Think 2019 / DOC ID / February 14, 2019 / © 2019 IBM Corporation

Jamming with a Quantum Computer
Because NISQ* begins with Noisy

James Weaver
Quantum Developer Advocate
@JavaFXpert

*Noisy Intermediate Scale Quantum computers

slides.com/javafxpert/jamming-with-ibm-quantum

These web-based slides:

Please note

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The development, release, and timing of any future features or functionality described for our products remains at our sole discretion.


Performance is based on measurements and projections using standard IBM benchmarks in a controlled environment. The actual throughput or performance that any user will experience will vary depending upon many factors, including considerations such as the amount of multiprogramming in the user’s job stream, the I/O configuration, the storage configuration, and the workload processed. Therefore, no assurance can be given that an individual user will achieve results similar to those stated here.

 

Think 2019 / DOC ID / February 14, 2019 / © 2019 IBM Corporation

About Presenter James Weaver

IBM Quantum Developer Advocate

 

Author of several Java/JavaFX/RaspPi books

 

Java Champion, JavaOne Rockstar, plays well with others, etc :-)

 

james.weaver@ibm.com
JavaFXpert.com
CulturedEar.com

@JavaFXpert

Concepts we'll address today

  • Quantum computing overview
  • Relationship between music and quantum computing
  • Species counterpoint musical style
  • Composing music probabilistically
  • Creating melodies and harmonies with quantum notes
  • Programming a quantum computer with open source Qiskit
  • Musical composition and jamming demos along the way

@JavaFXpert

ENIAC computer circa 1947

IBM Research quantum computer circa 2017

History repeating itself

Massive hardware, limited bits, software infancy

Quantum computers make direct use of quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data.

IBM Announces Q System One at CES 2019

Feasible on classical computers

Feasible on quantum computers

Solutions to problems

Why use a quantum computer?

Some problems may be solved exponentially faster

@JavaFXpert

“Nature isn't classical, dammit, and if you want to make a simulation of nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem, because it doesn't look so easy.”

Simulating nature

complex chemical reactions, for example

Dr. Richard Feynman, 1981

@JavaFXpert

en.wikipedia.org/wiki/Richard_Feynman

bigbangtheory.wikia.com/wiki/Richard_Feynman

newscientist.com/article/mg22029445-100-my-quantum-algorithm-wont-break-the-internet-yet/

“If you start factoring 10-digit numbers then it’s going to start getting scary”

Breaking RSA crypto

someday maybe, using Shor's algorithm, formulated in 1994

Dr. Peter Shor, 2013

@JavaFXpert

“Programming a quantum computer is particularly interesting since there are multiple things happening in the same hardware simultaneously.  One needs to think like both a theoretical physicist and a computer scientist.”

Quickly searching unsorted data

using Grover's algorithm

Dr. Lov Grover, 2002

@JavaFXpert

outlookindia.com/magazine/story/ring-o-stars/220719

Near-term quantum computing domains

Conspicuously absent:

Music composition & improvisation

@JavaFXpert

Machine Learning

Optimization

Chemistry

Finance

“Once a musical style has become part of the habit responses of composers, performers, and practiced listeners it may be regarded as a complex system of probabilities.”

Music and quantum mechanics are probabilistic

Leonard B. Meyer

@JavaFXpert

Music, the Arts, and Ideas

Bongo music isn't classical, dammit, and if you want to make a simulation of music, you'd better make it quantum mechanical.

To inaccurately paraphrase Dr. Feynman:

@JavaFXpert

The Big Idea:

Ask a quantum computer to compose music

We'll demo a simplified version of the species counterpoint style of music, as it is well defined and may be expressed using probabilities

From OpenMusicTheory.com Composing a second-species counterpoint

What is counterpoint?

The relationship between voices that are interdependent harmonically yet independent in rhythm and contour

From OpenMusicTheory.com Composing a second-species counterpoint

Tip: For a gentle introduction to counterpoint, check out the Species Counterpoint article by Nicholas H. Tollervey

Giovanni Palestrina

Italian Renaissance composer of sacred music

  • Created Palestrina-style counterpoint
  • Best known 16th-century representative of the Roman School of musical composition
  • Influenced music of composers such as Johann Sebastian Bach

@JavaFXpert

Johann Joseph Fux

Born in Austria, Johann codified Palestrina's techniques in the 1700s, calling it species-counterpoint, mainly for teaching students.

