Putting Quantum Information Resources to Work - PowerPoint Presentation

Putting Quantum Information Resources to Work
Putting Quantum Information Resources to Work

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No longer just theory MeetUp SlideS by Henning Dekant Mission IMPOSSIBLE Massively Condensed Short History of quantum computing I think I can safely say that nobody understands quantum mechanics ID: 733102 Download Presentation

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Slide1

Putting Quantum Information Resources to Work

No longer just theory

Meet-Up

SlideS

by Henning DekantSlide2

Mission IMPOSSIBLE

Massively Condensed, Short History of quantum computing

“I think I can safely say that nobody understands quantum mechanics”

Richard Feynman (May 11, 1918 – Feb 15, 1988)

Observed that most QM systems cannot be efficiently simulated on classical hardware (Turing machines). Unlike his

‘room at the bottom’ lecture (1959)

his suggestion of a quantum simulator went mostly unnoticed

(IJTP 6/1982

)Slide3

Quantum computing

The roots of the modern theoretical approach

Schrödinger's cat: If a single atom’s decaying, the flask is shattered, releasing the poison that kills the cat. The Copenhagen interpretation of quantum mechanics implies, the cat will be 

simultaneously

 alive 

and

 dead

. This is referred to as Quantum Superposition. The modern field of Quantum Information Science started with the question of what happens when we put a computer (Turing Machine) in such a superposition (

PRS Deutsch 1985

). 

Can’t put a brain into Schrödinger’s box. Slide4

Conflicting Headlines

So you can buy a quantum Computer?Slide5

Conflicting Headlines

So you

can’t

buy a quantum Computer?Slide6

QuantUM

Hardware

Many Ways To Make A Quantum Computer

Josephson JunctionsSlide7

QuantUM

Hardware

The KISS PRINCIPLE

Quantum Annealing promises to be better at finding the absolute minimum of an optimization function due to spontaneous global entanglement and quantum tunneling.

D-Wave implements a Spin glass (

Ising) modelNot universal but good for a wide class of optimization problems as diverse as protein folding and AI deep learningNo guaranteed quantum speed-up as with Shor’s algorithm. Slide8

Quantum computing

SHOR’s Algorithm

The field received a huge boost when Peter Shor’s factoring algorithm was published in 1994. With the right hardware, it can undermine all modern cryptography.Slide9

Quantum computing

Drowning in

PAPers

Subsequently the field exploded. The following graph shows the number per year of articles in

arXiv

(the major physics pre-print archive) containing the words “quantum computation” in their abstract.Slide10

Quantum SALES PITCH

Rose’s lawSlide11

Quantum SALES PITCH

Gate QC Moore’s lawSlide12

Annealer

Gate Model

Quantum Computing

TWO Major Architectures Slide13

Quantum Hardware

OUTLOOK

4

8

12Slide14

Big Data, Analytics,

QC Software and Software Patents

(QC=Quantum Computing)

What would your iPhone be without the software? It would make a nice paperweight.

Steve Jobs

Quantum computing

Where to go from hereSlide15

Quantum computing

Quantum computing report™

Government/Non-Profits

Private/Startup Companies

Public Companies

Universities

Venture Capital

Links to listings of companies and organizations that are active in the Quantum Computing space :Slide16

Quantum Resources

Quantum Superposition

Erwin Schrödinger mocked the Copenhagen Interpretation of Quantum Mechanics that he helped create with his ‘undead’ cat in a box thought experiment.

No animal has been harmed in the production of this thought experiment.

We can’t put a real brain into the box, but how does quantum superposition affect information processing?Slide17

Quantum Resources

The elementary building block: a bit with identity crisis

A classical bit is either 1 or 0. In quantum superposition it can be both at the same time, creating a more complicated state:

But there’s a catch. Nature insists on

α

and

β

to be complex numbers. This has far reaching consequences.Slide18

Quantum Resources

The elementary building block: a bit with identity crisis

Representing a Bit state with a (spin) vector.

0

1Slide19

Quantum Resources

Huge parameter space when combining

qubits

Before a result is measured a quantum computer essentially occupies every physically possible state that the ‘logic gates’ allow. But then in the end you can only read out classical bits.

