exploring quantum simulations with superconducting … · exploring quantum simulations with...

Team: J.-C. Besse, R. Buijs, M. Collodo, S. Garcia, S. Gasparinetti, J. Heinsoo, S. Krinner, P. Kurpiers,

M. Oppliger, M. Pechal, A. Potocnik, Y. Salathe, M. Stammeier, A. Stockklauser, T. Thiele, T. Walter

(ETH Zurich)

Exploring Quantum Simulations with Superconducting CircuitsAndreas Wallraff (ETH Zurich)www.qudev.ethz.ch

The ETH Zurich Quantum Device Labincl. undergrad and summer students

Former group members nowFaculty/PostDoc/PhD/IndustryA. Abdumalikov (Gorba AG)M. Allan (Leiden)M. Baur (ABB)J. Basset (U. Paris Sud) S. Berger (AWK Group)R. Bianchetti (ABB)D. Bozyigit (MIT)C. Eichler (Princeton)A. Fedorov (UQ Brisbane)A. Fragner (Yale)S. Filipp (IBM Zurich)J. Fink (IST Austria)T. Frey (Bosch)M. Goppl (Sensirion)J. Govenius (Aalto) L. Huthmacher (Cambridge)

D.-D. Jarausch (Cambridge) K. Juliusson (CEA Saclay) C. Lang (Radionor) P. Leek (Oxford)P. Maurer (Stanford)J. Mlynek (Siemens)M. Mondal (Johns Hopkins)G. Puebla (IBM Zurich)A. Safavi-Naeini (Stanford)L. Steffen (AWK Group)A. van Loo (Oxford)S. Zeytinolu (ETH Zurich)

Collaborations with (groups of): A. Blais (Sherbrooke)C. Bruder (Basel)M. da Silva (Raytheon) L. DiCarlo (TU Delft)

K. Ensslin (ETH Zurich)J. Faist (ETH Zurich)J. Gambetta (IBM Yorktown)K. Hammerer (Hannover)T. Ihn (ETH Zurich)F. Merkt (ETH Zurich)L. Novotny (ETH Zurich)T. J. Osborne (Hannover)B. Sanders (Calgary) S. Schmidt (ETH Zurich)R. Schoelkopf (Yale)C. Schoenenberger (Basel)E. Solano (UPV/EHU)W. Wegscheider (ETH Zurich)

Acknowledgementswww.qudev.ethz.ch

Classical and Quantum Electronic Circuit Elements

quantum superposition states of:

charge q

flux

basic circuit elements: charge on a capacitor:

current or magnetic flux in an inductor:

commutation relation (c.f. x, p):

Constructing Linear Quantum Electronic Circuits

Review: M. H. Devoret, A. Wallraff and J. M. Martinis, condmat/0411172 (2004)

classical physics:

basic circuit elements: harmonic LC oscillator:

quantum mechanics:

energy:electronic

photon

Constructing Non-Linear Quantum Electronic Circuits


circuit elements:

Josephson junction:a non-dissipative nonlinear element (inductor)

anharmonic oscillator: non-linear energy level spectrum:

electronicartificial atom

How to Operate Circuits in the Quantum Regime?


recipe:

avoid dissipation

work at low temperatures

isolate quantum circuit from environment

control circuit read-out circuitquantum circuit

Cavity QED with Superconducting Circuits

coherent quantum mechanicswith individual photons and qubits ...

... basic approach:

Isolating qubits from their environment

Maintain addressability of qubits

Reading out the state of qubits

Coupling qubits to each other

Converting stationary qubits to flying qubits

What is this good for?

