This is probably the most visually and auditory stunning

version of our episode that we've ever done. Uh,

absolutely. This has to be— this has to be seen. Yeah, yeah, seriously, like,

if you're listening to this, you're missing a lot of the, the

feel. Welcome to Impact Quantum.

Hello and welcome to Impact Quantum, the podcast where we explore the emerging

industry of quantum computing. And, um, you don't need

to be a PhD, you just need to be a little bit curious.

And with me on this journey is the most quantum curious person I know,

Candice Gooley. How's it going, Candice? It's great, thank you for

asking. I'm really excited. We have something different for today.

Yes, and very cool. It's going to be very cool.

We have, we have a gentleman by the name of, of Victor Mason. He's

a PhD. He is a pioneer of

quantum fractal art, and we're going to learn more

about that today. So hi, how are you? How are you doing

today? I'm good, thank you. Been looking forward to this. Thank

you for having me here today. And how are you guys doing? Doing

well, doing well. We, we just got a foot of snow, and, uh,

down here in Baltimore, and we're not used to that like they

are up in Montreal. And my grandfather was from Montreal, so

whenever we got snow, he'd be like, "Ah, this is like a spring day."

So, um, but, um, with that

in mind, um, I'm very excited to hear about this because I think art

is one of those things that's, uh, uniquely human, you

know, AI-generated images notwithstanding, but, but that's a whole

other rabbit hole. But I think it's uniquely— it's not only

uniquely human, but I also think it helps people process really

weird abstract ideas. Whether we're

talking about cave paintings where they show like, hey, look, this is how we hunt

the animals. And I mean, this is something that's very much

uniquely human. And, you know, up

until 2022, I suppose, but

we were the only ones that we knew of that, that used art. And art

is one of those things universal across all cultures. And whether

it's cave paintings in Lesotho, or caves,

caves paintings, or, you know, rock paintings, all all the way up

to modern art. And what's really exciting is

that you've kind of taken this really weird abstract aspect

of mathematics, which is not everyone's cup of tea,

um, and you've made something beautiful out of it. I think that's cool because

I think everyone can appreciate beauty. Obviously what

constitutes beauty is, is very subjective, but the fact that you,

um you know, everyone can appreciate beauty, I think is universal.

And if I can add to it, what I think also been missing for me

at least, I've been in the quantum field for like 5 years, I'm gonna explain

that. Where are the visuals? Mm-hmm. Where's the beauty

in quantum? I see a lot of papers, nice, nice,

nice papers. It's not that, but you know, how can you see

quantum? You can't see that, right? So every, every person

has their own idea or something, you know, abstract. And I'm trying

to make that a bit concrete. We find that we haven't found

some kind of a logic way of how to visualize that.

That's a great way to put it, because I first saw, um, the thing that

made it click for me was I saw a vector graph where they were

basically— and that's kind of— it was like a 2D block sphere, right? Block spheres

are helpful too, but if you don't know the concept— but, but like,

the, you know, when I saw that, because I'm like, how could How could 0

1 be something else, right? Because going back to

kindergarten, you know, 0 1 is still 1. Like, what is that?

And then the presenter, um, was like, no, no, no, you're

adding vectors. And I was like, oh, that makes a lot

more sense, right? And then when you see a Blox Sphere where it's

like, wait, it's really more complicated than even just the 2D map—

the 2D map was the first thing that got my head around it. And then

when I saw the Bloksphere and like the 3D— and, and maybe it goes up

to more dimensions than 3, for all we know, um, or for all

I know anyway. You have the PhD. Yeah, I would love

to see this because I'm fascinated by it. You know, in the virtual green room

you did kind of, you know, there's a preview of it and I'm like, this

is awesome. Because I remember, I remember

when fractals— not when they first come out, I don't know when they first came

out— but I remember in the '90s I was in university and they were like,

no, this is mathematically generated art. And I'm like, that's crazy. You zoom in, it's

the same thing. You zoom in again, it's the same thing. You zoom out infinitely,

it's the same thing. It's a bit like a, a coastline, right?

A coastline from space is this jagged kind of— and you

zoom in, it's still jagged. And it's kind of the— I

don't know, for me, like, it was the, the mystery of

nature almost. Yeah, exactly. And that's why I think it connects good with quantum, where

we are saying, right, we're working with the fundamentals of nature, with particles.