Quantum algorithms are clever set-ups that facilitate probabilistic amplification effects that, via repeat measurements, enable the quantum computer to derive results with high fidelity. It is like reading the face of a multidimensional

rubics

cube after it went through an algorithmically prescribed set of turns.Slide20

Quantum Resources

Huge parameter space when combining

qubits

The infinite state possibilities of qubits are additionally augmented by non trivial QM specific correlations. This spans a huge parametric space much larger than just provided by simple state multiplication.

These specific quantum states are called

entangled because single qubits

cannot be separated out

, they become physically fused into one Quantum state. Slide21

Quantum Resources

Entanglement – The non-LOCAL “Spooky” Kind

Alice and Bob each have one qubit of an entangled pair.

Bob performs a quantum operation on his qubit depending on which two classical bits he wants to communicate.

Bob sends his qubit to Alice.

Alice conducts the final measurement on the entangled pair.Slide22

Quantum Resources

Entanglement – The non-LOCAL “Spooky” Kind

Two qubits are involved in protocol

BUT Bob only interacts with one

and sends only one

along his quantum communications channel In this protocol two bits are communicated sending a single qubit. There is no equivalent protocol for a classical communications channel.Slide23

Quantum Resources

“Local Entanglement” - NMR QC

Qubits can be encoded in the magnetic nucleus spin of organic molecules, setup and calculation can be accomplished via nuclear magnetic resonance (NMR) spin control and tomography. Slide24

Quantum Resources

“Local Entanglement” - NMR QC

This has been successfully deployed to implement and test quantum algorithms, but it doesn’t scale very well, as the number of qubits is limited by the underlying molecule.

Biliverdin

Derivatives, up to 11 qubits

CH

2

CH

2

NHC

48N12 derivatives, up to 12Slide25

Quantum Resources

“Local Entanglement” - NMR QC

Despite the early success of the liquid NMR approach, doubts about the presence of quantum entanglement remained because it can be performed at room temperature, rather than close to absolute zero.

Entanglement cannot not be sustainable under these conditions

.

Could

Quantum Discord

come to the rescue?Slide26

Quantum Resources

Quantum Discord - How Quantum is Quantum enough?

Systems can exhibit different degrees of “

quantumness

”. While mathematically difficult to formulate, quantum discord can be understood as specifying how much a system can be disrupted via measurement. It is a way to assess quantum correlations below the entanglement threshold.Slide27

Quantum Resources

How Quantum is Quantum enough?

A simple test algorithm

[1]

(matrix tracing) proved in 2008 that quantum speed-up could be had with a system that exhibits no entanglement and only minimal quantum discord.

QC With Full Entanglement Control

The usefulness of the measure is controversial, as it has been shown that essentially all quantum systems exhibit discord

[2]

, and it is not clear that it can highlight which quantum correlations are essential to attain meaningful speed-up.

QC With Quantum Discord

Measuring the protected qubit and averaging over many runs surprisingly still gives the correct answer. Slide28

Quantum Resources

Quantum Correlation – The Complete Picture

Arbitrary quantum systems have more than a qubit-like two state spectrum. Also, unless a system is highly controlled, we will find it in a thermodynamic mix of possible quantum states. Generally, this is described with an ensemble averaged density matrix

1

.

Example for a Bell State

(i.e. maximal entanglement)

Slide29

Quantum Resources

Why Complex Numbers? Wave-Particle Duality

Complex numbers translate to wave like interference patterns due to Euler’s identity:Slide30

Quantum Computing Apps

From D-Wave’s Light Switch game to

FinTech

and AI

Visualizing the

Ising

Model as implemented by Quantum Annealing.

Goal is to set the switches to minimize the cost function E(s)Slide31

Quantum Computing Apps

Mapping a Cost Function for Portfolio

OPtimization

An asset manager needs to invest K dollars in a set of N assets with an investment horizon divided into T time steps. Taking into account transaction, temporary market impact costs, the forecast of future returns and the risk of each asset, the asset manager must find the optimal asset allocation at each time step

[1]

.

Implementation challenge:

Recasting an integer-based cost function to a binary one.