Cavity QED

A. Blais, et al., PRA 69, 062320 (2004)A. Wallraff et al., Nature (London) 431, 162 (2004)

R. J. Schoelkopf, S. M. Girvin, Nature (London) 451, 664 (2008)

coherent interaction of photons with quantum two-level systems ...

with Superconducting Circuits

J. M. Raimond et al., Rev. Mod. Phys. 73, 565 (2001)S. Haroche & J. Raimond, OUP Oxford (2006) J. Ye., H. J. Kimble, H. Katori, Science 320, 1734 (2008)

Properties: strong coupling in solid state sys. easy to fabricate and integrate

Research directions: quantum optics quantum information hybrid quantum systems

Realization

device fabrication: L. Frunzio et al., IEEE Trans. on Appl. Supercon. 15, 860 (2005)

J. Mlynek et al., Quantum Device Lab, ETH Zurich (2012)

Sample Mount

M. Peterer et al., Quantum Device Lab, ETH Zurich (2012)

~ 2 cm

Cryostate for temperatures down to 0.02 K

Microwave control & measurement equipment

~ 20 cm

How to do the Measurement

prevent leakage of thermal photons (cold attenuators and circulators)

average power to be detected (r/2 = 6 GHz, /2 = 1 MHz)

efficient with cryogenic low noise HEMT amplifier TN = 6 K

Resonant Vacuum Rabi Mode Splitting

first demonstration in a solid: A. Wallraff et al., Nature (London) 431, 162 (2004)this data: J. Fink et al., Nature (London) 454, 315 (2008)


... with one photon (n=1): very strong coupling:

forming a 'molecule' of a qubit and a photon

Resonant Vacuum Rabi Mode Splitting

first demonstration in a solid: A. Wallraff et al., Nature (London) 431, 162 (2004)this data: J. Fink et al., Nature (London) 454, 315 (2008)


... with one photon (n=1): very strong coupling:

forming a 'molecule' of a qubit and a photon

vacuum Rabi oscillations

Quantum Optics with Supercond. CircuitsStrong Coherent CouplingChiorescu et al., Nature 431, 159 (2004)Wallraff et al., Nature 431, 162 (2004)Schuster et al., Nature 445, 515 (2007)

Parametric Amplification & SqueezingCastellanos-Beltran et al., Nat. Phys. 4, 928 (2008)Abdo et al., PRX 3, 031001 (2013)

Microwave Fock and Cat StatesHofheinz et al., Nature 454, 310 (2008)

Hofheinz et al., Nature 459, 546 (2009)Kirchmair et al., Nature 495, 205 (2013)Vlastakis et al., Science 342, 607 (2013)

Wang et al., Science 352, 1087 (2016)

Waveguide QED Qubit Interactions in Free Space

Astafiev et al., Science 327, 840 (2010)van Loo et al., Science 342, 1494 (2013)

Root n NonlinearitiesFink et al., Nature 454, 315 (2008)Deppe et al., Nat. Phys. 4, 686 (2008)Bishop et al., Nat. Phys. 5, 105 (2009)

Hybrid Systems with Superconducting Circuits

CNT, Gate Defined 2DEG, or nanowire Quantum DotsM. Delbecq et al., PRL 107, 256804 (2011)T. Frey et al., PRL 108, 046807 (2012)K. Petersson et al., Nature 490, 380 (2013)

Spin Ensembles: e.g. NV centersD. Schuster et al., PRL 105, 140501 (2010)Y. Kubo et al., PRL 105, 140502 (2010)

Nano-MechanicsJ. Teufel et al., Nature 475, 359 (2011)X. Zhou et al., Nat. Phys. 9, 179(2013)

Polar Molecules, Rydberg, BECP. Rabl et al, PRL 97, 033003 (2006)

A. Andre et al, Nat. Phys. 2, 636 (2006)D. Petrosyan et al, PRL 100, 170501 (2008)

J. Verdu et al, PRL 103, 043603 (2009)

Rydberg AtomsS. Hoganet al., PRL 108, 063004 (2012)

zx

vz

and many more

TeleportationL. Steffen et al., Nature 500, 319 (2013) M.. Baur et al., PRL 108, 040502 (2012)

Quantum Computing with Superconducting Circuits

Circuit QED ArchitectureA. Blais et al., PRA 69, 062320 (2004)

