ISING MACHINES - GitHub Pages
Transcript of ISING MACHINES - GitHub Pages
ISING MACHINESAnil PrabhakarDept. of Electrical EngineeringIIT Madraswww.ee.iitm.ac.in/~anilpr
47-779: Quantum Integer Programming
Outline
ā¢ Some properties of lightā¢ Superposition, Entanglementā¢ Wave ā Particle Dualityā¢ Classical versus Quantum Experiments
ā¢ Photonic Ising Machinesā¢ Multiplexed in Time ā Poor Manās Ising Machineā¢ Multiplexed in Space ā Spatial Light Modulation
ā¢ Chip-based Ising Computing Machinesā¢ Electronic oscillatorsā¢ Magnetic oscillators
47-779: Quantum Integer Programming
Properties of Light
ā¢ Polarizationā¢ Color
ā¢ Wavelength, Frequencyā¢ Phase ā¢ Spatial Modes
47-779: Quantum Integer Programming
How does Quantum Computing work?ā¢ Classical bits versus quantum qubits
47-779: Quantum Integer Programming
A B0 00 11 01 1
2 bits of informationState of A and of B
A B probability0 0 Ī±0 1 Ī²1 0 Ī³1 1 Ī“
4 bits of informationSuperposition state
ā¢ Extend this to 3 qubits ā 8 bits of informationā¢ n-qubits will have 2^n bits of information
Waves interfere, we use them for computation
How does Photonic Computing work?
ā¢ Double slit experiment ā wave particle dualityā¢ Analogy ā massively parallel computation
47-779: Quantum Integer Programming
(a) Particles (b) Waves (c) Particles as Waves
Testing a Single Photon Source
ā¢ Hong-Ou-Mandel Interferometer
HOM dip as a function of T
47-779: Quantum Integer Programming
Coincidence of counts shows a non-classical dip
Ļp
How does a laser work?
ā¢ Optical wave (photons) oscillating inside a resonant cavity
47-779: Quantum Integer Programming
Stimulated Emission is in phase with the incoming photon
A laser is Coherent.All the photons are locked in phase.
Can measure a coherence time.
How do we resolve photon numbers?
ā¢ Redistribution into different spatial or temporal bins
Pulses with 5 photons
47-779: Quantum Integer Programming
Temporal redistribution47-779: Quantum Integer Programming
ā¢ Average power reduced by half for each circulation
ā¢ Synchronized detection using gating at GAPD
Detection probabilities
ā¢ Decreasing detection probabilities with subsequent redistribution
47-779: Quantum Integer Programming
Predicting detections
ā¢ If it is classical, we can predict patternsā¢ 10ā¦, 11ā¢ 100ā¦, 101, 110, 111ā¦ā¢ 1000, 1001, 1010, 1011 ā¦ etc
47-779: Quantum Integer Programming
The Ising Model
ā¢ Popular model in Statistical Physicsā¢ Phase Transitionā¢ Percolation Theoryā¢ Ferromagnetic vs Antiferromagnetic
47-779: Quantum Integer Programming
coupling J e -J e J
Bloch Wall
ā¢ Spins will orient themselves based on the minimum energy configuration
ā¢ Costs less energy to create a Wall than to flip one spin
47-779: Quantum Integer Programming
E = 0
E = e-J
E = e-2J
The Poor Manās Ising Machine
ā¢ Mach Zender Modulator with optoelectronic feedbackā¢ Bohm et al, Nature Communications, 10:3538,2019.
47-779: Quantum Integer Programming
The Optical-Electronic-Optical Model
ā¢ Self bias term Ī±ā¢ Coupling coefficient Ī²ā¢ Weights between spins Jā¢ What does the optics do?
