[PPT] - qubits Michael Hatridge Department of Applied Physics, Yale PowerPoint Presentation

SLIDE 1

Department of Applied Physics, Yale University

Michael Hatridge

Remote entanglement of transmon qubits

Katrina Sliwa Anirudh Narla Shyam Shankar Zaki Leghtas Mazyar Mirrahimi Evan Zalys-Geller Chen Wang Luigi Frunzio Steven Girvin Robert Schoelkopf Michel Devoret

35

SLIDE 2

What is remote entanglement and why is it important?

How do we engineer interactions

ver arbitrary length scales?

Q1 Q2 Q3 Alice Bob Monroe, Hanson, Zeilinger QN+1 QN+2 QN+3 Direct interaction Remote entanglement via msmt of ancilla

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SLIDE 3

Remote entanglement with flying qubits

ALICE BOB bert arnie

|𝐻 |𝑕 |𝑕 |𝐻

1/ 2 |𝐻𝑕 + |𝐹𝑓 ⊗ 1/ 2 |𝐻𝑕 + |𝐹𝑓

How can we do this with a superconducting system?

Instead of qubits use coherent states How do we entangle flying qubits? How well can we transmit our flying qubit? How do we build efficient detector?

quantum-limited amplification

𝑆𝑦 𝜌/2

,

𝑆𝑦 𝜌/2

,

1/ 2 |𝐻𝐻 + |𝐹𝐹

r

1/ 2 |𝐻𝐻 − |𝐹𝐹

r

1/ 2 |𝐻𝐹 + |𝐹𝐻

r

1/ 2 |𝐻𝐹 − |𝐹𝐻 measure X (sign) measure Z (parity)

33

SLIDE 4

Part 1: measurement with coherent states

32

SLIDE 5

microwave cavity coherent pulse

phase meter

dispersive cavity/pulse interaction

Dispersive measurement: classical version

|𝑕

transmission line

31

SLIDE 6

microwave cavity coherent pulse

phase meter

dispersive cavity/pulse interaction

Dispersive measurement: classical version

|𝑕 |𝑓

transmission line

30

SLIDE 7

microwave cavity coherent pulse

dispersive cavity/pulse interaction

Now a wrinkle: finite phase uncertainty

|𝑕 |𝑓

transmission line

phase meter

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SLIDE 8

microwave cavity coherent pulse

dispersive cavity/pulse interaction

|𝑕 |𝑓

phase meter

Measurement with bad meter (still classical)

noise added by amp. AND signal lost in transmission

Each msmt tells us only a little
State after msmt not pure!
This example optimistic, best

commercial amp adds 20-30x noise

We fix this with quantum-limited

amplification

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SLIDE 9

Ideal phase-preserving amplifier



               

 

 

𝜍𝑗 → 𝜍𝑔 = 𝑈𝑠𝑉𝜍𝑗𝑉† 𝑇 𝜍𝑔 = 𝑇 𝜍𝑗

Phase-sensitive amps 180° hybrid (beam splitter) 𝜚 = 0 𝜚 = 𝜌 2

|0 |𝛽

𝐻 ≫ 1 𝐻 ≫ 1 Signal in Idler in 180° hybrid (beam splitter) These ports are often internal degrees

f freedom, in our amp they are accessible.

We’ll use this for remote entanglement Signal

ut

Idler

ut
Adds its inputs, outputs 2 copies of combined inputs
Adds minimum fluctuations to signal output*

* 𝜏𝑝𝑣𝑢2 = 2𝜏𝑗𝑜2 (Caves’ Thm)

Caves, Phys Rev D (1982)

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SLIDE 10

microwave cavity coherent pulse

Quantum-limited amplification: projective msmt

|𝑕 |𝑓

phase meter w/ P. P. pre-amp

state of qubit pure after each msmt
For unknown initial state

𝑑𝑕|𝑕 + 𝑑𝑓|𝑓 , repeat many times to estimate 𝑑𝑕

2, 𝑑𝑓 2

nly quantum

fluctuations coherent superposition

26

SLIDE 11

microwave cavity WEAK coherent pulse

Quantum-limited amplification: ‘partial’ msmt

|𝑕 |𝑓

phase meter w/ P. P. pre-amp

state of qubit pure after each msmt
counter-intuitive, but is achievable

in the laboratory

nly quantum

fluctuations coherent superposition

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SLIDE 12

Part 2: Partial measurement with transmon qubit and JPC

24

SLIDE 13

200 nm

The Josephson tunnel junction

SUPERCONDUCTING TUNNEL JUNCTION

𝐽 = 𝐽0 sin 𝜚 𝜒0

1nm

Al/AlOx/Al tunnel junction nonlinear inductor shunted by capacitor

2e  

LJ CJ

𝐽 𝜚

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SLIDE 14

Superconducting transmon qubit

Potential energy

f

Josephson junction with shunting capacitor  anharmonic oscillator

lowest two levels form qubit fge ~ 5.025 GHz, fef ~ 4.805 GHz

Koch et al., Phys. Rev. A (2007)

|𝑕 |𝑓 |𝑔

22

SLIDE 15

Measurement configuration

c     

 