A. Wallraff et al., Nature 431, 162 (2004)M. Sillanpaa et al., Nature 449, 438 (2007)

H. Majer et al., Nature 449, 443 (2007)M. Mariantoni et al., Science 334, 61 (2011)

R. Barends et al., Nature 508, 500 (2014)

Deutsch & Grover Algorithm, Toffoli GateL. DiCarlo et al., Nature 460, 240 (2009)L. DiCarlo et al., Nature 467, 574 (2010)M. Reed et al., Nature 481, 382 (2012)

Error CorrectionM. Reed et al., Nature 481, 382 (2012)Corcoles et al., Nat. Com. 6, 6979 (2015) Rist et al., Nat. Com. 6, 6983 (2015) Kelly et al., Nature 519, 66-69 (2015)

Quantum Simulation

simulatinga quantum system

difficult on classicalcomputer!

quantumsimulator

sufficient controllability, flexibility!

map!

describes physical system of interest

(physics, chemistry, biology,)

encodes hard classical problem

interesting toy model

universalquantum computeruse

Feynman, Int. Journal of Th. Phys. 21, 467 (1982)Llloyd, Science 273, 5278 (1996)

OR

still to be realized!

Systems for Quantum Simulation

Blatt & Roos, Nat. Phys. 8, 277 (2012)

Bloch et al.,Nat. Phys. 8, 267 (2012)

Aspuru-Guzik & Walther, Nat. Phys. 8, 258 (2012)

Ultracold gases Trapped ions

Optical photons

Nuclear magnetic resonance

Vandersypen & Chuang, RMP 76, 1037 (2004)

Solid state quantum devices

Georgescu et al., RMP 86, 153 (2014)

more established

under development

Quantum Simulation with Superconducting Circuits

Salathe et al., PRX 5, 021027 (2015)

Digital simulation of exchange, Heisenberg, Ising spin models

two-mode fermionic Hubbard models

Analog simulations with cavity and/or qubit arrays

Houck et al., Nat Phys. 8, 292 (2012)

Barends et al., Nat. Com. 6, 7654 (2015)

Eichleret al., Phys. Rev. X 5, 041044 (2015)OMalley et al., arXiv:1512.06860 (2015)

Quantum simulation of correlated systems with variational Ansatz based on MPS

Raftery et al., Phys. Rev. X 4, 031043 (2014)

Heisenberg Model Simulated with Supercon. Circuits

Salathe et al., PRX 5, 021027 (2015)

Digital simulation of Heisenberg spin model

Quantum Properties of Propagating Microwaves

Bozyigit et al., Nat. Phys 7, 154 (2011)Lang et al., PRL 107, 073601 (2011)

Single photon sources and their anti-bunching

Preparation and characterization of qubit-propagating photon entanglement

Eichler et al., PRL 109, 240501 (2012)Eichler et al., PRA 86, 032106 (2012)

Full state tomography and Wigner functions of propagating photons

Hong-Ou-Mandel: Two-photon interference incl. msrmnt of coherences at microwave freq.Lang et al. , Nat. Phys. 9, 345 (2013)

Eichler et al., PRL 106, 220503 (2011)

On-Demand Pulsed Single Photon Source

Step 1:Prepare qubit state by Rabi oscillation

Step 3:Measure at the output using linear amplifier and signal processing hardware

Step 2:Map qubit state to resonator by 1/2 vacuum Rabi oscillation

D. Bozyigit et al., Nat. Phys. 7, 154 (2011), S. Deleglise et al. Nature 455, 510514 (2008) M. Hofheinz et al., Nature 454, 310 (2008), A. Houck et al., Nature 449, 328 (2007)

Single Sided Cavity and Beam Splitter

Detection Scheme using Beam Splitters, Amplifiers ...

linear amplifier:

beamsplitter:

bosonicfield operators

signal mode

noisemode

output mode

C. Caves, PRD 26, 1817 (1982).

... and Quadrature Detectors

IQ mixer

measured observable

signal opticalanalogue

homodynedetectionscheme

M. P. da Silva et al., PRA 82, 043804 (2010).

measuring field amplitude instead of photon number:

The Signal in One Channel of the Setup

signal mode , vacuum mode

Beam splitter

Linear amplifier

Mixer

effective noisemode

analogous forsecond channel!

