Quantum Science Seminar 2020 · QSS#13 07/16/2020. Quantum computing over the rainbow: the quantum optical frequency comb as a platform for measurement-based universal quantum computing

QSS#13 07/16/2020

Quantum computing over the rainbow: the quantum optical frequency comb as a platform for

measurement-based universal quantum computing

1

Olivier PfisterUniversity of Virginia

Quantum Fields and Quantum Information website: https://sites.google.com/view/qfqi

https://sites.google.com/view/qfqi



QSS#13 07/16/2020

Quantum computing over the rainbow: the quantum optical frequency comb as a platform for

measurement-based universal quantum computing

1

Olivier PfisterUniversity of Virginia

Quantum Fields and Quantum Information website: https://sites.google.com/view/qfqi

OR How I learned to stop worrying and love the comb




QSS#13 07/16/2020 2

RajveerNehra

Rafael Alexander(now UNM)

XuanZhu

Chun-HungChang

AyeWin

(now U.OK.)

MillerEaton

Carlos González Arciniegas

The QFQI group

QSS#13 07/16/2020

Collaborators3

Avi Pe’er

Bar-Ilan U.

Paulo Nussenzveig U. São Paulo

Marcelo Martinelli

U. São Paulo

Nick Menicucci

RMIT

Israel Klich UVA

Sae Woo Nam NIST

Raf Alexander

UNM

Andreas Beling

UVA ECE

Joe Campbell UVA ECE

Xu Yi

UVA ECE

Leandro Aolita

U. Fed. Rio Janeiro

Myungshik Kim

Imperial College

Thomas Gerrits NIST

Simonetta Liuti UVA

QSS#13 07/16/2020

• Large-scale cluster-state entanglement • Quantum state engineering and characterization (quantum error correction encodings) • Quantum photonics on chip. Collab. w/ UVA ECE: Campbell, Beling, Yi • Quantum simulation of nuclear physics • Quantum simulation of condensed matter physics

Today I will address the first two topics.

Current projects

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QSS#13 07/16/2020

Gaussian quantum optics (fields) • Large-scale entanglement (squeezing) • No postselection

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Building a continuous-variable quantum computer with light

Non-Gaussian quantum optics (photons) • Exponential speedup • Quantum error correction

QSS#13 07/16/2020

1. Circuit-based

2. Measurement-based

Two main flavors of universal quantum computing

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QSS#13 07/16/2020

1. Circuit-based



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QSS#13 07/16/2020

1. Circuit-based



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QSS#13 07/16/2020

1. Circuit-based



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QSS#13 07/16/2020

Teleportation as a qubit gate primitive

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QSS#13 07/16/2020


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QSS#13 07/16/2020


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QSS#13 07/16/2020


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QSS#13 07/16/2020


7


M(±)