We're working with nature-based So if you can connect that to

some nature math, which I think fractal math is,

then suddenly, uh, things are coming together. Yes, that's a good

way to, to poke at it. I'm excited. I've seen some of your work,

so I want to, want to share with the audience. And if you're watching us—

if you're listening to us, not watching us— be sure to check out the YouTube

link that we'll send. So let me share

the presentation. Okay, please, for

sure. Include the

sound. Okay. Okay, so you hopefully see some

nice images. Yes,

yes, yes. So, uh, as I said, uh, um, as

I said, this is a personal project of mine, like independent of

my work. But, but let me start, uh, by asking,

so I, uh, I alluded to this before,

but, uh, but the way I normally present this, then I say, imagine you could

see quantum mechanics. I mean, imagine you could

see quantum states, and I'm gonna explain that later, come alive in art

so you can discover just how intricate and beautiful quantum

phenomena can be. So I studied at the

Technical University, uh, of Denmark like 30 years ago at the Department

of Physics. I studied something called chaos theory. Perhaps you heard about the

butterfly effect, soothing patterns and fractals. And then I

was quite amazed that you could create these

beautiful patterns with, with very simple recursive

math. It was a very simple equation, and I'm going to show

that. So if we fast forward a bit, then around 5 years ago, I started

to upskill in quantum computing because I wanted to learn. So I

became a Qiskit advocate. Which means I know a little bit about

quantum computing. I'm not super duper expert in all areas. I know a little bit,

but I was very interested in how you can program a

quantum computer. And then, you know, one day I was upskilling

and suddenly I, I, I still can't remember exactly how, whether it was

a dream or how it came to me, but, but suddenly it like

hit me. Why hadn't anybody cobbled these complex

numbers, the complex amplitudes that you use in quantum mechanics

and quantum computing with the complex numbers you use to

create fractals. And ever since I got that idea, I combined these two

domains, and that's how I ended up with these, I think, amazing

patterns that I'm, that I'm real thrilled to, to share with you

here today. So if it's okay, I'm going to just tell a little bit about

the math connection between fractals and quantum computing

and show how these states the quantum states can be visualized

and also how they can be combined with music. And

I'm also thrilled to present, I think, a first-of-its-kind

short film, the jazz quantum fractal film. But I'm going

to show you guys this, and I'm very eager to hear what you think

about it. So first of all,

what are fractals? And Frank, you already said that there are coastlines,

and you— and that's exactly right, but Just, just to zoom out

a little, a little bit. Some people know fractals, some people do not, but

they're like complex geometric patterns that

exhibit self-similarity at different scales. You have the coastlines, just as

you said, Frank, you have the Romanesco broccoli where each

floret is— where each floret is like a miniature copy of the whole. You

have the cactus here, the Agave cactus with the fractal spiral

patterns, and you have snowflakes. I really love snowflakes where each snowflake's

like intricate design shows the fractal beauty— one of nature's

smallest scales. And then when we zoom out to like the largest scale at

all, then in galaxies you see these

fractal spiral patterns. So, so also on the largest scales you see

patterns that resemble fractals. So now we

have some idea of, of, of where to find fractals. So let's have

just a short look, just two slides here, uh, on the math

part of it. So, so there are many different ways that you

can create fractals, and I showed it here to the left. So one of the

ways you can create fractals are something called

the escape time fractals or Julia set fractals.

So with Julia set fractals, you iteratively

or recursively update this famous function, and I call it

famous after Mandelbrot. Perhaps some of you have heard about,

uh, Mandelbrot. And this equation is really like this— from a math point

of view, it's like a very simple equation: z is equal to z

squared plus c, nothing else, just

this nice three-term math equation. And c,

this last c, this is, this is the part that I've been focusing on, and

I'm gonna, uh, explain that. So, and it's known

with this function that if this absolute value of z

stays below 2 after a finite number of iterations, then we say that that point

is within the Julia set, and then we color accordingly. I'm going to

show you some, some examples of that. But just, but just, uh, like,

hold on, that come to the complex numbers are important when you

are creating fractals. They are essential. Now, in quantum mechanics, on the other

side, on the right side, in quantum computing,

the quantum states— this is supposed to be some kind of a Bloch sphere. I'm

going to show you the real one afterwards. Then, then

you use some— then you represent quantum states with something called

a state vector. And a state vector is

made up of complex amplitudes, which

mathematically are complex numbers. So now we see that there can

be a link— not, not that there is, but there can be a link

between the complex numbers that you use in quantum mechanics and quantum

computing and the complex numbers that you use

to create fractals. And just, um, I, I had the

question sometimes, what are complex numbers? Um, so

they're complex— that— so there are numbers that consist like of two parts. There's a

real part like this a, and there's an imaginary

part, this bi, where i is this imaginary unit. And

you— and to simplify this a bit, so you use complex numbers in

math when you cannot— when ordinary numbers are not

enough. Signal analysis, quantum physics, and some fractal math. That's

where you use complex numbers. That's— yeah. So in

that kind of special occasions, complex numbers

really make sense. So that formula there is a

b × i, right? That's like the— that's how you normally,

uh, would write a complex number. A real number a, b is a

real number, but i

is this imaginary unit. Okay, exactly. And the Mandelbrot

equation is this one: z

z² C. And C is a constant?

Yes, that's a constant. Exactly. Just checking. Exactly. Last time— the last time I

did any kind of math like this academically was,

uh, um, Kurt Cobain was still alive. So

for me, it's been also a long time ago, so, you

know, I had to refresh and, and look some things up.

