James L. Weaver
Quantum Developer Advocate



james.weaver@ibm.com
JavaFXpert.com

CulturedEar.com

@JavaFXpert

Jamming with a Quantum Computer

Because NISQ* begins with Noisy

*Noisy Intermediate Scale Quantum computers

slides.com/javafxpert/jamming-with-a-quantum-computer

Browser-based slides:

About Presenter James Weaver

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

Author of several Java/JavaFX/RaspPi books

Quantum Developer Advocate at IBM

@JavaFXpert

Concepts we'll address today

  1. Quantum computing overview
     
  2. Relationship between music and quantum computing
     
  3. Species counterpoint musical style
     
  4. Composing music probabilistically
     
  5. Creating melodies and harmonies with quantum notes
     
  6. Musical composition and jamming demos along the way

@JavaFXpert

History repeating itself

ENIAC computer circa 1947

IBM Research quantum computer circa 2017

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.

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IBM Announces Q System One at CES 2019

Why use a quantum computer?

Feasible on classical computers

Feasible on quantum computers

Solutions to problems

some problems may be solved exponentially faster

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Breaking RSA crypto

someday maybe, using Shor's algorithm

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”

Dr. Peter Shor, 2013

Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

Related paper published 25 Jan 1997 by Dr. Shor:

Note: Shor's algorithm was formulated in 1994

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Quickly searching unsorted data

using Grover's algorithm

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

"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."

Dr. Lov Grover, 2002

Quantum Mechanics helps in searching for a needle in a haystack

Related paper published 17 Jul 1997 by Dr. Grover:

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Simulating nature

complex chemical reactions, for example

“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.”

Dr. Richard Feynman, 1981

en.wikipedia.org/wiki/Richard_Feynman

bigbangtheory.wikia.com/wiki/Richard_Feynman

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Near-term quantum computing domains

Conspicuously absent: Music composition & improvisation

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Machine Learning

Optimization

Chemistry

Finance

Music and quantum mechanics are probabilistic

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"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."

- Leonard B. Meyer, Music, the Arts, and Ideas

To inaccurately paraphrase Dr. Feynman...

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

http://bigbangtheory.wikia.com

The Big Idea:

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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

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

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From OpenMusicTheory.com Composing a second-species counterpoint

Giovanni Palestrina

Text

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

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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)

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Quantum Music Composer app

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Transition matrix

edition

Expressing melodic characteristics

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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

in a transition matrix

Expressing harmonic characteristics

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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.

in a transition matrix

What's Quantum Got to Do with It?

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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

\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle
= \begin{bmatrix} 1 \\ 0 \end{bmatrix}
=[10]= \begin{bmatrix} 1 \\ 0 \end{bmatrix}
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle
= \begin{bmatrix} 0 \\ 1 \end{bmatrix}
=[01]= \begin{bmatrix} 0 \\ 1 \end{bmatrix}
= \begin{bmatrix} \sqrt{\frac{1}{3}} \\ \sqrt{\frac{2}{3}} \end{bmatrix}
=[1323]= \begin{bmatrix} \sqrt{\frac{1}{3}} \\ \sqrt{\frac{2}{3}} \end{bmatrix}
\sqrt{\frac{1}{3}}
13\sqrt{\frac{1}{3}}
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle
+
++
\sqrt{\frac{2}{3}}
23\sqrt{\frac{2}{3}}
\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

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\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

Modifying transition matrices

@JavaFXpert

using degree of freedom rotations

.33\approx\frac{1}{3}
.33≈13.33\approx\frac{1}{3}
.67\approx\frac{2}{3}
.67≈23.67\approx\frac{2}{3}
.57\approx\sqrt{\frac{1}{3}}
.57≈13.57\approx\sqrt{\frac{1}{3}}
.82\approx\sqrt{\frac{2}{3}}
.82≈23.82\approx\sqrt{\frac{2}{3}}

Quantum computer composing a melody

@JavaFXpert

\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
\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}
13\frac{1}{3}
\frac{2}{3}
23\frac{2}{3}

wp

wp

Sample melody:

...

...

Quantum computer composing a song

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Quantum Musical Composition from Melbourne

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Representing Qubits with the Bloch Sphere

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Grokking the Bloch Sphere

IBM Q Experience

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Composing quantum circuits

IBM Q Experience Composer

IBM Q Experience

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Quantum Assembly Language (QASM)

IBM Q Experience QASM Editor

IBM Q Experience measurement results

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Developing quantum apps

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Qiskit open source quantum computing framework

Qiskit quantum computing framework

Developing quantum apps

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Qiskit Terra foundational stack

Qiskit Terra

Minimal Qiskit example

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Sample output:

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

Expresses circuit:

Composing in the Bell states

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\sqrt{\frac{1}{2}}
12\sqrt{\frac{1}{2}}
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle
+
++
\sqrt{\frac{1}{2}}
12\sqrt{\frac{1}{2}}
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle

00

C

11

F

\sqrt{\frac{1}{2}}
12\sqrt{\frac{1}{2}}
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle
-
−-
\sqrt{\frac{1}{2}}
12\sqrt{\frac{1}{2}}
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle

01

D

10

E

\sqrt{\frac{1}{2}}
12\sqrt{\frac{1}{2}}
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle
-
−-
\sqrt{\frac{1}{2}}
12\sqrt{\frac{1}{2}}
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle

00

C

11

F

\sqrt{\frac{1}{2}}
12\sqrt{\frac{1}{2}}
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle
+
++
\sqrt{\frac{1}{2}}
12\sqrt{\frac{1}{2}}
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle

01

D

10

E

Developing quantum apps

@JavaFXpert

Qiskit Aqua quantum algorithms

Qiskit Aqua

Near-term quantum computing domains

Conspicuously absent: Music composition & improvisation

@JavaFXpert

Machine Learning

Optimization

Chemistry

Finance

Close encounters of the minor third kind

@JavaFXpert

https://igius.com

rogerlinndesign.com

Hands-on Qiskit workshop

Now it's your turn to play!

@JavaFXpert

Instructions are in my Learning Qiskit: Guided exercises for developers project on GitHub

Jamming with a Quantum Computer

{\frac{1}{\sqrt2}}
12{\frac{1}{\sqrt2}}
\vert{Q}\rangle
∣Q⟩\vert{Q}\rangle
+
++
\vert{A}\rangle
∣A⟩\vert{A}\rangle
{\frac{1}{\sqrt2}}
12{\frac{1}{\sqrt2}}

Because NISQ begins with Noisy

James L. Weaver
Quantum Developer Advocate


 

james.weaver@ibm.com
JavaFXpert.com

CulturedEar.com

@JavaFXpert