HZ1�m

2 | i<latexit sha1_base64="MuhAKeEn99Paa57rpijiO8geeo8=">AAACBXicbZC7TsMwFIadcivlFmCEwaJCYqFKKiQYK1g6FoleRBMqx3Vaq7YT2Q5SFbKw8CosDCDEyjuw8Ta4bQZo+SVLn/5zjo7PH8SMKu0431ZhaXllda24XtrY3NresXf3WipKJCZNHLFIdgKkCKOCNDXVjHRiSRAPGGkHo6tJvX1PpKKRuNHjmPgcDQQNKUbaWD37sH57l3qhRDh1T3lWzR68WFFPIjFgpGeXnYozFVwEN4cyyNXo2V9eP8IJJ0JjhpTquk6s/RRJTTEjWclLFIkRHqEB6RoUiBPlp9MrMnhsnD4MI2me0HDq/p5IEVdqzAPTyZEeqvnaxPyv1k10eOGnVMSJJgLPFoUJgzqCk0hgn0qCNRsbQFhS81eIh8hEok1wJROCO3/yIrSqFdfw9Vm5dpnHUQQH4AicABecgxqogwZoAgwewTN4BW/Wk/VivVsfs9aClc/sgz+yPn8AmPSYoQ==</latexit><latexit sha1_base64="MuhAKeEn99Paa57rpijiO8geeo8=">AAACBXicbZC7TsMwFIadcivlFmCEwaJCYqFKKiQYK1g6FoleRBMqx3Vaq7YT2Q5SFbKw8CosDCDEyjuw8Ta4bQZo+SVLn/5zjo7PH8SMKu0431ZhaXllda24XtrY3NresXf3WipKJCZNHLFIdgKkCKOCNDXVjHRiSRAPGGkHo6tJvX1PpKKRuNHjmPgcDQQNKUbaWD37sH57l3qhRDh1T3lWzR68WFFPIjFgpGeXnYozFVwEN4cyyNXo2V9eP8IJJ0JjhpTquk6s/RRJTTEjWclLFIkRHqEB6RoUiBPlp9MrMnhsnD4MI2me0HDq/p5IEVdqzAPTyZEeqvnaxPyv1k10eOGnVMSJJgLPFoUJgzqCk0hgn0qCNRsbQFhS81eIh8hEok1wJROCO3/yIrSqFdfw9Vm5dpnHUQQH4AicABecgxqogwZoAgwewTN4BW/Wk/VivVsfs9aClc/sgz+yPn8AmPSYoQ==</latexit><latexit sha1_base64="MuhAKeEn99Paa57rpijiO8geeo8=">AAACBXicbZC7TsMwFIadcivlFmCEwaJCYqFKKiQYK1g6FoleRBMqx3Vaq7YT2Q5SFbKw8CosDCDEyjuw8Ta4bQZo+SVLn/5zjo7PH8SMKu0431ZhaXllda24XtrY3NresXf3WipKJCZNHLFIdgKkCKOCNDXVjHRiSRAPGGkHo6tJvX1PpKKRuNHjmPgcDQQNKUbaWD37sH57l3qhRDh1T3lWzR68WFFPIjFgpGeXnYozFVwEN4cyyNXo2V9eP8IJJ0JjhpTquk6s/RRJTTEjWclLFIkRHqEB6RoUiBPlp9MrMnhsnD4MI2me0HDq/p5IEVdqzAPTyZEeqvnaxPyv1k10eOGnVMSJJgLPFoUJgzqCk0hgn0qCNRsbQFhS81eIh8hEok1wJROCO3/yIrSqFdfw9Vm5dpnHUQQH4AicABecgxqogwZoAgwewTN4BW/Wk/VivVsfs9aClc/sgz+yPn8AmPSYoQ==</latexit><latexit sha1_base64="MuhAKeEn99Paa57rpijiO8geeo8=">AAACBXicbZC7TsMwFIadcivlFmCEwaJCYqFKKiQYK1g6FoleRBMqx3Vaq7YT2Q5SFbKw8CosDCDEyjuw8Ta4bQZo+SVLn/5zjo7PH8SMKu0431ZhaXllda24XtrY3NresXf3WipKJCZNHLFIdgKkCKOCNDXVjHRiSRAPGGkHo6tJvX1PpKKRuNHjmPgcDQQNKUbaWD37sH57l3qhRDh1T3lWzR68WFFPIjFgpGeXnYozFVwEN4cyyNXo2V9eP8IJJ0JjhpTquk6s/RRJTTEjWclLFIkRHqEB6RoUiBPlp9MrMnhsnD4MI2me0HDq/p5IEVdqzAPTyZEeqvnaxPyv1k10eOGnVMSJJgLPFoUJgzqCk0hgn0qCNRsbQFhS81eIh8hEok1wJROCO3/yIrSqFdfw9Vm5dpnHUQQH4AicABecgxqogwZoAgwewTN4BW/Wk/VivVsfs9aClc/sgz+yPn8AmPSYoQ==</latexit>

Z1�m

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QSS#13 07/16/2020


7


M(±)