So, but the thing that really got me, uh, interest, uh,

that really that bothered me, but that intrigued me for

some time, was that this equation z

z² c, this c is just one complex number, is

a constant, this one constant. But normally

when you deal with quantum computing and, uh, and quantum mechanics, and

when you use one qubit, just one qubit, the most simple

quantum circuit has just has one qubit. But one qubit,

then you already need two complex numbers to describe a quantum state

or like a state vector with just one qubit. So I was wondering this

in the beginning, how can you then make sure you

use all the quantum information instead of just compressing

any number of complex numbers into just one constant? How, how

can you do that differently? So it turns out— well, if I zoom out,

uh, just a second— so how many complex numbers at all can

you take into account? It turns out, you know, that we

are looking at, at an exponential growth here. So if you have

1 qubit, you have 2 complex numbers. With 2 qubits, you have 4. 3,

you have 8. 4 qubits, you have 16, and so forth. So you

can see easily that's gonna explode to a huge number. But one way you can—

is that one of the ways that you get all this, like,

mathematical firepower from a quantum computer over a conventional system? Yes. I'm sorry,

I didn't mean to cut your flow, but I was

just like, oh, okay, got you. Right, but only up to

a certain limit, then my computer simply breaks down because it's, it's just the

number. If you just have, I don't know, 10, 15

qubits, the number gets so high that my memory, uh, you know, crashes. So

only up to a

certain limit I can do this way. Okay, so one of

the ways— there's something called UAC mating. And there you— and, and I had to

look the math up again. There's something called a rational function

math where you have a numerator and a denominator. So basically this

equation you saw before, this Mandelbrot equation you saw here,

basically I split up in two parts with one of the complex numbers in

the numerator and the other one in the denominator. As you

hopefully see, uh, the first equation I have here. And what I very much

like about this field, I mean, nobody has really looked a

lot, into this. So you can define the function any way

you like, any way you like. So like

a huge canvas, they're just waiting to be, uh, explored. So I show you—

here's an alternative way that you can make use of

both complex numbers. Again, a rational

function but defined slightly differently. And as I mentioned before, you know,

with 2 qubits you have 4 complex numbers:

C₀, C₁, C₂, C₃. With 3 qubits,

you have these 8 complex numbers going from C0 to, uh, to

C7. So one of the ways you can try to

incorporate all this quantum information is by expanding this rational function. And this is

one way that you can do it, and there are

really many different ways. And each time you play around and you find a

new way to express that math,

you get a new visual expression. Of the fractal math. So this

is really like, how do you define the fractal math

that makes use of the quant—

um, of these complex numbers? So the Bloch sphere, Frank,

you hopefully see the Bloch sphere to the left, right? So here you see the

Bloch sphere that you normally use to visualize like a

1-qubit, uh, state vector. And here you see 3

different fractal equations and they are

coming alive in this case from a superposition state. Hopefully it's

kind of clear that this state vector like travels along, uh,

the equator here. So in this case, for each 6°— for each 6° it

could have been anything, but in this case for each 6° I take

a snapshot and I get the state vector, I get the two

complex numbers for each

6°, and then I generate these three different, fractal, uh,

math, uh, animations. So in the first animation, I compress the two numbers,

I divide them, so just have one complex number. So

this is like kind of the Mandelbrot version,

the very first animation you see here. And these two other, uh,

animations, I make use of both complex numbers by using

this rational function I showed you before, like this Julius Zettmating, one

way of doing it and the other way of doing it. So hopefully

it's clear that depending on

the kind of math you use, you get different visual expressions. Uh, does

it make sense somehow? Yeah, yeah, and it makes— it's interesting. What happens if

you're just— right now you're along the

equator, like, how does it— the visual change when you

go, uh, in different directions? So you will get a different

kind of— I'm not sure it's going to be that different, Mhm. But, but, uh,

no, from all the time I played around, as long as you

are off the axis and get more into some different parts of

the space, you do get some different visual, uh, expressions. You do.

But this is, this is just here to illustrate that really

depending on where you take the snapshots, you get a different

expression. But yes, but you would get a

different kind of, uh, of, of, uh, of, uh, fractals. So, uh,

some of these, uh, initial art—

quantum artwork here called the Qubit Carousel— was

actually exhibited in 2023 at the Microscope Gallery in New

York. So here, uh, you see a slightly

younger version of myself here in front of three

noisy 7-qubit fractal pieces, because the criteria to exhibit

at this exhibition was that the art was

created using real quantum computers. So

let me, uh, explain what I mean by that.

Uh, so here in the middle,

the middle image, this mostly yellow fractal, this has been

created from a— I would call this an ideal or

perfect fractal because it has been created

with an ideal or noiseless simulator, quantum simulator, no noise, this would be

the result you would be

if you ran exactly this quantum circuit. So it turns out that every time you

take a circuit and you send it off to a quantum

computer, and we know we are in the

NISQ era, so quantum hardware is imperfect, it's noisy. So every time

you get a result back, you get a new noisy

and, yeah, a new noisy and imperfect outcome back.