The hardware graph is very sparse and in general does not match the problem graph. To solve problems that are denser than the hardware graph, additional qubits are consumed for coupling.

For square Chimera hardware graphs, the size V of the largest fully dense problem that can be embedded on a chip with q qubits is V = √ 2q + 1 = 4s + 1, assuming no faulty qubits or couplers. For example, the latest chip is the

DWave 2X, which has s = 12 unit cells along each side, giving q = 1152 qubits, for which we get V = 49. The number of required variables necessary depends on the chosen encoding of the cost function. I.e. for binary encoding it is V=T N log2 (K’+1) with K’ the # of largest allowed holding for any asset.Slide32

Some Results:

K is the number of units to be allocated at each time step and the maximum allowed holding (with K0 = K), “encoding” refers to the method of encoding the integer problem into binary variables, “

vars

” is the number of binary variables required to encode the given problem, “density” is the density of the quadratic couplers, “qubits” is the number of physical qubits that were used, “chain” is the maximum number of physical qubits identified with a single binary variable, and S(α) refers to the success rate given a perturbation magnitude α%.

Quantum Computing Apps

Mapping a Cost Function for Portfolio

OPtimizationSlide33

Quantum Computing Apps

Quantum Chemistry - Big Vision in Reach with Gate Computing

Matthias Troyer (ETH Zürich) made the case in a recent Google talk that QC will allow us to unlock the secret of natural nitrogen fixation. This is based on his theoretical work that will allow quantum chemistry with a few hundred fully entangled qubits

[1]

.

The Haber-Bosch

process made BASF, and made famine a distant memory in industrialized countries.

But it comes at a cost. It consumes 2% of the global energy supply and is the No.1 industrial source of CO

2

Soil microbes

accomplish nitrogen fixation much more efficiently, QC will give us the power to understand how they do that.Slide34

Quantum Computing Apps

Quantum Chemistry - Big Vision in Reach with Gate Computing

QC will flatten the vexed hyperbola of quantum chemistry.

# of Electrons

AccuracySlide35

Quantum Computing Apps

Quantum Chemistry - Big Vision in Reach with Gate Computing

Disrupting Research: Chemistry will no longer be lab but simulation driven. Slide36

Quantum Computing Apps

Artificial Intelligence

Compare and contrast an artificial neural network architecture such as a Boltzmann machine with a Quantum

Annealer

such as the D-Wave device.

D-Wave’s chip is

out-of-the-box a Restricted Boltzmann Machine

, and can be seamlessly integrated into Deep Learning structures

[1]

.Slide37

Quantum Computing Apps

Artificial Intelligence

Quantum Annealing can also be used to learn the structure of a Bayesian (Belief) Network (B-nets) from Data. NASA research demonstrated how to recast this problem as a Quadratic unconstrained binary optimization (QUBO) which in turn can be mapped to the

Ising

Model.

Unlike Boltzman

machines or any other artificial neural network architectures, B‑Nets represent explicit knowledge. They are complementary to other AI methods, when human interpretability is a key requirement (such as when diagnosing a medical condition, uncovering functions of a genome sequence, or implementing critical controller software).Slide38

Quantum Computing Apps

Artificial Intelligence

B-nets can have thousands of nodes yet remain readable, and unlike an artificial neural network, expert human knowledge can be incorporated, so that the learning does not have to start from scratch.Slide39

Quantum Computing Apps

Development Environments

Owning the hearts and minds of developers for a new platform is an established way for a software company to gain market dominance. A company like Microsoft has this etched in its DNA, and hence is already spending considerable resources developing its proprietary, closed IDE for Quantum Computing.Slide40

Quantum Computing Apps

Development Environments

My company has invented an alternative graphical development paradigm to the prevalent low level circuit model. Our co-founder Robert R.

Tucci

discovered a complex-valued extension of B-Nets that make for Quantum Bayesian Networks capable of expressing arbitrary density matrices

[1]. We are developing our IDE as an Open Source alternative to Microsoft’s

LiquiD

on

Github

.

Come and join our Open Source Quantum Computing Revolution!Slide41

Q&A and DISCUSSION

Shom More....