QSS#13 07/16/2020

Can also shape cluster states with measurements

8

|+i |+i |+i

CZ CZ

QSS#13 07/16/2020


8

Measure Z

|+i |+i |+i

CZ CZ

QSS#13 07/16/2020


8

Measure Z

feed forward|+i |+i |+i

CZ CZ

QSS#13 07/16/2020


8

Measure Z


CZ CZ

QSS#13 07/16/2020


8

Measure Z


CZ CZ

QSS#13 07/16/2020


8

Measure Z

Measure X


CZ CZ

QSS#13 07/16/2020


8

Measure Z

Measure X

feed forward

feed forward

|+i |+i |+i

CZ CZ

QSS#13 07/16/2020


8

Measure Z

Measure X

feed forward

feed forward

|+i |+i |+i

CZ CZ

QSS#13 07/16/2020


8

Measure Z

Measure X

feed forward

feed forward

|+i |+i |+i

CZ CZ

QSS#13 07/16/2020


8

Measure Z

Measure X

feed forward

feed forward

|+i |+i |+i

CZ CZ

QSS#13 07/16/2020


8

Measure Z

Measure X

feed forward

feed forward

|+i |+i |+i

CZ CZ

QSS#13 07/16/2020


8

Measure Z

Measure X

feed forward

feed forward

|+i |+i |+i

CZ CZ

QSS#13 07/16/2020

Qubits Qumodes

Discrete vs. continuous variables, qubits vs. qumodes

9

{| q i}q2R{| 0 i , | 1 i}

{| p i}p2R =

⇢Zeipq | q i dq

�

p2R{|± i} = {| 0 i± | 1 i}

P =ip2(a† � a)

Q =1p2(a+ a†)

[Q,P ] = i

�Q�P =1

2

Hadamardtransform

Fouriertransform

| i = 0|0i+ 1|1i<latexit sha1_base64="uqIn/dsSY7MSJa5QdS+4C8z5eLI=">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</latexit>

| i =Z (q)|qidq

<latexit sha1_base64="4NRF8B+bvoWt1KWUEvmFVjDdreI=">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</latexit>

e.g. eigenstates of Sz

e.g. eigenstates of Sx

e.g. eigenstates of Q: position / amplitude quadr.

e.g. eigenstates of P: momentum / phase quadr.

| 00 i+ | 11 iBell state

Z| q i1 | q i2 dq

EPR state

O. Pfister, Continuous-variable quantum computing in the quantum optical frequency comb, J Phys B 53, 012001 (2020).

QSS#13 07/16/2020

Qubits Qumodes


9

{| q i}q2R{| 0 i , | 1 i}

{| p i}p2R =

⇢Zeipq | q i dq

�

p2R{|± i} = {| 0 i± | 1 i}

P =ip2(a† � a)

Q =1p2(a+ a†)

[Q,P ] = i

�Q�P =1

2

Hadamardtransform

Fouriertransform

| i = 0|0i+ 1|1i<latexit sha1_base64="uqIn/dsSY7MSJa5QdS+4C8z5eLI=">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</latexit>

| i =Z (q)|qidq

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e.g. eigenstates of Sz

e.g. eigenstates of Sx

e.g. eigenstates of Q: position / amplitude quadr.

e.g. eigenstates of P: momentum / phase quadr.

| 00 i+ | 11 iBell state

Z| q i1 | q i2 dq

EPR state


QSS#13 07/16/2020


9

P =ip2(a† � a)

Q =1p2(a+ a†)

[Q,P ] = i

�Q�P =1

2

Because CV SCALE


QSS#13 07/16/2020

Gaussian quantum optics (EM fields)

10

QSS#13 07/16/2020

The eigenmodes of a cavity form a large ensemble of classically coherent modes

...why not turn it into a quantum computer?

... ...nonlinear gain

Optical Parametric Oscillator(OPO)

quantum OFC

11

Carrier-envelope-phase locked mode-locked laser = optical frequency comb (OFC) (106 modes oscillating in phase)

... ...linear gain

LaserJohn L. Hall Theodor W. Hänsch

A good starting point: the quantum optical frequency comb

Why not turn the QOFC into a quantum computer?

QSS#13 07/16/2020





quantum OFC

11


... ...linear gain




QSS#13 07/16/2020





quantum OFC

11


... ...linear gain




QSS#13 07/16/2020





quantum OFC

11


... ...linear gain




QSS#13 07/16/2020





quantum OFC

11


... ...linear gain




QSS#13 07/16/2020





quantum OFC

11


... ...linear gain




QSS#13 07/16/2020





quantum OFC

11


... ...linear gain




QSS#13 07/16/2020





quantum OFC

11


... ...linear gain




QSS#13 07/16/2020





quantum OFC

11


... ...linear gain




QSS#13 07/16/2020





quantum OFC

11


... ...linear gain




QSS#13 07/16/2020





quantum OFC

11


... ...linear gain




QSS#13 07/16/2020





quantum OFC

11


... ...linear gain


Multipartite cluster entanglement in one fell swoop:

a top-down, large-scale quantum register



QSS#13 07/16/2020

QSS#13 07/16/2020

Larger...

