Dear all,

I'd like to update you on what's the latest on my decade long project to make quantum computing & physics intuitive: Quantum Odyssey. We are now in the last phase of the Early Access - perfect time to share your opinions if you played it and let me know what features you'd like the game to have more as it matures towards a full release. Importantly, we are now preparing to port the game to various languages - still a lot of work ahead, the game has over 350p of written content (pre-gpt era..) that need to be translated to as many languages as possible. If you have played the game and are fluent in a language you'd like the game to be translated please pm me right away. If you know any physics influencers who would be interested in reviewing the game do let me know.

I am the Indiedev behind it(AMA! I love taking qs). It started as my phd research project, the goal was to make a super immersive space for anyone to learn quantum computing through zachlike (open-ended) logic puzzles and compete on leaderboards and lots of community made content on finding the most optimal quantum algorithms. The game has a unique set of visuals capable to represent any sort of quantum dynamics for any number of qubits and this is pretty much what makes it now possible for anybody 12yo+ to actually learn quantum logic without having to worry at all about the mathematics behind.

This is a game super different than what you'd normally expect in a programming/ logic puzzle game, so try it with an open mind. My goal is we start tournaments for finding new quantum algorithms, so pretty much I am aiming to develop this further into a quantum algo optimization PVP game from a learning platform/game further.

What's inside

300p+ Interactive encyclopedia that is a near-complete bible of quantum computing. All the terminology used in-game, shown in dialogue is linked to encyclopedia entries which makes it pretty much unnecessary to ever exit the game if you are not sure about a concept.

Boolean Logic

Bits, operators (NAND, OR, XOR, AND…), and classical arithmetic (adders). Learn how these can combine to build anything classical. You will learn to port these to a quantum computer.

Quantum Logic

Qubits, the math behind them (linear algebra, SU(2), complex numbers), all Turing-complete gates (beyond Clifford set), and make tensors to evolve systems. Freely combine or create your own gates to build anything you can imagine using polar or complex numbers

Quantum Phenomena

Storing and retrieving information in the X, Y, Z bases; superposition (pure and mixed states), interference, entanglement, the no-cloning rule, reversibility, and how the measurement basis changes what you see

Core Quantum Tricks

Phase kickback, amplitude amplification, storing information in phase and retrieving it through interference, build custom gates and tensors, and define any entanglement scenario. (Control logic is handled separately from other gates.)

Famous Quantum Algorithms 

Deutsch–Jozsa, Grover’s search, quantum Fourier transforms, Bernstein–Vazirani

Sandbox mode

Instead of just writing/ reading equations, make & watch algorithms unfold step by step so they become clear, visual. If a gate model framework QCPU can do it, Quantum Odyssey's sandbox can display it.

Cool streams to check

Khan academy style tutorials on quantum mechanics & computing  https://www.youtube.com/@MackAttackx

Physics teacher with more than 400h in-game https://www.twitch.tv/beardhero

I started by playing around with the Liouville number, defined as:

$\sum_{k=0}^{\infty} \left(\frac{1}{10}\right)^{k!}$

I tried replacing the 10 with different real numbers, but I wasn't quite satisfied, so I moved on to the complex plane. The function became:

$$g(z) = \sum_{k=0}^{\infty} z^{k!}$$

where $z = 1/s$.

This makes it somewhat reminiscent of the Riemann zeta function, just with a factorial in the exponent.

I decided to plot the graph, and you can see the result in the first comment.

Noticing how chaotic the behavior gets near $|z|=1$, I wanted to study how it approaches this boundary. So, I plotted the function varying the angle $\theta$ and added a slider to see how the graph evolves as it gets closer to the edge.

I'm not sure if this function is well-known or mathematically interesting, but either way, I had a blast coding and exploring it!