Field Quadrature and Photon Number MeasurementsMeasure quadratures at channel b: Measure cross-power between channel e&f:

Single-Channel Power vs. Two-Channel Cross Power

Single channel power:

... vs. cross power:

similar for higher order moments:

signal photonssystem noise is Gaussian with

vanishing mean

added noise photons

whereas

in vacuum Noise in 2 detection channelsuncorrelated

system noise uncorrelated from signal

G(2) Measurement of Pulsed Single Photon SourceFirst measurement of intensity/intensity correlation function of a microwave frequency single photon source

D. Bozyigit et al., Nat. Phys. 7, 154 (2011)M. P. da Silva et al., PRA 82, 043804 (2010)

C. Eichler et al., PRA 86, 032106 (2012)

Photon Blockade: A Single Photon Turnstile

Mollow-type triplet:

Vacuum Rabi mode splitting:

Effective two-level system (polariton)

Photon blockade: first photon enters cavity second is blocked

mediated photon/photon interactions

Level diagram:

Drive:

C. Lang et al., PRL 107, 243601 (2011)

Polariton Mollow Triplet Measurement(cross-)power spectrum:

observations: Rayleigh scattering resonance fluorescence

C. Lang et al., PRL 106, 243601 (2011)

thermal (bunching) & coherent (poissonian) fields

G(2) of Continuously Pumped Single Photon Source anti-bunching and sub-poissonian photon statistics

C. Lang et al., PRL 106, 243601 (2011)M. P. da Silva et al., PRA 82, 043804 (2010)

C. Eichler et al., PRA 86, 032106 (2012)

resonant photon blockade:

G

Microwave Photon Field Detectionamplitudedetector

linearamplifier

complex amplitude:Eichler et al., PRA 86, 032106 (2012)

M. P. da Silva et al., PRA 82, 043804 (2010)C. M. Caves, PRD 26, 1817 (1982)

noise added by HEMT amplifier :

= ADC &digital filtering

signal

adds vacuum/thermal

noise

noise

signal photon

.. .~50 noise photons

G

Full Tomography of a Single Propagating Mode

G

noise modephoton source

1) prepare in vacuum :

record histogramof measurement results

normal distribution with variance

introduces thermal noisewith mean photon number

vacuum noise

Coherent State Histograms

2) prepare in coherent state :

MW generator

3) rotate phase :

Question: What can we learn about statewhen ?

MW generator

store 2D histogram from measurement results:

signal mode in single photon

Fock state

signal mode in vacuum

correspondingphase spacedistribution

subtracted histogramsto visualize difference

Q - functionof noise mode :

Single Photon Source Histogram

C. Eichler, et al., PRL 106, 220503 (2011), PRA 86, 032106 (2012)

separate noise fromsignal systematically!

convolutionwith P function

of signal

Statistical Analysis of Histograms

systematic mode separation:

Fock state

vacuum

1. calculate histogram moments

2. algebraic inversion

histogram moments:

reminder:


State Dependent Moments of Probability Distribution

moments for different prepared states:

Fock statemean photon

number

superposition

mean amplitude

coherent state coherent state

anti bunching


Reconstructed Wigner Function of Itinerant Photon

Wigner function reconstructed from measured moments:

Fock state superposition

with


Reconstruct Density Matrices and Wigner Functions

C. Eichler, et al., PRL 106, 220503 (2011)C. Eichler et al., PRA 86, 032106 (2012)

for propagating multi-photon Fock states and their superpositions:

measured using near-quantum-limited parametric amplifier

Density matrices

Wigner functions

Two Single Photon Sources and Beam Splitter

Hong-Ou-Mandel g () for Microwave Photons

Observations:

Photon-Pair anti-bunching

For > 0:

Broadening of satellite peaks

Triple-peak structure of satellite peaks

Full recovery of double-peak at

(2)

Exp.: C. Lang, C Eichler et al. , Nat. Phys. 9, 345 (2013)

Theo.: M. Woolley et al. , New J. Phys. 15, 10502519 (2013)

Learning More: Two-Channel Tomography

Idea: Measure 4D histogram and evaluate relevant photon statistics

analogous to1-channel case

1 average photonin each channel

no simultaneous click in both channels

2-photon bunching

quantum superposition!