𝑏 𝑕 ⊗ 𝛽𝑕, 0 + 𝑐 𝑓 ⊗ 𝛽𝑓, 0

𝐽𝑛 = 𝐽 𝑢 𝑒𝑢

𝑈

𝑛

𝑅𝑛 = 𝑅 𝑢 𝑒𝑢

𝑈

𝑛

𝐽𝑛 = 𝐽 𝑢 𝑒𝑢

𝑈

𝑛

Readout phase tan−1 𝑅𝑛 𝐽𝑛 𝜌 2 width 𝜆 Readout amplitude 𝐽𝑛

2 + 𝑅𝑛 2

𝑔 dispersive shift 𝜓 Qubit + resonator + qubit pulses

JPC

|𝑕 |𝑓 |𝑕 |𝑓

𝜘 = 2 tan−1 𝜓 𝜆 readout pulse at 𝑔

𝑒

𝑔 Ref 𝑅𝑛 = 𝑅 𝑢 𝑒𝑢

𝑈

𝑛

Sig Idl Pump

𝑔

𝑒

HEMT

− 𝜌 2 vacuum 50Ω

21

SLIDE 16

Isolating the transmon from the environment

transmon

utput coupler

Purcell filter waveguide-SMA adapter input coupler Cavity fc,g = 7.4817 GHz 1/ = 30 ns 10 mm 25 mm Qubit fQ=5.0252 GHz T1 = 30 s T2R = 8 s

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SLIDE 17

The 8-junction Josephson Parametric Converter

~100’s of MHz

~88% of output noise is quantum noise! → quantum fluctuations

n an oscilloscope

Idler Signal

Bergeal et al Nature (2010) See also Roch et al PRL (2012)

20 15 10 5 G (dB) 7.50 7.48 7.46 7.44 7.42 x10

9

F 7.42 7.46 7.50 Frequency (GHz) Direct G (dB) 20 10 not a defect! quantum jumps

f connected qubit

10 m

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SLIDE 18

𝐽𝑛/𝜏 𝑅𝑛/𝜏

|𝑕

10 5 10 5

5
10

102 104 1

|𝑓 𝑔 , …

𝑅𝑛/𝜏 𝐽𝑛/𝜏

6000 10 5 10 5

5
10

|𝑕 |𝑓

MA

𝑔 , … Rotate to z=0 State preparation Confirm state

8.6 σ

Rotate to z=0 State preparation Confirm state

𝑆𝑦 𝜌/2 𝑆𝑦 𝜌 𝐽𝑒

r

𝑜  11 𝑜  11 640 ns 𝑈𝑛  320 ns

Trep = 20 µs

See also Riste et al PRL (2012) Johnson et al PRL (2012)

Preparation by measurement + post-selection

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SLIDE 19

Rotate to z=0 State preparation Confirm state

𝑆𝑦 𝜌/2 𝑆𝑦 𝜌 𝐽𝑒

r

𝑜  11 𝑜  11 640 ns 𝑈𝑛  320 ns

|𝑓

102 104 1

MA MB|MA = |𝑕

Trep = 20 µs

𝐽𝑛/𝜏 𝑅𝑛/𝜏

10 5 10 5

5
10

|𝑕 |𝑓 𝑔 , … 𝑆𝑦 𝜌 “|𝑓 ”

𝑅𝑛/𝜏 𝐽𝑛/𝜏

10 5 10 5

5
10

|𝑕 |𝑓 𝑔 , … 𝐽𝑒 “|𝑕 ”

Now that we have outcomes MA= |𝑕 either do nothing to retain |𝑕 OR rotate qubit by 𝑆𝑦 𝜌 to create |𝑓

Preparation by measurement + post-selection

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SLIDE 20

𝑅𝑛/𝜏 𝐽𝑛/𝜏

10 5 10 5

5
10

|𝑓

𝐽𝑛/𝜏 𝑅𝑛/𝜏

10 5 10 5

5
10

102 104 1

|𝑕 |𝑓 𝑔 , … |𝑕 |𝑓 𝑔 , … 𝑆𝑦 𝜌 “|𝑓 ” 𝐽𝑒 “|𝑕 ”

How ideal is this operation?

Fidelity=0.994!

