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

Jamming with a Quantum Computer
Because NISQ* begins with Noisy

James Weaver
@JavaFXpert

*Noisy Intermediate Scale Quantum computers

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

These web-based slides:

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

Author of several Java/JavaFX/RaspPi books

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

james.weaver@ibm.com
JavaFXpert.com

CulturedEar.com

• 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

### 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

“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

“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

“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

### Near-term quantum computing domains

Conspicuously absent:

Music composition & improvisation

### 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

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.

### 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

### Johann Joseph Fux

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

• 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?

\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 Musical Composition from Melbourne

\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

## Axioms of Quantum Mechanics

\vert\space\space\space\rangle

## My microscopic cat is often grumpy

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

## Axiom 1: Superposition principle

### 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
\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)

\vert\space\space\space\rangle

### 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}

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

## 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}

## 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

## 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

\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

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

\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 Qiskit notebooks

Qiskit open source quantum computing framework

### Developing quantum apps

Qiskit Terra foundational stack

### Developing quantum apps

Sample output:

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

Expresses circuit:

### Minimal Qiskit example

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)

Qiskit Aqua quantum algorithms

### Example Aqua algorithm: Grover search for boolean satisfiability

Throwing a party while avoiding the drama

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)

Solves combinatorial optimization problems such as Traveling Salesman (TSP)

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!

and Science

### Notices and disclaimers

© 2018 International Business Machines Corporation. No part of this document may be reproduced or transmitted in any form without written permission from IBM.

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Information in these presentations (including information relating to products that have not yet been announced by IBM) has been reviewed for accuracy as of the date of initial publication and could include unintentional technical or typographical errors. IBM shall have no responsibility to update this information. This document is distributed “as is” without any warranty, either express or implied. In no event, shall IBM be liable for any damage arising from the use of this information, including but not limited to, loss of data, business interruption, loss of profit or loss of opportunity. IBM products and services are warranted per the terms and conditions of the agreements under which they are provided.

IBM products are manufactured from new parts or new and used parts. In some cases, a product may not be new and may have been previously installed. Regardless, our warranty terms apply.”

Any statements regarding IBM's future direction, intent or product plans are subject to change or withdrawal without notice.

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

Performance data contained herein was generally obtained in a controlled, isolated environments. Customer examples are presented as illustrations of how those customers have used IBM products and the results they may have achieved. Actual performance, cost, savings or other results in other operating environments may vary.

References in this document to IBM products, programs, or services does not imply that IBM intends to make such products, programs or services available in all countries in which IBM operates or does business.

Workshops, sessions and associated materials may have been prepared by independent session speakers, and do not necessarily reflect the views of IBM. All materials and discussions are provided for informational purposes only, and are neither intended to, nor shall constitute legal or other guidance or advice to any individual participant or their specific situation.

It is the customer’s responsibility to insure its own compliance with legal requirements and to obtain advice of competent legal counsel as to the identification and interpretation of any relevant laws and regulatory requirements that may affect the customer’s business and any actions the customer may need to take to comply with such laws. IBM does not provide legal advice or represent or warrant that its services or products will ensure that the customer follows any law.

### Notices and disclaimers continued

Information concerning non-IBM products was obtained from the suppliers of those products, their published announcements or other publicly available sources. IBM has not tested those products about this publication and cannot confirm the accuracy of performance, compatibility or any other claims related to non-IBM products. Questions on the capabilities of non-IBM products should be addressed to the suppliers of those products. IBM does not warrant the quality of any third-party products, or the ability of any such third-party products to interoperate with IBM’s products. IBM expressly disclaims all warranties, expressed or implied, including but not limited to, the implied warranties of merchantability and fitness for a purpose.

The provision of the information contained herein is not intended to, and does not, grant any right or license under any IBM patents, copyrights, trademarks or other intellectual property right.

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
@JavaFXpert

*Noisy Intermediate Scale Quantum computers

By javafxpert

# Jamming with an IBM Quantum Computer

Because NISQ begins with Noisy

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