C. Lang, C Eichler et al. , Nat. Phys. 9, 345 (2013)

Density Matrix Displaying Two-Mode Entanglement

Density matrix reconstruction: linear mapmoments Fock space density matrix

use maximum likelihood procedure

F = 0.93 F = 0.86

C. Lang, C Eichler et al. , Nat. Phys. 9, 345 (2013)

final state:

Dissipative Bose Hubbard Dimer

Simulate quantum many body physics with light

Greentree et al. Nat. Phys., 2 856 (2006)Angelakis et al, PRA 76, 031805 (2007)

Hartmann et al., Nat Phys 2 849 (2006)Schmidt et al., PRB 82 100507 (2010)

Realize nondegenerateparametric amplifier

Unconventional photon blockade effect

Josephson oscillations

Liew & Savona, PRL 104 18 (2010)Bamba et al., PRA 83, 021802 (2011)

Gerace et al. Nat. Phys., 5 281 (2009)Abbarchi et al. Nat. Phys., 9 275 (2013)

Eichler et al., Phys. Rev. Lett. 113, 110502 (2014)

hoppingemission

photon-photon interaction

Why parametric amplifiers?

G

QUANTUM LIMITED AMPLIFICATION FOR

Detection efficiency:

Qubit readout

Quantum feedback

Mallet et al. Nat. Phys., 5 791 (2009)Vijay et al, PRL 106, 110502 (2011)

Sank et al., arXiv (2014)

SqueezingCV Entanglement

MW photon correlations

Microwave spectroscopy/Hybrid systems

ANY CRYOGENIC SETUPOPERATING at MW FREQUENCY!

Castellanos-Beltran et al., Nat. Phys. 4, 929 (2008)Eichler et al., PRL. 107, 113601 (2011)Flurin et al., PRL 109, 183901 (2012).Menzel et., PRL109, 250502 (2012).

Riste et al., PRL 109, 240502 (2012)Vijay et al., Nature 490, 77 (2012)

Steffen et al., Nature 500, 319-322 (2013)

Mallet et al., PRL. 106, 220502 (2011)Eichler et al., PRL & PRA (2012)Pechal et al., PRX 4, 041010 (2014)Mlynek et al., Nat. Com. 5, 5186 (2014)

Quantum dots,Mechanical devices,

Rydberg atoms,

2-5% best commercial amps-> 100% parametric amps

Parametric amplifier: Basic working principle

Yurke et al., PRL 60, 764 (1988)Castellanos-Beltran et al., Nat. Phys. 4, 929 (2008)

Eichler and Wallraff, EPJ 1, (2014)

coherentPump

nonlinearmedium

signal

idler

4-wave mixing:

Conversion stimulated by:1) vacuum fluctuations -> spontaneous parametric down-conversion (SPDC)2) input (quantum) signals ->parametric amplification

Spectraldensity

signal + idler photon pairs

pump

occupy samemode

degenerateparamp

Degenerate vs. nondegenerate parampDegenerate paramp

signalgain

idlergain

Non-degenerate paramp

pump

desirable for: conventional phase-preserving

amplification multiplexed readout photon correlation measurements

desirable for: single mode squeezing fast readout quantum feedback

JPD amplifier: implementation

Features: Arrays with M SQUIDs to control nonlinearity: asymmetric SQUIDs -> homogeneous coupling to external flux

array ofSQUIDs

fingercapacitor


JPD amplifier: implementation

Features: Arrays with M SQUIDs to control nonlinearity: lumped element -> large bandwidth possible asymmetric SQUIDs -> homogeneous coupling to external flux


