Microwaves for quantum simulation in superconducting ...

PrincetonUniversity

Microwaves for quantum simulationin superconducting circuits and semiconductor quantum dots

Christopher Eichler - 29.01. 2016ScaleQIT Conference, Delft

In collaboration with:

C. Lang, J. Mlynek, Y. Salathe, S. Schmidt, J. Butscher, P. Kurpiers, A. Wallraff (ETH Zurich) K. Hammerer, T. Osborne (Universität Hannover)Y. Liu, J. Stehlik, J. Petta (Princeton University)

Solid State Systems for Quantum Control

Gate-defined/Self-assembled Quantum Dots(2DEG, nanowire, CNT, SiGe)

Wiel et al., RMP ( 2003)Hanson et al., RMP (2007)

Defects & Donors in solids (e.g. NV centers)Jelezko et al., PRL (2004)

Opto- and electromechanicsAspelmayer et al., RMP (2014)

Superconducting circuitsA. Wallraff et al., Nature (London) 431, 162 (2004)

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

…and many more.

EM Radiation for Quantum Control and Measurement

Quantum System

Control with EM radiation(Optical, Microwave, RF,…)

• Readout & probe system• Exhibit Quantum correlations!

Use radiation fields as a quantum register for QIP

Here: Simulate GS of interacting bose gas in 1D

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 …

… 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

MicrocavityPolaritons

Deng et al., RMP 82, 1489 (2010)Kasprzak, Nature (2006)

Typically:

Find Ground State of Hamiltonian

Quantumsystem

Coolingor

Annealing

Ground state

How about flexibility?

New Paradigm for Quantum Simulation

Specific class of states:- Matrix product states (MPS)- Projected entangled pair states

Controllable quantum system

Ground state well described by …

Use to createNot necessarilyidentical!

Alternative:

Verstraete, Murg & CiracAdvances in Physics (2008)

Variational Quantum Simulation using Cavity QED

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

1) Generate radiation emulating MPS state 2) Program simulated Hamiltonian into measurement

apparatus. Measure3) Vary state using external control

What we Simulate

chemical potentialkinetic energyrepulsive interaction

Here: Gas of interacting bosons in 1D

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 open quantum system:SC circuit realization

2) Efficient & programmablemeasurement apparatus

3) Simulation of the Lieb-Liniger model

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)

with Superconducting Circuits

Cavity transmission line resonator

Atom Josephson junction

atom

cavity

• small mode volume (1D)• large dipole moments• strong coupling

Srinivasan et al., PRL 106, 083601, (2011)

• asymmetric resonator coupling• control using global

field + local flux line

• tunable frequency and tunable coupling

Circuit QED Device with Tunable Coupling Transmon

InOut

Local flux line

Spectroscopic Cavity Measurements

measuretransmission

Tune at Tune at

• tunable & stable cavity QED system

• individual control of coupling & frequency

Lieb-Liniger Hamiltonian Radiation field

Field operator Cavity output field

Measurement Apparatus

Measure photon correlation functions!

At GHz frequencies?

Microwave Photon Field Detection

much smaller photon energy:

instead:• linear amplifiers/ADC• signal processing

xxxx

No photon counters yetfor microwaves!

in the visible

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• Quantum Dot Lasing• …

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)Macklin et al., Science (2015)

improved detection efficiency with quantum limited amplifiers

reduce g(2) measurement time by ~10000

See ETH Qudev & Princeton Petta lab publications

Simulate Lieb-Liniger Hamiltonian

How to measure ?

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

Time-resolved Correlation Measurements Drive nonlinear cavity mode

vs. two variational parameters:

Energy in variational space

Effective anharmonicity:Drive rate

Measured Energy Landscape

Energy landscape vs. variationalparameters:

• Local minimum in variationalspace

• Ground state depends on interaction strength v

variationalground state

Parametric Amplifier reducesmeasurement time by ~10000

Properties of the Simulated Ground State

Ground 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

Eichler et al., PRX 5, 041044 (2015)

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• Numerical result with small D similar to experimental data

Eichler et al., PRX 5, 041044 (2015)

Properties of the Simulated Ground State

Experimentally obtainedparticle-particle correlations:

• crossover from weakly interacting Bose gas to Tonks-Giradeau gas• anti-bunching reveals fermionization• qualitative agreement already for a simulation with two variational

parameters!Eichler et al., PRX 5, 041044 (2015)

What tools are behind it?

Photon

statistics

G

Quantum limitedamplifiers

•1 mm

•500 nm

•S •D

Quantum Dot “Gain Medium”

SD DS

Y. Liu, J. Stehlik, CE, et al., Science 347, 285 (2015)M. Delbecq et al., PRL 107, 256804 (2011)T. Frey et al., PRL 108, 046807 (2012)

MASER?

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

Maser emission from double quantum dot device

Photon

statistics

Photon Statistics below and above threshold0 600300

I0 10-10

10

-10

Q

Counts

0

Off/On

I

0

0 100-100

100

-100

120 60

Q

Counts 0

On/On

Liu, Stehlik, CE, et al., Science 347, 285 (2015)

Gaussian

0.01

00 8000 16000

Data

p n(%

)

0.02

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

p n(%

)

5

10

00 40 80

n

Data

ThermalPoisson

Interdisciplinary connections revealed

High level ofcontrol/tunability:

Efficient correlationmeasurement

• Highly flexible platform

• Desirable scalability features

• Many-body physics• Biophysics• Quantum information

theory• Extension to higher

dimensions

• Quantum field theories• Discrete Lattice models• Vector fields• Fermionic systems