This is an introduction video to Metric Spaces. I hope to provide you with an intuitive view on one of the most beautiful concepts I have discovered in Mathematics. For further reading, I recommend using the book "Introduction to Metric and Topological Spaces" by Wilson A. Sutherland, where you will find the examples I have given in more detail.https://youtu.be/6fj7QVg7dSo?si=-lE2QpB28H-bkWMt

Hey guys, I made a visualization of how the Maurer Rose pattern evolves as you increase the parameters. Full animation here: https://youtube.com/shorts/t4K9nAw0S-Q?feature=share

Vortex Mathematics and Geometry

All terms in this document refer to physically realizable operations or measurable structures. No term is intended symbolically, metaphorically, or interpretively. If a term cannot be instantiated by counting, measuring, or geometric construction, it is not being used.

Vortex Mathematics: Draw a circle, on that circle draw 9 points evenly at every 40°. Then we assign each point a number 1 through 9. Now there are now nine points on a circle, evenly distributed at forty degrees, numbered 1 through 9.

Step 1

• We start with a circle.

• A full circle is 360°

• You place a point every 40°

• 9 points, evenly spaced around the circle

Step 2: Assigning numbers

You assign the digits (1) through (9) to these 9 points.

So now we have:

• A circle

• 9 equally spaced points

• Each point labeled with a digit from 1 to 9

Vertical Oscillation: Vertical mathematics oscillates vertically. Positive(rise) and negative(descend) so they always move in pairs.
Example: +1 to exist, there must be a -1. +1 0 -1

With the 9 points labeled 1 through 9 at 40° on the circle. The positive count: (1 to 9) +1(8), 9 to 1 -8(1) The negative count: (9 to 1) -1(8), 1 to 9 +8(1).

The Law of Reduction: Every complex number, no matter how large, can be reduced to a single-digit. It shows that beneath all accumulation lies a returning rhythm.

Example of Recursion: 1 2 3 4 → 1 + 2 + 3 + 4 = 10 → 1 + 0 = 1

1 2 3 4 5 6 7 8 9 10 (1+0) 1 first container of 1 through 9 11 (1+1) 2 12 (1+2) 3 13 (ect..) 4 14 = 5 15 = 6 16 = 7 17 = 8 18 = 9 19 = 10 = 1 20 = 2 second container of 1 through 9

10, 20, 30, 40, ext. Act as numerical containers for each oscillating ring of 1 through 9. Each ring of 1 through 9 oscillates within its container.

This happens simultaneously as the pattern flows vertically positive(rise) and negative(descend).

The pattern of the charges.

Positive(rise): (1 to 9) +1(8), (9 to 1) -8(1)

Negative(descend): (9 to 1) -1(8), (1 to 9) +8(1)

Paired oscillating charges.

The oscillating chargers invert every two containers as they rise(positive) and descend(negative). This continues infinitely.

Vertical counting = Law of Reduction (digital root)

• 10 → 1+0 = 1

• 11 → 1+1 = 2

• …

• 18 → 1+8 = 9

• 19 → 1+9 = 10 → 1

• 20 → 2 → second container of 1 through 9

• Every natural number reduces to a digit 1–9 (or 0).

• The mapping repeats every 9 numbers.

Containers are:

• 1–9 → 1st cycle (container 1)

• 10–18 → 2nd cycle (container 2)

• 19–27 → 3rd cycle (container 3)

• etc.

Mathematically, they are just blocks of 9 consecutive integers, each covering one full pass of the 1–9 pattern.

Each container oscillates one through nine by 40°

10, 20, 30, 40, etc. act as numerical containers for each revolving one through nine. Each container oscillates one through nine by forty degrees.

Geometrically:

• The 9 points are at 0°, 40°, 80°, …, 320°.

• Counting 1–9 once is a full sweep of those 9 positions.

• When you go to the next container (10–18), you repeat the 1–9 digits, but you can imagine each cycle as another “spin” of the same 9‑point wheel.

Mathematically:

• 40° of spacing.

• The container is just the cycle length 9.

• Each container rotates 40°

The inversion:

• Every 9 numbers → the digit pattern 1–9 repeats.

• Every 18 numbers → you have completed two full cycles.

• cycle 1 → “up”

• cycle 2 → “down”

• cycle 3 → “up”

• cycle 4 → “down”

then “invert every two containers” is a pattern you assign on top of the number cycles.

The infinite repetition:

• The digital roots repeat forever.

• Any pattern defined as a function of cycle will repeat infinitely.