Linear spectroscopy of JPD device

Extract

From fit to input-output model


Frequency Tuneability: Linear Response


JPD amplifier: non-degenerate operation

~ 0.5 GHz

Signal gainIdler gain

Increasepump power


JPD amplifier: degenerate operation

Signal gainIdler gain


Entanglement of signal and idler noise

vacuum noise+ pump

Entangledsignal + idlerphotons+ pump

How does the entanglement become evident?

detuning from pump

signalidler

phase between LO and pump

Vacuumfluctuations

Entanglement of signal and idler fields

detuning from pump

phase between LO and pump

Vacuum level

squeezing

anti-squeezing

sque

ezin

g


Summary JPD

G

Very good properties in terms of dynamic range, bandwidth, noise, tunability,

Two-mode squeezing of more than -12 dB Degenerate and Non-degenerate operation possible Broadly applicable in cryogenic systems


Quantum Simulation

simulatinga quantum system

difficult on classical computer!

quantumsimulator

sufficient controllability, flexibility!

map!

describes physical system of interest

(physics, chemistry, biology,)

encodes hard classical problem

interesting toy model

universalquantum computeruse

Feynman, Int. Journal of Th. Phys. 21, 467 (1982)Llloyd, Science 273, 5278 (1996)

OR

large scale one still to be realized!

Typically:

Find Ground State of Hamiltonian

Quantumsystem

Coolingor

Annealing

Ground state

Alternative Paradigm for Quantum Simulation

Variational Ansatz

Here, specific class of states:- Matrix product states (MPS)- Projected entangled pair states

Controllable quantum system

Ground state well described by

Use to simulateNot necessarilyidentical!

Verstraete, Murg & CiracAdvances in Physics (2008)

Barrett et al., PRL 110, 090501 (2013)Eichleret al., Phys. Rev. X 5, 041044 (2015)

Variational Quantum Simulation using Cavity QED

Proposal: Barrett et al., PRL 110, 090501 (2013)Realization: Eichleret al., Phys. Rev. X 5, 041044 (2015)

1) Create variational (cMPS) states using CQED 2) Evaluate Hamiltonian of interest using

correlation measurements of .3) Vary state using external control

(Discrete) Matrix Product States1D lattice model (d levels per site):

has coefficients

Most general state

Idea: Reduce states space to relevant one.

with D-dim. matrices-> matrix elements

Properties: Satisfy area law for the entanglement entropy Represent exact ground state of specific models Generalization to higher dimensional lattices Close relation to DMRG Continuous limit Connection with cavity QED and input/output

theory

Reviews:Verstraete et al., Adv. Phys. (2008)Schollwoeck, Ann. Phys (2012)Orus, Ann. Phys. (2014)

cMPS and cavity QED:Verstraete et al., PRL 104, 190405 (2010) Barrett et al., PRL 110, 090501 (2013)Osborne et al., PRL 105, 260401 (2010)

(Continuous) Matrix Product States

Verstraete and Cirac, PRL 104, 190405 (2010)

Definition:

with

act on auxiliary systemEquivalence to discrete MPS by choosing(for bosons):

and taking the continuum limit .

field operator

Features: Also possible for fermionic fields Generalization to vector fields with multiple components

Cavity QED output as cMPS

generated by auxiliary system through

Assumptions made here: Cavity input field is in the vacuum Internal decay negligible

with

Compare with non-Hermitian representation of cavity QED Hamiltonian

Cavity acts like auxiliary system to generate MPS in the 1D continuum.

Osborne et al., PRL 105, 260401 (2010)Barrett et al., PRL 110, 090501 (2013)

What we Simulate

chemical potentialkinetic energy

repulsive interaction

Here: Gas of interacting bosons in 1D continuum

Described by the Lieb-Liniger model

onlyone parameterin the model!

Lieb & Liniger Phys. Rev. 130, 1605 (1963)Paredes et al., Nature 429, 277 (2004)

What is needed?