So what I did here, I actually took 8 such images that I got back,

and again, it depends on fractal math, but I use the same

kind of fractal math. And hopefully

you see that these images are variations of the

ideal one you see in the middle. So, so from

an artistic point of view, I really do believe

that noise can be so much more beautiful than the

ideal result that we are looking at here in the

middle. So if it's okay, I become slightly philosophical, you know, that makes me like

think, you know, perhaps we shouldn't strive for

perfection as imperfection can be so much more beautiful. So all these small

things, you know, getting out from, from playing around with quantum computers, looking at

the ideal result, and then what happens when you get noisy

results back, all the beautiful variations that you

can get back. That's amazing. Yeah, if you have

any questions, comments, please, please, uh, your comment about noise is interesting because there

used to be a tool that was a plugin for

Photoshop, uh, when I was in university

called, um, Kai's Power Tools Convolver. And it was basically, you have— you start with

the ideal, then like each one of them kind of would mutate in like different

directions and you would click it and you would basically get— because you were strategically

picking what type of noise, you were able to get a very different

and very, I think, much more improved version of your graphic that you were

building,

uh, by adding noise strategically. And I thought that was interesting. But also I kind

of like it from an artistic point of view because all

the focus, uh, for all the hardware companies, right, is how

can we get rid of the noise. Right? So, and here I, I, and then,

and it makes sense because we want to trust the results, we want to have,

we want to have as precise and accurate

results as we can.

But from an art point of view, hmm,

I like noise. Um, so I use Python, I program this in

Python and Qiskit and PennyLane.

I use different programming, uh, language, but primarily Python. So, uh, so instead of

using a default Python colormap, to the left here you see two fractal

images with different colors. And to the left— so, so my wife

one day asked me, why don't you let a

quantum computer choose the colormap? I was like, yeah, why not? Actually,

that's a good idea. We all heard about these quantum computing random

generated numbers, so why not let a quantum computer generate the numbers? So

to the right You see the same

patterns, exactly the same patterns, but just with different, uh,

quantum computer random generated color maps. The patterns aren't the same,

but hopefully you see that the visual expressions are very different. So that's

another dimension that you can add to our— let the quantum computer—

you can set up the code, sure, but then

let the quantum computer choose what kind of colors to, to, to, to propose, and

then you can choose

between

the colors. So it's kind of human quantum human interaction. Okay,

um, so in, in, in, in, uh, this piece

here, I implemented an alternative version of an algorithm that's

called the Bernstein-Vezzerani algorithm. That's not that important here, but what

it— that enables is that you can enter any date

or word, and then you can get a quantum state And as soon as

you have the quantum state— I love quantum states because then you have the complex

amplitudes, you have the complex numbers, and then I can generate the

fractals. So I could take any words, any words. I could take Impact Quantum, I

could take your names, I could take my name, any name, and then see what

kind of a quantum fractal you would get out of that. So here I, you

know, last year we had the International Year of Quantum Science and

Technology. So this is the kind of fractal that I I

entered these words and then I got this, uh, fractal piece. And so, um, so

I'm trying— so I try to figure out, is there anything called

quantum colors? So I look it up. So here I, I found something. I thought,

you know, with a little bit of imagination,

it could look like a particle cloud. Okay, I mean,

it's subjective, but I'll try to color here

with the quantum colors, the 3 quote colors and 3 anti-colors. So I love playing

around not just with the technical stuff, but

how can I also somehow connect it with a small

story. I'm gonna, uh, expand on that, especially on this one.

Oh wow. So this, this is one of my latest artworks.

So here I entered the words, the four, uh, the four seasons,

uh, where did I put that? Yeah, the, the four seasons. And I combine

it with photos. So, uh, I live here in Denmark, so I

taken some photos during the different seasons in Denmark. And my wife and I, we

love going to Sweden. So one of these photos, the last ones, is actually from

a park, uh, in Sweden. And then I

use AI to overlay. So what I think is, uh, what's

important to me is, you know, just not

just everything is quantum, but how, how can we somehow tell the story

try to connect it to the world that

we live in because it easily gets

so, uh, uh, abstract when we talk about, uh, quantum. So as, as, uh, so

I wanted to, as, as here to explore different ways by combining these

visuals. And I also like to add like a slightly poetic

angle. This is really what I love about, you know, letting this be

a side project. I can try to express, you know, creativity in a much different

way than I can in my day job. And this is what

I love about being, you know, a technical person, but here, whatever comes to your

mind, you know, whatever you would like to express, you can

do that in this creative way. So I tried

here to, to combine these visuals as I said, with

slightly poetic, uh, angle exactly to relate the quantum principles

to the seasonal cycles of nature and try this way

to bridge the quantum world with the world we know it. So

if you— if it's okay with you,

I will just read the text on this.