Strong measurements allow rapid, high-fidelity state preparation and tomography

Say : “practically useful, but doesn’t tell us improvement in signal processing”

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SLIDE 21

A picture is worth a thousand math symbols * : Mapping (𝐽𝑛, 𝑅𝑛) to the bloch vector

𝜖𝑦𝑔 𝜖𝑅𝑛

𝐽𝑛,𝑅𝑛=0

= η 𝐽𝑛

𝑕 − 𝐽𝑛 𝑓

2

𝜃 =

𝜏𝑛 𝜏 2

𝑦𝑔, 𝑧𝑔

𝑹𝒏 𝑱𝒏 𝜽 < 𝟐 𝑅𝑛 𝐽𝑛 𝐽𝑛 gives latitude information 𝑅𝑛 gives longitude information 𝑦 𝑧 𝑨

*Gambetta, et al PRA (2008); Korotkov/Girvin, Les Houches (2011); M. Hatridge et al Science (2013)

The equator is a dangerous place: lost information pulls trajectory towards the z-axis

15

SLIDE 22

Back-action characterization protocol

c     

 

𝑜  11 𝑜  11

Tomography

𝑆𝑦 𝜌/2 𝑆𝑦 𝜌/2

,

𝑆𝑧 𝜌/2 , 700ns qubit cavity 𝑦𝑔, 𝑧𝑔, 𝑨𝑔 variable 𝑜 𝐽𝑒

r

𝑈𝑛  320 ns

Variable strength measurement State preparation

X = 1 𝑦 𝑧 𝑨

r
r

Y = 1 Z = 1

(𝐽𝑛, 𝑅𝑛)

14

SLIDE 23

histogram of measurement after p/2 pulse tomography along X, Y and Z after measurement

Measurement with 𝑱 𝒏 𝝉 = 0.4

Probability of ground 1

1

Counts

Max

𝑅𝑛/𝜏 𝐽𝑛/𝜏 𝑅𝑛/𝜏 𝐽𝑛/𝜏

6 6

6

6 6

6

6 6

6

𝑌 𝑑 𝑍 𝑑 𝑎 𝑑

6 6

6

𝐽

𝑛

𝜏

13

SLIDE 24

histogram of measurement after p/2 pulse tomography along X, Y and Z after measurement

Measurement with 𝑱 𝒏 𝝉 = 1.0

Probability of ground 1

1

Counts

Max

𝑅𝑛/𝜏 𝐽𝑛/𝜏 𝑅𝑛/𝜏 𝐽𝑛/𝜏

6 6

6

6 6

6

6 6

6

𝑌 𝑑 𝑍 𝑑 𝑎 𝑑

6 6

6

𝐽

𝑛

𝜏

12

SLIDE 25

histogram of measurement after p/2 pulse tomography along X, Y and Z after measurement

Measurement with 𝑱 𝒏 𝝉 = 2.8

Probability of ground 1

1

Counts

Max

𝑅𝑛/𝜏 𝐽𝑛/𝜏 𝑅𝑛/𝜏 𝐽𝑛/𝜏

6 6

6

6 6

6

6 6

6

𝑌 𝑑 𝑍 𝑑 𝑎 𝑑

6 6

6

𝑔 , … show at ~10-4 contamination

𝐽

𝑛

𝜏

11

SLIDE 26

𝑜 𝐽𝑛/𝜏 𝑅𝑛/𝜏 𝑅𝑛/𝜏 𝑜

x- and y-component along 𝑱𝒏 = 𝟏

𝐽𝑛/𝜏 𝑍 𝑑 𝐽𝑛 = 0 𝑌 𝑑 𝐽𝑛 = 0 𝑌 𝑑, 𝑍 𝑑

6

1

1 Amplitude determined by one fit parameter: 𝜽 = 0.57 ± 0.02

𝑱 𝒏 𝝉 = 0.82 𝑌 𝑑 = sin 𝑅𝑛 𝜏 𝐽

𝑛

𝜏 + 𝜄 exp − 𝐽

𝑛

𝜏

2 1 − 𝜃

𝜃 𝑍 𝑑 = cos 𝑅𝑛 𝜏 𝐽

𝑛

𝜏 + 𝜄 exp − 𝐽

𝑛

𝜏

2 1 − 𝜃

𝜃

6

𝜽 ≥ 𝟏. 𝟔 → 3 body entanglement (qubit, signal, idler)

