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
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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