Yes, please. Yeah, so, um, I call

it the Haiku of Continuizy Quantum Fractal

Symphony of the Seasons. So quantum

fractals fall spring to winter, states unfolding, fractals shape the

year. So, and you're held

in 4 quantum states. First, blooming, then we have,

uh, blazing, then we have blazing, right? And, um, sorry, just need to

go back. Then we have, uh, softening, and then we

have, uh, resting. And each season, that's like a fractal

that's unfolding each pattern, a moment in the spiral of

time. So across this cycle, quantum phenomena

echo through the shifting forms. We have spring

rising in coherence, and summer that's bright with

resonance, and autumn that's dissolving, uh, through entanglement, fate,

and winter that's settling into quiet, quiet decoherence. So a

year shaped by

the transitions of light and state unfolding in self-similar breath. Okay,

so that's cool. That's

a, you know, that's something everyone can, can can relate to, um, the, the

changing of the seasons. That's cool. Exactly, exactly. And that's what I

try to convey and also somehow connect it to the smallest,

you know, to the quantum nature, but also make it

more, uh, tangible, something

that we can see and relate to. So now this 5-qubit fractal I'm, I'm, I'm

very fond of— my wife and I are very

fond of this one because in my view it looks hopefully

both like a yin and yang symbol, like this wave in the

middle, but also the bird. With a little bit of

imagination, perhaps you see the bird's head

here, right? The eyes, some feathers, the mouth up here. So, so we call— or

I call this piece the quantum bird

in the dance of yin and yang. Bridging Opposites in Balance. And, uh, allow

me here to again read the caption from, from my Instagram

post here. So, in the infinite space

of the quantum realm, a bird takes flight,

navigating a path shaped by the entanglement of unseen forces.

And encircled by yin and yang's eternal dance,

it bridges the dualities and the interconnectedness of opposites—

light and dark, Chaos and order, known and unknown. And the bird

emerges as a symbol of unity, reminding us that

even in contrast, there's a balance. Through quantum

entanglement and cosmic balance, it finds its way home. The

one funny— funny, I don't know— funny thing about this is I live

in Europe, and I, and I, uh, read some time ago

that there's something, you know, that, uh, birds think— some birds can navigate

based on quantum principles. I know you had

an earlier podcast episode about quantum biology.

So that's the European Robin is said to navigate

using quantum entanglement in its eye by sensing the Earth

magnetic field. He use that when it migrates. So

this is also kind of slowly— not slowly, but whenever the

opportunity is there, trying to connect

again what happens in the quantum world with a slightly,

uh, philosophical angle, but also to nature again. To,

to nature as we know it. So I like

this, uh, connecting things from sitting something, you know, on my computer,

seeing what happens when I get back, you know, from, from, from

the quantum, uh, technology I'm using, and then relating

it again out to what happens, uh, in

the wider world. So yeah, this is

like a whole journey, if that

makes sense. In some way. Um, it's amazing, right? It's fantastic. I'm just—

I'm, I'm really enjoying listening to your explanation as

to why we're seeing it how we're

seeing it. Um, I, I— please continue. I think it's fantastic.

So I also turn my attention to, you know, fractal

animations because, as you said, Frank, Fractals are known for— you can

zoom in or out and you see the same patterns, they're repeating. So

here I want to show you like what I call like a,

like a short journey I call into the mind of a quantum

computer from this fractal art perspective. And why do I call it that? I

call that because it's based on a 7-qubit, on a 7-qubit

quantum circuit. So 7-qubit, if we translate that to

the complex numbers, that's 128 complex numbers I use in this kind of

math. But this quantum circuit has been run

on real quantum hardware. It's not a simulator, real

quantum hardware. So I'm gonna play and let's see, uh, how well it

goes through here in this recording. But I'm gonna play this, this

recording, you will see this fractal zoom. So we're

gonna zoom into this mind of a quantum computer, into

this fractal. And I call this work like

quantum

horigan thoughts. So let me show you. This, uh, video. That

was cool. Yes, it was fantastic. What impressed me is like you had the

sense of volume, like you were

traveling through something, through the image. Yeah, thank

you. Yes, yeah, so, and it's really, uh, again, this post-processing. I have this fractal,

so how can I do it to, uh, what can I do to make it

more alive so it's not just still images? And I think this is

one of the ways where you also where I also make use of

the unique properties that fractals have, that

you can keep zooming in. So, and so I also want to show you

this one. So I also started to look at 3D

animations. And here I want to show like two

short 3D videos, which I

call like sensory journeys into quantum fractal universes. And

I would, I would encourage you to pay

attention to these fine details because the fractal's fine details

become even more clear when we look at them in 3D. So let's have

a look at this piece, at this piece, or, uh, these two

short pieces that I call, that I call

Echoes of the Quantum: A

Slow

Journey

into

the Fractal Landscape. So let me play this. [MUSIC] [MUSIC]

Oh, that's some hippie trippy stuff. That's very cool. That was very cool. I,

uh, the second animation with the fly— it looked like a flower.

Yeah, yeah, that's what I

thought. It had a very, very real organic feel to it. Mm, that was cool.