1315 pump modes into YZY, ZZZ, ZYY

Single-OPO scalable square-grid cluster

QSS#13 07/16/2020 14

QSS#13 07/16/2020 15

QSS#13 07/16/2020

PZT Laser1 x2

Laser2 x2

Laser3

~

~

Pump OPO comb

LO

OPO locking

PZT PZT

PLL

PLL

SA

SA

flip mirror HWP

HWP

PBS

PPKTP

PPKTP

Filter Cavity

OPO

~

~

PDH Lock

PDH Lock

zzz

yyy

𝟐𝒎∆𝝎

9.2 MHz

9.2 MHz

~ 𝝎𝒐𝒇𝒇 ± 70 MHz

AOM

70 MHz

EOM EOM

~ 𝛀 = (𝒏 +

𝟏𝟐)∆𝛚

Entanglement Verification

𝜽𝟎

SA

Beams

Experimental setup

16

QSS#13 07/16/2020

Interference between identical frequencies of different combs

Interfering quantum combs

17

Chen, Menicucci, and Pfister, Experimental realization of multipartite entanglement of 60 modes of a quantum optical frequency comb, PRL 112, 120505 (2014)

0

0~104 modes long

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17


0

0~104 modes long

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17

0 ⟵ ...

0 0

0


Wang, Chen, Menicucci, and Pfister, Weaving quantum optical frequency combs into hypercubic cluster states, PRA 90, 032325 (2014)

0

0~104 modes long

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17

0 ⟵ ...

0 0

0



0

0~104 modes long

QSS#13 07/16/2020



17

0 ⟵ ...

0 0

0



0

0~104 modes long

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QSS#13 07/16/2020 19

QSS#13 07/16/2020

Time-domain proposal

20

• Akira Furusawa’s group: sequential entanglement of 104 qumodes (2 at a time)

“Dual-rail quantum wire”

TMS

QSS#13 07/16/2020

Time-domain proposal

20

• Akira Furusawa’s group: sequential entanglement of 104 qumodes (2 at a time)

“Dual-rail quantum wire”

TMS

106

QSS#13 07/16/2020

2D cluster states have arrived

21

QSS#13 07/16/2020

3D states (and beyond) just around the corner are

22

QSS#13 07/16/2020


22

QSS#13 07/16/2020


22

QSS#13 07/16/2020


22

QSS#13 07/16/2020

The generation of sophisticated, QC-universal cluster states on a very large scale (thousands of qumodes) is

EASY

over continuous variables and is also

highly compatible with an integrated optics approach. (Stay tuned.)

Take-home message

23O. Pfister, Continuous-variable quantum computing in the quantum optical frequency comb, Journal of Physics B: Atomic, Molecular, and Optical Physics 53, 012001 (2020); invited topical review.

https://www.google.com/url?q=https%3A%2F%2Fdoi.org%2F10.1088%2F1361-6455%2Fab526f&sa=D&sntz=1&usg=AFQjCNHow5sDsmc4jiUKExWCArIOFlfe6Q

https://www.google.com/url?q=https%3A%2F%2Fdoi.org%2F10.1088%2F1361-6455%2Fab526f&sa=D&sntz=1&usg=AFQjCNHow5sDsmc4jiUKExWCArIOFlfe6Q

QSS#13 07/16/2020

Non-Gaussian quantum optics (photons)

24

QSS#13 07/16/2020

An experimentally accessible non-Gaussian operation: photon-number detection

25

Sae Woo Nam(NIST)

Aaron Miller(Quantum Opus)

QSS#13 07/16/2020

POVM set ≡ (ideally!)

Superconducting transition-edge sensor


25

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Physics Today 71, 8, 28 (2018)

Sae Woo Nam(NIST)


QSS#13 07/16/2020




25


�T�R

TTbias0

R


Sae Woo Nam(NIST)


QSS#13 07/16/2020




25


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TTbias0

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Sae Woo Nam(NIST)


QSS#13 07/16/2020




25


�T�R

TTbias0

R

Physics Today 71, 8, 28 (2018) 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

−200

0

200

400

600

800

1000

1200

Time (s)

TES

Sign

al (a

rbitr

ary

units

)

One−Photon

Two−Photon

Three−Photon

Sae Woo Nam(NIST)


QSS#13 07/16/2020

Processing TES signal: PNR detection

26

~6μs

30μs

1

5

3

2

4

Lowphotonflux

Highflux

~15μs

TESSignal(a.u.)

Time(a.u.)

QSS#13 07/16/2020


26

~6μs

30μs

1

5

3

2

4

Lowphotonflux

Highflux

~15μs

TESSignal(a.u.)