𝑅𝑛/𝜏

10

SLIDE 27

Part 3: remote entanglement experiment

9

SLIDE 28

Two qubit readout schematic

𝑈

1 = 30 𝜈

𝑈2𝑆 = 15𝜈 𝑔

𝑅 𝑕𝑓 = 4.672 𝜓 2𝜌 = 2.7 𝜆 2𝜌 = 6.7

𝑈

1 = 15𝜈

𝑈2𝑆 = 15 𝜈 𝑔

𝑅 𝑕𝑓 = 6.074 𝜓 2𝜌 = 3.5 𝜆 2𝜌 = 4.1

𝑔

𝑞 = 16.58 GHz

𝑔

𝑠 𝑒 = 7.464 GHz

𝑔

𝑠 𝑒 = 9.116 GHz

50 Ω

8

SLIDE 29

Simultaneous readout of two qubits

Signal Alone 𝑅𝑛 𝐽𝑛

|𝑓𝑡 |𝑕𝑡

Idler Alone 𝑅𝑛 𝐽𝑛

|𝑓𝑗 |𝑕𝑗

Together 𝑅𝑛 𝐽𝑛

|𝑓𝑓 |𝑕𝑕 |𝑕𝑓 |𝑓𝑕

“Joint Readout”

|𝑓𝑡 |𝑕𝑡 |𝑕𝑗 |𝑓𝑗

𝐽𝑛 encodes Z info 𝑅𝑛 encodes Z info

7

|𝑓𝑓 |𝑕𝑕 |𝑕𝑓 |𝑓𝑕

SLIDE 30

How to perform “entangling readout”

Signal Alone 𝑅𝑛 𝐽𝑛

|𝑓𝑡 |𝑕𝑡

Idler Alone 𝑅𝑛 𝐽𝑛 Together 𝐽𝑛 encodes Z info 𝐽𝑛 encodes Z info 𝑅𝑛 (sign) 𝐽𝑛 (parity)

|𝑓𝑓 |𝑕𝑕 |𝑕𝑓 , |𝑓𝑕

“Entangling Readout”

|𝑓𝑗 |𝑕𝑗 |𝑕𝑗 |𝑓𝑗

𝐽𝑛 is now blind to contents of

|𝑕𝑓 , |𝑓𝑕

With/ appropriate initial state, outcome

is Bell state w/ 50 % success rate

𝑅𝑛 encodes phase of Bell state

6

|𝑓𝑓 |𝑕𝑕 |𝑕𝑓 , |𝑓𝑕

SLIDE 31

Back action of two qubit msmt creates entanglement

𝜖𝑦𝑔 𝜖𝑅𝑛

𝐽𝑛,𝑅𝑛=0

= η 𝐽𝑛

𝑕 − 𝐽𝑛 𝑓

2

𝜃 =

𝜏𝑛 𝜏 2

𝑦𝑔, 𝑧𝑔

𝑹𝒏 𝑱𝒏 𝜽 < 𝟐 𝑅𝑛 𝐽𝑛 𝐽𝑛 gives info on even vs. odd parity (a bit too much, actually) 𝑅𝑛 gives sign info for odd parity states Even parity states: = |𝑕𝑕 = |𝑓𝑓 = |𝑕𝑓 − |𝑓𝑕 = |𝑕𝑓 + 𝑗|𝑓𝑕 = |𝑕𝑓 + |𝑓𝑕 = |𝑕𝑓 − 𝑗|𝑓𝑕 Odd parity states: Make note about which we keep…which are good ones The climax… this is my favorite part..

5

SLIDE 32

Probability of ground

1

+1

Tomography of strong entangling msmt

Histogram 𝑅𝑛 𝜏

𝑌𝑌 𝑑 𝑎𝐽 𝑑 𝑎𝑎 𝑑

𝐽𝑛 𝜏 10

10
10

10 𝑅𝑛 𝜏 𝐽𝑛 𝜏

10 10

10
10

𝑅𝑛 𝜏

10

10

10

10

10

10

10

10

4

SLIDE 33

Probability of ground

1

+1

Tomography of weak entangling msmt

Histogram 𝑅𝑛 𝜏

𝑌𝑌 𝑑 𝑎𝐽 𝑑 𝑎𝑎 𝑑

𝐽𝑛 𝜏 5

5
5

5 𝑅𝑛 𝜏 𝐽𝑛 𝜏

5 5

5
5

𝑅𝑛 𝜏

5

5

5

5

5

5

5

5

3

SLIDE 34

XX YY ZZ

Average a strip along 𝑅𝑛 ≃ 0 Bloch comp. value 5 𝑅𝑛 𝜏 𝐽𝑛 𝜏 𝑅𝑛 𝜏

5

5 0.5

0.5

𝑌𝑌 𝑑

5

5
5

𝑅𝑛 𝜏

Signature of entangling operation

currently, too much information is lost
correct dependence of qubit correlations
expect to demonstrate entanglement soon (F > 0.5)

2

SLIDE 35

Evolution of single-qubit readout vs time

Year

1 0.5

Total efficiency 𝜃

2010 2012 2014

Conclusions

Coherent states can be used as flying qubits
Quantum mechanics goes through the amplifier
New tools for building large-scale quantum

entanglement

Compare with optical systems: 𝜃~10−3 due to collector/detector inefficiencies

1