Thank you. That was, that was

the intention. Yeah. Yeah, that was fantastic. So thank

you. So now I've also been, uh, wondering, you

know, whether can these quantum fractals, can they be used to, uh, you know, to,

to capture the attention, you know, of, of, of people who do not

have a quantum physics background or don't know anything about quantum computing. And

start to get them interested, just

to start to get them curious about

certain topics, about certain quantum topics. So I put together this,

uh, animation, uh, recently, and, and let me show you

this, um, this video about coherence, right? So coherence is when

you have a quantum state, and when the quantum states are coherent, then

you can do all kinds of calculations why they are coherent.,

but due to different kind of environmental noise or errors,

they can quickly decohere, and then you lose the ability

to make calculations in that time. So

here I try to visualize, uh, the, uh, coherence

using three different fractals. And instead of always using entanglement like

between two particles, I thought, okay, let's expand

this a bit into three particles. So Let

me

show

you this, uh, this, this piece

here, uh, on, on, on coherence. That was

interesting. Mm-hmm. That was cool. I think this also can, can help visualize kind

of like some

of the weird things that are going on in, in

quantum physics. Yes, right? Because, yeah, because

how do you even try to explain stuff like that, right? Right. And especially,

especially if you're a visual learner, right? Like, if you're a visual learner, like,

this stuff is hard to get

your head around because it's so counterintuitive

to how we experience everyday physics, like everyday reality. So no, that's

cool. I agree. I wish when I was studying

at the university back then, we only had the

books, right? Big books, a lot of, uh,

text, almost no visuals, a lot of formula. It was tough, right? It

was pretty tough if, if, if, if you guys, uh, remember that time.

If there have been visual learning, much more YouTube back then, or different ways of,

of learning some of the hard stuff, I think that could be, uh, For some

of us, it would

have been much more easy to grasp

the concepts. Yeah, there was a, there was a series of mathematical lectures that was,

uh, I think it was a

guy at Stanford. This was on PBS

in like the '80s, and accompanying his lectures about these very weird,

uh, very— I didn't say abstract, but they were basically Maxwell's formula was the one

that that I remember the most, where he kind of

shows that the lines of force and all that, and very rudimentary computer graphics, you

know, for the time, but,

you know, cutting edge at the time, right? But, um, it helped me understand

it, right? And I remember, and I still think back to

like, you know, those crazy, like, you know,

probably done on Amiga graphics or, you know, something like that. Like, but,

uh, no, you're right, like, it helps you get your

head around things. That's interesting because the, the visual cortex is there,

you might as well use it for learning, right? Like,

yeah, exactly. I, I just feel that,

you know, with the representation

that you're showing, you've, you've added like an emotional and an

aesthetic kind of resonance

to something that could really just be seen as engineering.

When did you start thinking about, thinking about the

emotional and the aesthetic resonance of, of, of, of these quantum equations? That's a good

question, Kenz. I think when I got the idea that I

suddenly, not suddenly, but then, you know, that I could visualize these

quantum states using fractal sense, then suddenly, you know, it like became even

more apparent to me. You know, how long time I've been looking too much

at these books, as I said, in the

past. So I was really missing the visual component,

component. And also instead of everything having to be scientifically correct in papers,

all that, I was really missing to, you know,

to express the, the creative side. So I was kind

of, how can I do this differently? How can this appeal? I'm trying to imagine

how it could appeal, you know, to somebody who's

not in the field. How can I try to

make these very, um, theoretical concepts something a bit more tangible? So,

um, besides my, uh, besides my, uh, academic,

uh, educations, I also have an education as a psychotherapist. So I do like

to— how can you connect this to people in a different way?

Because I think that can make such a much more powerful connection instead of

just seeing some formulas or

some papers. So I'm trying to bring different

parts of my past into play because I think

that creates something, uh, unique that hopefully some people can relate to.

Interesting. I think that's an interesting, like, kind

of cross-discipline, uh, because one of the things that, you know, you know, Candace

kind of said it

like it looked very hippie dippy trippy, right? Like, I paraphrasing,

right? It— there's a psychedelic feel to this, uh, with fractals

in general. Like, and what does that say about our systems of

perception? Or is it our systems of perception, or is it something

fundamental in the universe? Because you have a lot of

these things, you know, popping up,

whether they're mandalas in the Eastern tradition, whether it's, uh,

you know, um, you know fractals in kind of modern Western

math, or, you know, you mentioned yin and yang, like these things, common themes

tend to pop up. And I'm a believer, like, you know, if

not everyone's going to agree on everything, but if you have people who don't agree