1) Tunable cavity QED system

2) Efficient & programmablemeasurement apparatus

3) Simulation of the Lieb-Liniger model

4) Future perspectives

Cavity QED

A. Blais, et al., PRA 69, 062320 (2004)A. Wallraff et al., Nature (London) 431, 162 (2004)


with Superconducting Circuits

Cavity Transmission line resonator

Atom Superconducting qubit

atom

cavity

Small mode volume (1D) Large dipole moments Strong coupling

Circuit QED Approach to Creating cMPS

=cavity

piece of a coax cable

Radiation field stored inside:

sum of harmonic oscillators

atom

=JosephsonJunction

=Nonlinearinductor

g

ef

anharmonicsystem

Changetransition energyon ns timescales!

Ener

gy

qubit

transmon

Y. Nakamuraet al., Nature 398, 786 (1999)J. Koch, et al., PRA 76, 042319 (2007)

Eichleret al., Phys. Rev. X 5, 041044 (2015)Srinivasan et al., PRL 106, 083601, (2011)

asymmetric resonator coupling control using global

field + local flux line tunable frequency and tunable

coupling

Mediate effective photon-photon interactions with tunable strength

Circuit QED Device with Tunable Coupling Transmon

InOut

Local flux line

Lieb-Liniger Hamiltonian Radiation field

Field operator Cavity output field

Measurement Apparatus

Measure photon correlation functions!

At GHz frequencies?Variational parameters:

Experiments with Propagating Quantum Microwaves

Lang et al., PRL 107, 073601 (2011)Bozyigit et al., Nat. Phys 7, 154 (2011)Eichler et al., PRL 106, 220503 (2011)

Time-correlations functions for continuous single photon source since then experiments on:

Squeezing Wigner Tomography Qubit-Photon-Entanglement Hong-Ou-Mandel interference Photon shaping Superradiance

linearamplifier

adds vacuum/thermal

noise

Quantum limited amplifiers:(Special requirements in terms of dynamic

range, bandwidth, phase-insensitivity)

Eichler et al., PRL . 113 110502 (2014)c.f.: Castellanos-Beltran et al., Nat. Phys. 4, 929 (2008)

Bergeal et al., Nature 465, 64 (2010)

improved detection efficiency with quantum limited amplifiers

reduce g2 measurement time by ~10000

See ETH Qudev lab publications

Time-resolved Correlation Measurements Drive nonlinear cavity mode

vs. two variational parameters:

Effective anharmonicity:Drive rate

Eichleret al., Phys. Rev. X 5, 041044 (2015)

Simulate Lieb-Liniger Hamiltonian

How to measure ?

Barrett et al., PRL 110, 090501 (2013)

Correlations vs. Variational ParametersMeasured correlations vs. variational parameters:

Energy in variational space

Chemical Potential: Kinetic energy: Interaction energy:


Measured Energy Landscape

Energy landscape vs. variationalparameters:

Local minimum in variationalspace

Ground state depends on interaction strength v

variationalground state

Parametric amplifier reduces g2measurement time by ~10000


Properties of the Simulated Ground StateGround state energy vs. interaction strength

We can do more than that: We can probe any quantity of interest!

Tonks-Giradeaulimit

Exact numerical result

Experimentallyobtained

at particle density


Properties of the Simulated Ground State

Experimentally obtained first order correlation function:

Conversion of temporal into spatial coordinates Decrease of correlation length with increasing interaction strength No Bose condensation in 1D (Mermin Wagner) Numerical result with small bond dimension D similar to experimental data

Properties of the Simulated Ground State

Experimentally obtainedparticle-particle correlations:

crossover from weakly to strongly interacting Bose gas (Tonks-Giradeau) qualitative agreement already for a simulation with two variational

parameters quantitative agreement requires additional variational parameters in

experiments

Continuous Matrix Product States: Summary Variational approach System suitable for creating cMPS

experimentally Efficient correlation measurements High level of control/tunability Some potential for scaling

Many-body physics Atomic, solid state, bio-physics Quantum information

Quantum field theories Discrete Lattice models Vector fields Fermionic systems Extension to higher dims


The ETH Zurich Quantum Device Labincl. undergrad and summer students

Want to work with us?Looking for Excellent Postdoc and PhD Candidates!

exploring quantum simulations with superconducting … · exploring quantum simulations with...

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