Time(a.u.)

Counts

Height(a.u.)

01 2 3 4 5

6

QSS#13 07/16/2020


26

~6μs

30μs

1

5

3

2

4

Lowphotonflux

Highflux

~15μs

TESSignal(a.u.)

Time(a.u.)

𝑃(𝑛)

𝑛

Counts

Height(a.u.)

01 2 3 4 5

6

QSS#13 07/16/2020

TES @ PfisterLabs

27

QSS#13 07/16/2020

Quantum tomography with photon counting

28

S. Wallentowitz & W. Vogel, PRA (1996)K. Banaszek & W. Wódkiewicz, PRL (1996)

W (q, p) =1

2⇡

Z 1

�1eiyp

Dq � y

2

�� ⇢�� q +

y

2

Edy

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- Only function whose marginals yield the quantum probability distributions - Can be NONPOSITIVE (i.e., nonGaussian for a pure state)

WIGNER FUNCTION

QSS#13 07/16/2020

- Expectation value of the photon-number parity - Easily measured directly with photon-number-resolving detection - Raster scan of phase space by amplitude/phase shifts gives whole W(q,p)

Quantum tomography with photon counting

28

S. Wallentowitz & W. Vogel, PRA (1996)K. Banaszek & W. Wódkiewicz, PRL (1996)

W (q, p) =1

2⇡

Z 1

�1eiyp

Dq � y

2

�� ⇢�� q +

y

2

Edy

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W⇢̂(↵) =1

⇡Tr[D†(↵)⇢̂D(↵)(�1)n̂]

<latexit sha1_base64="LTgiq7rD5DKsRo+DFx5Vbj2eoZg=">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</latexit><latexit sha1_base64="LTgiq7rD5DKsRo+DFx5Vbj2eoZg=">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</latexit><latexit sha1_base64="LTgiq7rD5DKsRo+DFx5Vbj2eoZg=">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</latexit><latexit sha1_base64="LTgiq7rD5DKsRo+DFx5Vbj2eoZg=">AAACRnicbVDPS9xAGP2ytmq3rY167GXoUlgPXRIp6EUQ9dCjwv6CTVy+zE42g5NJmJkIS8hf58WzN/8ELx4qpVdnf9F2tw8GHu+975uZF+WCa+N5j05t483bza3td/X3Hz7ufHJ397o6KxRlHZqJTPUj1ExwyTqGG8H6uWKYRoL1opvzqd+7ZUrzTLbNJGdhimPJY07RWGnohr1hGSRoykAlWVU1AxR5ggfkhASxQlr6VRnkvGqrwcV1MMLxmKll5s/YxVJqfvMPruf7ZFWRcOg2vJY3A1kn/oI0YIHLofsQjDJapEwaKlDrge/lJixRGU4Fq+pBoVmO9AbHbGCpxJTpsJzVUJGvVhmROFP2SENm6t8TJaZaT9LIJlM0iV71puL/vEFh4uOw5DIvDJN0flFcCGIyMu2UjLhi1IiJJUgVt28lNEFbn7HN120J/uqX10n3sOV7Lf/qe+P0bFHHNnyGL9AEH47gFH7AJXSAwh08wU94ce6dZ+eX83serTmLmX34BzV4BVO9sZo=</latexit>