on everything agree on

a handful

of things, that says something very true and fundamental. Agree. Yeah. So

So I, I, I very much like when you combine art

forms. So, uh, it turns out also that you can

take any sound or any piece of music and you can

transform this— let's call it classical sound

data— you can transform that into a quantum

state using something called the, the quantum Fourier transform signal, uh,

analysis, quantum Fourier transform. So you can take this, this piece of

normal music or sound into a quantum state. And then, as you see, when you,

when you have a quantum state, I like that a lot because then I

can turn it into fractals. So one of our good friends

here in Denmark is called Christine Dahl, and she's like

a professional jazz musician. She has won several prizes in Denmark, in

Germany, and in Norway. So together with

a colleague, we created this prototype film,

and it features these quantum fractals that are generated based on

segments of one of Christina's tracks called

Souls of the Wind, and then it's combined with some AI-generated images. So there's

the details, uh, you can read about the details in this article, but I want

to show you like 2 minutes of

what I believe, like, the first— the world's first jazz pornographic film. So it's okay

with you? I'm just going to play like 2 minutes of this jazz. Oh sure,

yeah, no, I'd love to see this because that was my next question. How does

this relate to sound, right? Because there's also auditory

for auditory learners, but also too, like, there's

a lot of harmonics could

be involved in here.

So,

so

be

prepared

for some Nordic jazz. Yeah, 2 minutes. [MUSIC] [MUSIC] Sam.

[MUSIC] Mm, that's cool, you

know. And, and, and

by using, using

music and using these visualizations, again,

you are really substantially making something understandable using like

all the senses. I, I just— I'm, I'm just

totally blown away. Thank you. I, I really hope that many

other people will also get into this

so we can show different aspects of

quantum, right? More the creative sides, the visual, the auditory. So

I think there's a little room for

a lot more going on in this, uh,

in this field. Wow. That is cool. So last summer,

then I presented my artwork at the, at the,

at United Nations Quantum for Good Summit in

Geneva, Switzerland, together with McKenna McGrew. And

she's a quantum information scientist and quantum musician. So together we

formed, um, this, this band that we called Echoes from the Quantum,

and we showcase quantum fractals and quantum music based on

the same quantum states. So she composes music based on quantum

states, and I create the fractals based on the same quantum states.

So, uh, I'm just going to play here like 4

sections of, of this quantum music, around 30 seconds each. And for each

section, then you will see a quantum fractal with some text again, where

I again try to relate what goes on, uh,

or try to describe what goes

on

in the quantum world from a, a artistic point of view.

[MUSIC] See, first I was really excited by the huskies and, and the, the,

the sound that they made. I thought that was

really, really exciting. But then, um, you just showed us one. What was the last

one that you showed us? Oh yeah, the living cell. The living—

like, and the complexity of this— of the,

of the quantum cell. Oh my God, that one blew me away. Yeah, same here.

And I was like, based on one qubit, and I was like, I wonder how

we would hear that. And then when you get to the ones that are multiples,

like, oh, I hear it now. I can't put my— I can't explain it.—

I can't explain it in words, but I'm like, I heard

it. I— you can hear the different

nodes, for lack of a better term. You, you

can almost hear it. So the sound— I'm not a sound expert, but

McKenna, she's really a sound expert, so she can explain this much better than, than

I do. But I just want to say that this Quantum

Cell, my wife and I got so, uh, so fond of this one that we

actually printed it out and we have it hanging on the wall,

like in a like, uh, what do you

call it, like a gallery print, like

80 times 80 centimeters. It's really astonishing to, to look

at. Nice. So, so this is cool. This is

probably the most visually and auditory stunning version of our episode that we've

ever done. Uh, absolutely. This has to be— this has to be seen.

Yeah, yeah, seriously. Like, if you're listening to this, you're missing a

lot of the the feel. Plus you, you

might— you're not seeing my funky, my funky glasses. I'll go to

the YouTube, right? And, and, and, and, and look

at it afterwards, right? So, but also I just

have a few more, uh, slides, two more slides. So, so

what Makeda and I also did, we look into complexity in quantum arts. So

that means that we're going from simple arts, and by simple art

I mean this is based on quantum circuits that are easy

to simulate on a classical computer, on a normal computer,

to the more complex art, which means art that is based on

quantum circuits where you have different

gates in them that make it more difficult to simulate classically. Without

going into much— too many, uh, technical details, there is

something to do with Clifford gates and non-Clifford gates, but

let's not go into these technical details right now. But what we showed uh,

in an article where I can provide, uh, the link,

of course, is that the artistic complexity can be measured

by something called the Shannon entropy, right, which is a

measure of the amount of complexity and unpredictab— unpredictability you have

in a system. And we could see, we

could measure that the Shannon entropy is notably higher in

the more complex art compared to

the more simple art both with the visuals but also with the audio.