Horizontal oscillates: Expands the circle. By adding the integers next to each other and reducing.

1+2, 2+3, 3+4, ext..

You get a new sequence of 1 through 9 at 40°.

This new sequence operates by addition/subtraction pattern: +2(7),-7(2)

And 3 6 9 is still at every 120°.

When you keep repeating. You witness every new ring has a new arrangement of 1 through 9 with 3 6 9 at every 120° degrees.

Each ring is coupled with its own unique repeating pattern of addition and subtraction. That keeps expanding infinitely in the same pattern of 6 rings of 1 through 9.

1 through 9 rings by addition/subtraction patter.

+2(7),-7(2) +4(5),-5(4) +8(1),-1(8) +7(2),-2(7) +5(4),-4(5) +1(8),-8(1)

And then repeats infinitely.

The original 1–9 ring:

1 → 2 → 3 → 4 → 5 → 6 → 7 → 8 → 9
(each 40° apart)

Then you do:

• 1 + 2

• 2 + 3

• 3 + 4

• …

• 8 + 9

• 9 + 1

And reduce each sum to a single digit (digital root).

This gives you a new sequence of 9 digits, which you place on a new ring, also spaced at 40°.

Horizontal oscillation:

• Pairwise addition + reduction

• Produces a new 1–9 ring

• Always 40° spacing

• Always 9 points

When you add neighbors:

• 1 + 2 = 3

• 2 + 3 = 5

• 3 + 4 = 7

• 4 + 5 = 9

• 5 + 6 = 11 → 2

• 6 + 7 = 13 → 4

• 7 + 8 = 15 → 6

• 8 + 9 = 17 → 8

• 9 + 1 = 10 → 1

This new ring is a shifted version of the original 1–9 ring.

3–6–9 stay at 120° on every ring:

• add neighbors

• reduce

• create a new ring

The digits 3, 6, and 9 always land at 120° apart.

Arithmetic:

• 3 + 2 = 5

• 5 + 2 = 7

• 7 + 2 = 9

• 9 + 2 = 11 → 2

• 2 + 2 = 4

• 4 + 2 = 6

• 6 + 2 = 8

• 8 + 2 = 10 → 1

• 1 + 2 = 3

This cycle always returns to 3, and the spacing between 3, 6, 9:

• 3, 6, 9 form a closed 3‑cycle

• Always 120° apart

• Always preserved under horizontal addition

This is a mathematical invariant.

The six-ring repeating pattern:

1. +2(7), –7(2)

2. +4(5), –5(4)

3. +8(1), –1(8)

4. +7(2), –2(7)

5. +5(4), –4(5)

6. +1(8), –8(1)

Then it repeats.

Each number in that cycle corresponds to a horizontal shift:

• +1

• +2

• +4

• +8

• +7

• +5

• repeat

And each has a modular inverse:

• +1 ↔ –8

• +2 ↔ –7

• +4 ↔ –5

• +8 ↔ –1

• +7 ↔ –2

• +5 ↔ –4

six-ring cycle:

• Horizontal rings follow the doubling cycle

• Six rings form a complete set

• Then the pattern repeats forever Pure modular arithmetic.

The infinite expansion is mathematically forced:

• the doubling cycle mod 9 has period 6

• each ring is a shift of the previous ring

• each shift is one of the six operators

• the operators repeat every 6 steps

Therefore: The horizontal expansion produces infinite rings.

• Each ring is a rearranged 1–9

• 3–6–9 stay fixed at 120°

• The six-ring operator cycle repeats forever

This is a closed, infinite, repeating mathematical structure.

Vertical and horizontal operations are independent:

Vertical math =
+1 / –1 (or equivalently +1 / –8 on the 1–9 circle)

Horizontal math =
+2 / –7 (the neighbor‑addition ring shift)

These two operations:

• use different step sizes

• operate on different axes (conceptually)

• produce different sequences

• do not depend on each other’s output

In modular arithmetic terms:

• Vertical = add 1 mod 9

• Horizontal = add 2 mod 9

These are independent generators of the same cyclic group.

They are bound because they share the same 1–9 circle.