  • Published in Gradus ad Parnassum *
  • Describe valid pitch and rhythmic relationships between notes
  • Influenced music of Hayden, Mozart and Beethoven

* Steps to Mt. Parnassos (which was the home of the muses)

Transition matrix

edition

Quantum Music Composer app

Example characteristics of counterpoint melodies:

- mostly stepwise motion, but with some leaps (mostly small leaps)

- tendency for melodies to move by descending step more than ascending

Expressing melodic characteristics

in a transition matrix

Example characteristics of counterpoint harmonies:

- All harmonic consonances are allowed.

- Imperfect consonances are preferable to perfect consonances

- Unisons should only be used for first and last intervals.

Expressing harmonic characteristics

in a transition matrix

Volkmar Putz and Karl Svozil, “Quantum music,” (2015), arXiv:1503.09045 [quant-ph]

In Quantum Music Composer, note pitches are represented by quantum states

Melodic and harmonic transitions are realized by quantum logic gates

What's Quantum Got to Do with It?

@JavaFXpert

\vert\space\space\space\rangle
= \begin{bmatrix} 1 \\ 0 \end{bmatrix}
\vert\space\space\space\rangle
= \begin{bmatrix} 0 \\ 1 \end{bmatrix}
= \begin{bmatrix} \sqrt{\frac{1}{3}} \\ \sqrt{\frac{2}{3}} \end{bmatrix}
\sqrt{\frac{1}{3}}
\vert\space\space\space\rangle
+
\sqrt{\frac{2}{3}}
\vert\space\space\space\rangle
\vert\space\space\space\rangle
\vert\space\space\space\rangle

Representing quantum states

\vert\space\space\space\space\rangle
\vert\space\space\space\space\rangle
\vert\space\space\space\space\rangle
\vert\space\space\space\space\rangle
\vert\space\space\space\space\rangle
\vert\space\space\space\space\rangle
\vert\space\space\space\rangle

using degree of freedom rotations

.33\approx\frac{1}{3}
.67\approx\frac{2}{3}
.57\approx\sqrt{\frac{1}{3}}
.82\approx\sqrt{\frac{2}{3}}

Modifying transition matrices

\vert\space\space\space\rangle
\vert\space\space\space\rangle
\vert\space\space\space\rangle
\vert\space\space\space\rangle
\vert\space\space\space\rangle
\vert\space\space\space\rangle
\frac{1}{3}
\frac{2}{3}

wp

wp

Sample melody:

...

...

Quantum computer composing a melody

@JavaFXpert

Quantum computer composing a song

@JavaFXpert

Quantum Musical Composition from Melbourne

@JavaFXpert

\sqrt{\frac{1}{2}}
\vert\space\space\space\rangle
+
\sqrt{\frac{1}{2}}
\vert\space\space\space\rangle

00

C

11

F

\sqrt{\frac{1}{2}}
\vert\space\space\space\rangle
-
\sqrt{\frac{1}{2}}
\vert\space\space\space\rangle

01

D

10

E

\sqrt{\frac{1}{2}}
\vert\space\space\space\rangle
-
\sqrt{\frac{1}{2}}
\vert\space\space\space\rangle

00

C

11

F

\sqrt{\frac{1}{2}}
\vert\space\space\space\rangle
+
\sqrt{\frac{1}{2}}
\vert\space\space\space\rangle

01

D

10

E

Composing in the Bell states

Grokking the Bloch Sphere

Representing Qubits with the Bloch Sphere

Axioms of Quantum Mechanics

\vert\space\space\space\rangle

featuring grumpy cat (or is it grumpy ket)? 