↵ := q + ip<latexit sha1_base64="iJC/7ntVLbMUWQMvhbe1ES+Osh8=">AAAB9XicbVDLSgNBEOz1GeMr6tHLYBAEIeyKoAhC0IvHCOYByRp6J7PJkNnZdWZWCUv+w4sHRbz6L978GyePgyYWNBRV3XR3BYng2rjut7OwuLS8sppby69vbG5tF3Z2azpOFWVVGotYNQLUTHDJqoYbwRqJYhgFgtWD/vXIrz8ypXks78wgYX6EXclDTtFY6b6FIukhubgkD8c8aReKbskdg8wTb0qKMEWlXfhqdWKaRkwaKlDrpucmxs9QGU4FG+ZbqWYJ0j52WdNSiRHTfja+ekgOrdIhYaxsSUPG6u+JDCOtB1FgOyM0PT3rjcT/vGZqwnM/4zJJDZN0sihMBTExGUVAOlwxasTAEqSK21sJ7aFCamxQeRuCN/vyPKmdlDy35N2eFstX0zhysA8HcAQenEEZbqACVaCg4Ble4c15cl6cd+dj0rrgTGf24A+czx8XM5GU</latexit><latexit sha1_base64="iJC/7ntVLbMUWQMvhbe1ES+Osh8=">AAAB9XicbVDLSgNBEOz1GeMr6tHLYBAEIeyKoAhC0IvHCOYByRp6J7PJkNnZdWZWCUv+w4sHRbz6L978GyePgyYWNBRV3XR3BYng2rjut7OwuLS8sppby69vbG5tF3Z2azpOFWVVGotYNQLUTHDJqoYbwRqJYhgFgtWD/vXIrz8ypXks78wgYX6EXclDTtFY6b6FIukhubgkD8c8aReKbskdg8wTb0qKMEWlXfhqdWKaRkwaKlDrpucmxs9QGU4FG+ZbqWYJ0j52WdNSiRHTfja+ekgOrdIhYaxsSUPG6u+JDCOtB1FgOyM0PT3rjcT/vGZqwnM/4zJJDZN0sihMBTExGUVAOlwxasTAEqSK21sJ7aFCamxQeRuCN/vyPKmdlDy35N2eFstX0zhysA8HcAQenEEZbqACVaCg4Ble4c15cl6cd+dj0rrgTGf24A+czx8XM5GU</latexit><latexit sha1_base64="iJC/7ntVLbMUWQMvhbe1ES+Osh8=">AAAB9XicbVDLSgNBEOz1GeMr6tHLYBAEIeyKoAhC0IvHCOYByRp6J7PJkNnZdWZWCUv+w4sHRbz6L978GyePgyYWNBRV3XR3BYng2rjut7OwuLS8sppby69vbG5tF3Z2azpOFWVVGotYNQLUTHDJqoYbwRqJYhgFgtWD/vXIrz8ypXks78wgYX6EXclDTtFY6b6FIukhubgkD8c8aReKbskdg8wTb0qKMEWlXfhqdWKaRkwaKlDrpucmxs9QGU4FG+ZbqWYJ0j52WdNSiRHTfja+ekgOrdIhYaxsSUPG6u+JDCOtB1FgOyM0PT3rjcT/vGZqwnM/4zJJDZN0sihMBTExGUVAOlwxasTAEqSK21sJ7aFCamxQeRuCN/vyPKmdlDy35N2eFstX0zhysA8HcAQenEEZbqACVaCg4Ble4c15cl6cd+dj0rrgTGf24A+czx8XM5GU</latexit><latexit sha1_base64="iJC/7ntVLbMUWQMvhbe1ES+Osh8=">AAAB9XicbVDLSgNBEOz1GeMr6tHLYBAEIeyKoAhC0IvHCOYByRp6J7PJkNnZdWZWCUv+w4sHRbz6L978GyePgyYWNBRV3XR3BYng2rjut7OwuLS8sppby69vbG5tF3Z2azpOFWVVGotYNQLUTHDJqoYbwRqJYhgFgtWD/vXIrz8ypXks78wgYX6EXclDTtFY6b6FIukhubgkD8c8aReKbskdg8wTb0qKMEWlXfhqdWKaRkwaKlDrpucmxs9QGU4FG+ZbqWYJ0j52WdNSiRHTfja+ekgOrdIhYaxsSUPG6u+JDCOtB1FgOyM0PT3rjcT/vGZqwnM/4zJJDZN0sihMBTExGUVAOlwxasTAEqSK21sJ7aFCamxQeRuCN/vyPKmdlDy35N2eFstX0zhysA8HcAQenEEZbqACVaCg4Ble4c15cl6cd+dj0rrgTGf24A+czx8XM5GU</latexit>

W⇢̂(↵) =1

⇡Tr[⇢̂D(↵)(�1)n̂D†(↵)]

<latexit sha1_base64="NaTxB8flrp6kwfzzaxgX+QaYhD4=">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</latexit><latexit sha1_base64="NaTxB8flrp6kwfzzaxgX+QaYhD4=">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</latexit><latexit sha1_base64="NaTxB8flrp6kwfzzaxgX+QaYhD4=">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</latexit><latexit sha1_base64="NaTxB8flrp6kwfzzaxgX+QaYhD4=">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</latexit>

- Only function whose marginals yield the quantum probability distributions - Can be NONPOSITIVE (i.e., nonGaussian for a pure state)

WIGNER FUNCTION

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Displacement Setup

QSS#13 07/16/2020

— PPKTP(YZY) — Doubly resonance — Well below

IF : Interference Filter. FC : Filter cavity TES : Transition Edge Sensor

TES

30

Heralding(idler) Channel

Heralded(Signal) Channel

⌘h = NcNi

= 0.58(2)

Overall efficiency of the signal path.