So if you have a look here at these, uh, three fractals here, um,

you have the same fractal math in all the columns from three

different ways of making these fractals. In the

top row, you see these nice symmetric ordered fractals

as we know them, very symmetric, very symmetrical. And this is

based on the simple classical systems what we can do on

a normal computer easily. But then when we get into

the more complex math, you start to see, uh, on more these more

complex circuits— sorry— then you see how the math

or how the fractal images also changes. And it's really a matter of,

of preference whether you like the more

ordered one or the more distorted, the more irregular ones. So I'm

just curious here, are there any— or which of these do you like? Uh, I

kind of like the upper middle one. Just because it

has that pop

art feel. I don't know. I also like the lower right one. Yeah. Mm-hmm. And

imagine this is just one set of colors, and imagine you can

add all kinds of different color maps to it. So you mentioned that

these are simulated. Have you, have you tried

to generate these on, on real quantum hardware? So these ones are simulated, uh, due

to, uh, to the time that we had

to do this, but I could also had used the hardware. You're right. Well, like,

how would it— would it— would you get a different result?

Would it be like a slightly different result, or— yeah, so I would expect

it, because every time you run a hardware, you

get this noisy result back, right? Uh, yeah, yeah,

yeah. So I would expect the result perhaps to become even

more distorted, but how much? Each

one, each one gives you a new noisy result back, but I would expect it

to become— I don't know if you could tell the difference

between running the top one on a

quantum computer and getting

the results back versus the

lower row where you already use complex, uh, circuits.

Does one type of— I'm sorry, does, does one type of

quantum computer generate a different result? So like, would an annealing circuit generate something

different than, say, photonic or trapped ion— and Candace, I know I'm leaving out

like two more other types— like, does the

type of hardware you're running it on

change the visual, or— because these are base quantum phenomena, it

shouldn't matter. That's a very good, uh, question, Frank. I really, uh, look

forward to getting access to different kind of hardware so I can

test it out, right, and see like

how big is the difference on different hardware. Versus the ideal one, right? How

different are we from the ideal on different hardware? Do they

make different visuals? That could be a great thing to,

to look into. Hadn't had that opportunity yet, but, uh, definitely worth exploring.

Well, hopefully somebody in our audience can make that happen for you. So, right,

so, so the final piece I want to show today, uh, is

called Infinity, as you see here. And this I've done

in collaboration with, uh, with a British contemporary artist, Michel-Jacques Pearce, who's like a who's

like a— I would call traditional painter, but that's not, uh, but,

but she paints, she paints, right? So, and we have created several pieces

of art inspired by each other. So to the left you

see her painting, uh, called Infinity, and here to the right you see

my quantum fractal art version of that one. And the reason why I want to

close with this one is that I got so lucky that

last year in Nature, the science journal Nature, they discovered my

quantum fractal piece, right? And they featured it in a Nature

review article that

was commem— that was commemorating the 100th anniversary of quantum mechanics. That's fantastic. So that

was kind of cool, just sitting and playing around,

and suddenly, you know, perhaps this can capture some

of the

complexity in some visual abstract way, you know, dealing with quantum

computers. So, so, so So, so I just want to say thank you, you know,

for, for joining me and for, you know, for, for having me

here. So, so hopefully you have an idea about what quantum fractal

art is, and also you have some idea at

least that quantum states can also be visualized as these intricate

and beautiful patterns, and that it can all be combined with music also. And

for those not watching this— watching this, it's, uh, that was a QR code for

your Instagram, which we'll make sure we have in the

show notes, because your Instagram is very fascinating. Yeah, it's

good. Um, very cool stuff. Um, want to be respectful of your time, plus I

do have kids

home from school and I, I, I can hear them decohering from here. Um,

you had your own visualization. I got my own visualization there. Yeah, I hear—

I, I, I, um, you know, I'm in the basement and the playroom is

upstairs and I slowly hear the chaos going from like this

noise level to like— yeah, there's a lot of quantum noise happening upstairs.

Uh, but thank you very much. This has been probably the most fascinating— and we

have a lot of fascinating guests, right? I'm not throwing shade at any of

our previous guests, Candace. No, I know. Wow, this is really cool. This

is different. Very different and very cool. And I appreciate what you're doing because I

think you're doing, you know, the Lord's work, you know what I mean? Like, you're

bringing— you're, you know, a lot of people think of art and science

as two very different realms, but, you

know, and then they are, but there's a significant overlap too. Exactly. Well, I want

to thank you again for, for allowing me time for this because I

know this was a different topic. I've listened to all the podcasts, so that's, you

know, curious at all, would you

be open to this kind of, uh, outside— Oh, absolutely. This is amazing. Yeah, no

problem. And I know Candace does a lot of work with neurodiversity

and things like that, um, and, and, and has experience in that space. And I

would suspect that there's— I don't— I mean, I, I just see an overlap there

too, right? In terms of how different people learn, different

learning styles and things like that. I think, I think

there's an enormous, um, a lot of directions this

could go. Yeah, exactly. Awesome. Well, thank you again so

much for your time, and, and we'll, we'll connect everyone to your

Instagram. Thank you.

Thanks a

lot. Awesome. Thanks for having us, and we'll play

the

outro music. They're connecting the dots. Candace and Frank,

they're the cosmic hotshot. Quantum Podcast, turn it up

fast. Candace and Frank blowing my mind at

last. Quantum Podcast, they're breaking the mold. Science and ska beats. It's bold and it's

gold.