@JavaFXpert

My microscopic cat is often grumpy

@JavaFXpert

\vert\space\space\space\rangle
\vert\space\space\space\rangle

sometimes he is actually happy

but I've never observed him in-between those states

desmos.com/calculator/0rpttswx6s​

Axiom 1: Superposition principle

@JavaFXpert

my cat can be in any combination of grumpy and happy

\vert\space\space\space\rangle
= \begin{bmatrix} 1 \\ 0 \end{bmatrix}
\vert\space\space\space\rangle
= \begin{bmatrix} 0 \\ 1 \end{bmatrix}
= \begin{bmatrix} \sqrt{\frac{1}{3}} \\ \sqrt{\frac{2}{3}} \end{bmatrix}
\sqrt{\frac{1}{3}}
\vert\space\space\space\rangle
+
\sqrt{\frac{2}{3}}
\vert\space\space\space\rangle
\vert\space\space\space\rangle
\vert\space\space\space\rangle

Representing quantum states

geometrically, ket notation, and vectors

\vert\space\space\space\space\rangle
\vert\space\space\space\space\rangle
\vert\space\space\space\space\rangle
\vert\space\space\space\space\rangle
\vert\space\space\space\space\rangle
\vert\space\space\space\space\rangle

@JavaFXpert

\vert\space\space\space\rangle
\vert\space\space\space\rangle

Axiom 2: Unitary evolution

gates modeled as matrices

X

\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \cdot \begin{bmatrix} 1 \\ 0 \end{bmatrix} = \begin{bmatrix} 0 \\ 1 \end{bmatrix}

NOT gate (Pauli/X, bit-flip)

@JavaFXpert

\vert\space\space\space\rangle

Hadamard gate

great for putting cats in equal superpositions

H

\begin{bmatrix} \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} \end{bmatrix} \cdot \begin{bmatrix} 1 \\ 0 \end{bmatrix} = \begin{bmatrix} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{bmatrix}

Hadamard gate

\sqrt{\frac{1}{2}}
\vert\space\space\space\rangle
+
\sqrt{\frac{1}{2}}
\vert\space\space\space\rangle

@JavaFXpert

\sqrt{\frac{1}{3}}
\vert\space\space\space\rangle
+
\sqrt{\frac{2}{3}}
\vert\space\space\space\rangle

Axiom 3: Measurement

probability is amplitude squared

When observed there is a:

\frac{1}{3}
\frac{2}{3}

probability of being grumpy

probability of being happy

@JavaFXpert

Multiple cats

\vert\space\space\space\space\space\space\space\rangle
\vert\space\space\space\rangle
\vert\space\space\space\rangle
=
\vert\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\rangle
= \begin{bmatrix} 1 \\ 0 \end{bmatrix}
\otimes \begin{bmatrix} 1 \\ 0 \end{bmatrix}

Composite quantum states

= \begin{bmatrix} 1 \\ \\ \\ \end{bmatrix}
= \begin{bmatrix} 1 \\ 0 \\ \\ \end{bmatrix}
= \begin{bmatrix} 1 \\ 0 \\ 0 \\ \end{bmatrix}
= \begin{bmatrix} 1 \\ 0 \\ 0 \\ 0 \end{bmatrix}

@JavaFXpert

Multiple cats

\vert\space\space\space\space\space\space\space\rangle
\vert\space\space\space\rangle
\vert\space\space\space\rangle
=
= \begin{bmatrix} 0 \\ 1 \\ 0 \\ 0 \end{bmatrix}
= \begin{bmatrix} 1 \\ 0 \end{bmatrix}
\otimes \begin{bmatrix} 0 \\ 1 \end{bmatrix}

Composite quantum states

\vert\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\rangle

@JavaFXpert

Multiple cats

\vert\space\space\space\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\rangle
=
= \begin{bmatrix} 0 \\ 0 \\ 0 \\ 1 \\ 0 \\ 0 \\ 0 \\ 0 \end{bmatrix}
= \begin{bmatrix} 1 \\ 0 \end{bmatrix}
\otimes \begin{bmatrix} 0 \\ 1 \end{bmatrix}

Composite quantum states

@JavaFXpert

\vert\space\space\space\rangle
\vert\space\space\space\rangle
\otimes \begin{bmatrix} 0 \\ 1 \end{bmatrix}
\vert\space\space\space\space\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\space\space\space\space\rangle
\sqrt{\frac{1}{2}}
+