Nd: YAG 532 nm, FWHM = 1kHz

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➢ Experimental results

31

Negativity was observed in the raw data without any inference or correcting for losses.

⌘fit = 0.57(3)<latexit sha1_base64="QQ+s+JiDndVHmEwjOp0R9Nt6gXQ=">AAAB/XicbVDJSgNBEO2JW4zbuNy8NAYhXoYZF+JFCHrxGMEskAxDT6cnadKz0F0jxCH4K148KOLV//Dm39hJ5qCJDwoe71VRVc9PBFdg299GYWl5ZXWtuF7a2Nza3jF395oqTiVlDRqLWLZ9opjgEWsAB8HaiWQk9AVr+cObid96YFLxOLqHUcLckPQjHnBKQEueedBlQLws4DDGV9i2LqqVsxPPLNuWPQVeJE5OyihH3TO/ur2YpiGLgAqiVMexE3AzIoFTwcalbqpYQuiQ9FlH04iETLnZ9PoxPtZKDwex1BUBnqq/JzISKjUKfd0ZEhioeW8i/ud1Uggu3YxHSQosorNFQSowxHgSBe5xySiIkSaESq5vxXRAJKGgAyvpEJz5lxdJ89RybMu5Oy/XrvM4iugQHaEKclAV1dAtqqMGougRPaNX9GY8GS/Gu/Exay0Y+cw++gPj8we76pNu</latexit><latexit sha1_base64="QQ+s+JiDndVHmEwjOp0R9Nt6gXQ=">AAAB/XicbVDJSgNBEO2JW4zbuNy8NAYhXoYZF+JFCHrxGMEskAxDT6cnadKz0F0jxCH4K148KOLV//Dm39hJ5qCJDwoe71VRVc9PBFdg299GYWl5ZXWtuF7a2Nza3jF395oqTiVlDRqLWLZ9opjgEWsAB8HaiWQk9AVr+cObid96YFLxOLqHUcLckPQjHnBKQEueedBlQLws4DDGV9i2LqqVsxPPLNuWPQVeJE5OyihH3TO/ur2YpiGLgAqiVMexE3AzIoFTwcalbqpYQuiQ9FlH04iETLnZ9PoxPtZKDwex1BUBnqq/JzISKjUKfd0ZEhioeW8i/ud1Uggu3YxHSQosorNFQSowxHgSBe5xySiIkSaESq5vxXRAJKGgAyvpEJz5lxdJ89RybMu5Oy/XrvM4iugQHaEKclAV1dAtqqMGougRPaNX9GY8GS/Gu/Exay0Y+cw++gPj8we76pNu</latexit><latexit sha1_base64="QQ+s+JiDndVHmEwjOp0R9Nt6gXQ=">AAAB/XicbVDJSgNBEO2JW4zbuNy8NAYhXoYZF+JFCHrxGMEskAxDT6cnadKz0F0jxCH4K148KOLV//Dm39hJ5qCJDwoe71VRVc9PBFdg299GYWl5ZXWtuF7a2Nza3jF395oqTiVlDRqLWLZ9opjgEWsAB8HaiWQk9AVr+cObid96YFLxOLqHUcLckPQjHnBKQEueedBlQLws4DDGV9i2LqqVsxPPLNuWPQVeJE5OyihH3TO/ur2YpiGLgAqiVMexE3AzIoFTwcalbqpYQuiQ9FlH04iETLnZ9PoxPtZKDwex1BUBnqq/JzISKjUKfd0ZEhioeW8i/ud1Uggu3YxHSQosorNFQSowxHgSBe5xySiIkSaESq5vxXRAJKGgAyvpEJz5lxdJ89RybMu5Oy/XrvM4iugQHaEKclAV1dAtqqMGougRPaNX9GY8GS/Gu/Exay0Y+cw++gPj8we76pNu</latexit><latexit sha1_base64="QQ+s+JiDndVHmEwjOp0R9Nt6gXQ=">AAAB/XicbVDJSgNBEO2JW4zbuNy8NAYhXoYZF+JFCHrxGMEskAxDT6cnadKz0F0jxCH4K148KOLV//Dm39hJ5qCJDwoe71VRVc9PBFdg299GYWl5ZXWtuF7a2Nza3jF395oqTiVlDRqLWLZ9opjgEWsAB8HaiWQk9AVr+cObid96YFLxOLqHUcLckPQjHnBKQEueedBlQLws4DDGV9i2LqqVsxPPLNuWPQVeJE5OyihH3TO/ur2YpiGLgAqiVMexE3AzIoFTwcalbqpYQuiQ9FlH04iETLnZ9PoxPtZKDwex1BUBnqq/JzISKjUKfd0ZEhioeW8i/ud1Uggu3YxHSQosorNFQSowxHgSBe5xySiIkSaESq5vxXRAJKGgAyvpEJz5lxdJ89RybMu5Oy/XrvM4iugQHaEKclAV1dAtqqMGougRPaNX9GY8GS/Gu/Exay0Y+cw++gPj8we76pNu</latexit>

