shor’s factoring algorithm

1

109

1018

1027

1036

1045

200 400 600 800 1000number of digits

num

ber o

f ope

ratio

ns

multiplication

classical factorin

g

quantum factoring

Exponential complexity reduction

about n3 elementary operations

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Superdense Coding Bob Lab.

Alice Lab.

Source of entangled states

2 classical bits00, 01, 10, 11

Û1 qubit

A

A

B

HH

|0

|0 XY ij

i

jAlice’s lab. Bob’s lab.

One-time pad cryptograph

Eve

Quantum communication

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( )( )

( )

( )

( )

( )

,

0,0

1,0

0,1

1,1

1 0 1 12

1 0 0 1 121 0 0 1 121 0 1 1 021 0 1 1 02

xx y a b a bab

a b a bab ab

a b a bab ab

a b a bab ab

a b a bab ab

B y y

B

B

B

B

+

-

+

-

= + -

= + = F

= - = F

= + = Y

= - = Y

H

Alice Lab.

ComunicaçãoClássica

a

b

x

y

In the Bob’s lab

0

0 0 , 00

0 1 , 1

1

1 0 , 01

1 1 , 1

a b

a b

a b

a b

a

a b

x

y inputoutput y

y input

x

y inputoutput y

y input

+

+

-

-

=

ì = ® = Fï= = í= ® = Yïî

=

ì = ® = Fï= = í= ® = Yïî

( )( )( )( )

( ) ( )

,

1 0 1 121 0 1 1 12

1 1 1 11 0 1 12 2 2

ab

a

x yab ab

x

a b a b

CNOT x

a b a b

x xH

a b a b

input B

y y

y y

y y

=

= + -

® + - Å

é ùæ ö æ ö+ - - -ê ú® + Åç ÷ ç ÷ç ÷ ç ÷ê úè ø è øë û

1 y yÅ =

UFABCHow to implement qubits in physical systems

Photonic systemsTraped Ions

Superconducting Circuit electrodynamics

Nuclear spins - NMR

Many others candidates

UFABCOpen Quantum System - Master Equation two level system interacting with a Markovian heat reservoir

System environment interaction

Initially uncorrelated

UFABCOpen Quantum System - Master Equation two level system interacting with a Markovian heat reservoir

where

is the Bose-Einstein distribution

is the vacuum decay rate

UFABCQuantum information w/ Nuclear Spins

He N

superconducting solenoid

rf-coil

sample

HC

Cl Cl

Clrf-field

system’s electronics

NMR magnetometer

B 0

B 1

125Mhz

Liquid state NMR experimental setup

NMR @ 500 Mhz UFABC, São Paulo

Trichloromethane diluted in acetone d6

nucleus 1H 2H 13C 19F 31Pv0 [MHz] 500 77 126 470 202

spin (nat. abund.) 1/2 (99%) 1 (1%) 1/2 (1%) 1/2 (100%) 1/2 (100%)

13C labeled CHCl3

UFABCThank you for your attention

quantum.ufabc.edu.br

MSc, PhD, and Postdoctoral positions in QIS available @ UFABC