Superpositions, evolution & measurement

putting the three axioms together

\vert\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\rangle
\sqrt{\frac{1}{2}}
\sqrt{\frac{1}{2}}
+
\vert\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\rangle
\sqrt{\frac{1}{6}}
+
\vert\space\space\space\space\space\space\space\rangle
\sqrt{\frac{1}{3}}
\vert\space\space\space\space\space\space\space\rangle

@JavaFXpert

quantum gates

quantum gates

measure

\downarrow
\downarrow
\downarrow
\vert\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\rangle

with 1/2 probability

with 1/6 probability

with 1/3 probability

\vert\space\space\space\rangle

Quantum entanglement

spooky actions at a distance

H

Hadamard gate

\vert\space\space\space\rangle

CNOT gate

\sqrt{\frac{1}{2}}
+
\vert\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\rangle
\sqrt{\frac{1}{2}}
\sqrt{\frac{1}{2}}
+
\vert\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\rangle
\sqrt{\frac{1}{2}}

Mars - ESA

Alice Cat

Bob Cat

Venus - NASA

\vert\space\space\rangle
=

IBM Q Experience - Circuit Composer

@JavaFXpert

IBM Q Experience (IQX, in Beta)

@JavaFXpert

IBM Q Experience measurement results

@JavaFXpert

IBM Q Experience Qiskit notebooks

Qiskit quantum computing framework

Qiskit open source quantum computing framework

Developing quantum apps

@JavaFXpert

Qiskit Terra

Qiskit Terra foundational stack

Developing quantum apps

@JavaFXpert

Sample output:

{'00': 496, '11': 528}

Expresses circuit:

Minimal Qiskit example

@JavaFXpert

@JavaFXpert

Put your paddle into a quantum state that collapses when the ball is near

Developed at a Qiskit Camp Hackathon by Junye Huang, Anastasia Jeffery, Jarrod Reilly, and James Weaver

Example app: Quantum Pong (uses Qiskit and Pygame libraries)

github.com/HuangJunye/QPong

Qiskit Aqua

Qiskit Aqua quantum algorithms

Developing quantum apps

@JavaFXpert

Near-term quantum computing domains

@JavaFXpert

Machine Learning

Optimization

Chemistry

Finance

Example Aqua algorithm: Grover search for boolean satisfiability

@JavaFXpert

Throwing a party while avoiding the drama

Jupyter notebook containing Grover search example

What are amiable combinations of people to invite?

  • Alice and Bob are in a relationship
  • Carol and David are as well
  • Alice and David aren't speaking
((A and B) or (C and D)) and 
not (A and D)

Example Aqua algorithm: Variational Quantum Eigensolver (VQE)

@JavaFXpert

Solves combinatorial optimization problems such as Traveling Salesman (TSP)

github.com/JavaFXpert/vqe-playground

@JavaFXpert

Now it's your turn to play! Visit qiskit.org to continue learning to develop quantum computing applications. Also, try out the self-paced workshop including guided exercises at learnqiskit.org

Next steps on your quantum computing journey

We are hiring developers that are actively contributing to the Qiskit quantum computing community!

Please reach out to james.weaver@ibm.com

and Science

https://igius.com

rogerlinndesign.com

Close encounters of the minor third kind

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Think 2019 / DOC ID / February 14, 2019 / © 2019 IBM Corporation

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Think 2019 / DOC ID / February 14, 2019 / © 2019 IBM Corporation

IBM, the IBM logo, ibm.com and [names of other referenced IBM products and services used in the presentation] are trademarks of International Business Machines Corporation, registered in many jurisdictions worldwide. Other product and service names might be trademarks of IBM or other companies. A current list of IBM trademarks is available on the Web at “Copyright and trademark information” at: www.ibm.com/legal/copytrade.shtml.

Think 2019 / DOC ID / February 14, 2019 / © 2019 IBM Corporation

Jamming with a Quantum Computer
Because NISQ* begins with Noisy

James Weaver
Quantum Developer Advocate
@JavaFXpert

*Noisy Intermediate Scale Quantum computers