QSS#13 07/16/2020

An even better way to do it

32

- Efficient reconstruction using semidefinite programming

QSS#13 07/16/2020 33

QSS#13 07/16/2020

Non-Gaussian resources => quantum error correction Gottesman-Kitaev-Preskill (GKP) States

34

Tzitrin et al. arXiv preprint arXiv:1910.03673 (2019).

AncillaGKPstates

Feed-forwarddisplacementtocorrecterror

Gottesmanetal.Phys.Rev.A(2001)

Simultaneouseigenstatesof𝑿 = 𝒆−𝒊�̂�𝜶, 𝒁 = 𝒆 𝒊𝝅

𝜶 �̂�

QSS#13 07/16/2020


34


AncillaGKPstates


Gottesmanetal.Phys.Rev.A(2001)

Walshe, et al. Physical Review A (2019).


𝜶 �̂�

Error corrected

GKP states

Cluster state nodes

QSS#13 07/16/2020


34


AncillaGKPstates


Gottesmanetal.Phys.Rev.A(2001)Δ = 0.3

Walshe, et al. Physical Review A (2019).


𝜶 �̂�

0̄⟩ ∝ 𝑒Δ2�̂�∞

∑𝑛1,𝑛2=−∞

𝑒−𝑖𝑛1�̂� 𝜋𝑒𝑖𝑛2Q̂ 𝜋 |𝑣𝑎𝑐⟩

Realistic implementation: Delta spikes ! peak width Δ

Error corrected

GKP states

Cluster state nodes

QSS#13 07/16/2020

Quantum engineering of GKP states for CV quantum error correction

35

! = 0

$(&) |)⟩ ≈ |,-.⟩

/ = 0

1 /|230⟩

1 / |230⟩

H. M. Vasconcelos, L. Sanz, and S. Glancy, “All-optical generation of states for ‘Encoding a qubit in an oscillator,’” Opt. Lett., OL, vol. 35, no. 19, pp. 3261–3263, Oct. 2010.

M. Eaton, R. Nehra, and O. Pfister, Non-Gaussian and Gottesman-Kitaev-Preskill state preparation by photon catalysis, New Journal of Physics 21, 113034 (2019).

QSS#13 07/16/2020

BIG PICTURE: beating lattice-gauge QCD calculations on classical supercomputers

36

QSS#13 07/16/2020

Conclusion

37

QSS#13 07/16/2020

The quantum optical frequency comb is a viable platform for universal quantum computing

Conclusion

37

QSS#13 07/16/2020


• LARGE-SCALE Gaussian entanglement• No postselection• Universal measurement-based QC, strictly equivalent to qubit model

Conclusion

37

QSS#13 07/16/2020



• FAULT TOLERANT non-Gaussian technology for universal QC

Conclusion

37

QSS#13 07/16/2020




• INTEGRABLE in photonic circuits

Conclusion

37

QSS#13 07/16/2020




• INTEGRABLE in photonic circuits

• TRANSLATABLE to any bosonic mode:• microwave cavity photons• phonons• transverse spatial modes (Hermite- or Laguerre-Gauss)• temporal modes

Conclusion

37

QSS#13 07/16/2020

A lesson in research from Ted Hänsch...

38

Documents

Quantum Science Seminar 2020 · QSS#13 07/16/2020. Quantum computing over the rainbow: the quantum optical frequency comb as a platform for measurement-based universal quantum computing