microwaves for quantum simulation in superconducting
TRANSCRIPT
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