ā¢ Nonlinear function ā cos2
47-779: Quantum Integer Programming
MZM Transfer Function
ā¢ Find the correct bias point, so we have two solutions - bifurcation
47-779: Quantum Integer Programming
xn
xn+1
Pitchfork Bifurcation
ā¢ Nonlinear function has two solutionsā¢ Uncoupled spins
47-779: Quantum Integer Programming
xn
xn+1
Pitchfork Bifurcation
ā¢ With 100 spinsā¢ Tune Ī± to observe the bifurcation
47-779: Quantum Integer Programming
Square Lattice
ā¢ 10 x 10 lattice, Ī± = 0.25, Ī² = 0.29ā¢ Can observe domain walls where spins are aligned upā¢ Lowest energy for the checkerboard pattern
47-779: Quantum Integer Programming
The Poor Manās Ising Machine
ā¢ Not quite Poorā¦.about $10,000
47-779: Quantum Integer Programming
The Poor Manās Ising Machine
ā¢ It is actually a little more complicatedā¢ Needed an optical isolator, a polarization controller, and an optical amplifier
47-779: Quantum Integer Programming
16 x 16 spin lattice
ā¢ Nearest Neighbours on a square latticeā¢ Gautham and Parth, IIT Madras
47-779: Quantum Integer Programming
Iteration
Spi
n Va
lue
Spin lattice (16x16, 24x24)47-779: Quantum Integer Programming
24 x 24 spin lattice
ā¢ Discontinuities are under investigationā¢ Gautham and Parth, IIT Madras
47-779: Quantum Integer Programming
Iteration
Spi
n Va
lue
How well does it scale?
ā¢ Photonic Chips, NUS,Singapore
47-779: Quantum Integer Programming
Spatial Light Ising Machine (SLIM)
ā¢ Optical beams have spatial divergenceā¢ Interactions are between different rays - phase
47-779: Quantum Integer Programming
Understanding Phase
ā¢ Different rays of light accumulate a different phase based on their propagation distance from the source
ā¢ Think of diffraction in 2-D, you will see rings
47-779: Quantum Integer Programming
Diffraction from a single slit
Fourier Optics
ā¢ The 4-f systemā¢ Every optical ray in 2-D interacts with every other rayā¢ A lens in 2-D acts as a Fourier Transformer, gives spatial frequency content
47-779: Quantum Integer Programming
Spatial Filters
ā¢ Easy to design high pass, low pass and vertical pass filters
47-779: Quantum Integer Programming
Blurred
Edge detection
ā¢ Amplitude maskā¢ Phase plane (SLM)ā¢ Cameraā¢ Feedback
47-779: Quantum Integer Programming
Far field intensity
Fourier transform of a rectangle
SLIM Algorithm
ā¢ Computer-generated holographic optical tweezer arraysā¢ Dufresne et al, Rev. Sci. Instr., 72, 2001
47-779: Quantum Integer Programming
What are its limitations?
ā¢ We need Ī¦(x,y)ā¢ Write an image to the SLMā¢ Read 1000 x 1000 pixels off a camera
Convergence Issuesā¢ We lose phase information with a camera
ā¢ SLM is slow and resets every so often
ā¢ 500 iterations takes 1 hour
Chip based Ising Computing Machineā¢ CICM oscillators can be optical, magnetic or electronic
47-779: Quantum Integer Programming
Magnetic Memory, and Oscillators
The āfreeā magnet aligns itself towards a preferred direction determined by the injected current
47-779: Quantum Integer Programming
The āfreeā magnet oscillates about an effective field (analogous to a top precessing in a gravitational field)
Coupled Nano Oscillators
ā¢ Arrays of oscillators can lock together
ā¢ How do we change the coupling?
47-779: Quantum Integer Programming
State of the Art
ā¢ Can do weighted oscillator networks ā vowel recognitionā¢ Romera et al, Nature 563, 2018
47-779: Quantum Integer Programming
Acknowledgements
ā¢ Gautham, Parth, Vikram and Vignesh, ā¢ Dr. Nitin Chandrachoodan, IITM
ā¢ Dr. Aaron Danner, Prof. Hyunsoo Yang, NUS
ā¢ Prof. Sridhar Tayur, CMU
ā¢ Centre for Quantum Information, Communication and Computing (quantum.iitm.ac.in)
47-779: Quantum Integer Programming