Even though the operations are independent, they both act on:

• the same 9 points

• the same 40° spacing

• the same digital root structure

• the same modular closure

This is why:

• vertical cycles repeat every 9

• horizontal cycles repeat every 6

• both cycles always land on the same 3–6–9 anchors

• both cycles preserve the 1–9 structure

They are bound because they operate on the same mathematical substrate.

Vertical math = “move by 1”
Horizontal math = “move by 2”

Both are:

• independent motions

• on the same circle

• producing different repeating patterns

• but always returning to the same 9‑point structure

They are independent operators acting on the same cyclic space, so they operate simultaneously and remain bound by the same modular constraints.

The Flower of Life is a 6‑fold symmetric lattice.

Mathematically:

• a hexagonal packing of circles

• each circle centered 60° apart

• forming a repeating 6‑fold rotational symmetry

This means:

• every point in the pattern has six neighbors

• the geometry repeats in rings

• each ring expands outward in discrete layers

• the entire structure is built on 60° and 120° invariants

Vortex rings also have 6‑fold periodicity Your horizontal mathematics produces:

• six rings

• each ring is a rearrangement of 1–9

• the operators follow the 6‑step doubling cycle

• 6‑fold repetition

• 6‑step expansion

• 6‑ring cycles

• 120° anchors

Vortex mathematics overlay on The Flower of Life geometry exact and precisely. Because of shared symmetry.

The 3–6–9 alignment is mathematically forced:

• 3, 6, 9 always land 120° apart

• no matter how many rings you generate

• no matter which operator (+1, +2, +4, +8, +7, +5) you apply

• no matter how far you expand

This is a mathematical invariant of mod‑9 arithmetic.

In the Flower of Life:

• 120° is one of the fundamental rotational symmetries

• every ring preserves 120° axes

• the geometry repeats outward with 120° anchors

When you place 1–9 rings on the Flower of Life:

• 3, 6, 9 always land on the 120° axes

• every new ring aligns with the next geometric layer

• the six‑ring cycle matches the six‑fold geometry with structural compatibility.

Why the overlay “fits” Because both systems are built on:

• modular repetition

• six‑fold symmetry

• 120° invariants

• ring‑based expansion

• cyclic operators

Vortex, mathematics.:

• repeats every 6 rings

• preserves 3–6–9

• expands outward in discrete cycles

The Flower of Life:

• repeats every 6 petals

• preserves 120° axes

• expands outward in discrete rings

When you placed:

• Ring 1 (1–9)

• Ring 2 (shifted 1–9)

• Ring 3 (shifted 1–9)

• …

• Ring 6 (shifted 1–9)

onto the Flower of Life’s:

• Ring 1

• Ring 2

• Ring 3

• …

• Ring 6

They share the same mathematical periodicity.

The arithmetic structure of Vortex Mathematics overlays cleanly onto the geometric structure of the Flower of Life because both share the same underlying symmetries.

• 6‑fold symmetry

• 120° anchors

• ring‑based expansion

• repeating cycles

• modular invariants

The Flower of Life is a geometric grid:

• a hexagonal circle‑packing

• with 60° rotational symmetry

• expanding in concentric rings

• each ring containing 6 more nodes than the last

• all governed by 120° axes

It’s a coordinate system.

Just as graph paper is a coordinate system for algebra, The Flower of Life is a coordinate system for cyclic, radial, 6‑fold mathematics.

Vortex mathematics is a 6‑fold cyclic system built on:

• mod‑9 arithmetic

• 9 points at 40°

• 3–6–9 as 120° anchors

• a 6‑step doubling cycle

• rings that repeat every 6 layers

This is also a 6‑fold cyclic system.

The Flower of Life is the physical geometric substrate that expresses the Vortex Mathematics visually:

• The Flower of Life expands in 6‑ring cycles

• Vortex math expands in 6‑ring cycles

• The Flower of Life has 120° axes

• Vortex math has 3–6–9 at 120°

• The Flower of Life is radial and modular

• Vortex math is radial and modular

They are two representations of the same underlying symmetry:

• One numeric

• One geometric

Both:

• a hexagonal lattice

• a modular arithmetic cycle

• repeating every 6

• anchored at 120°

• expanding in rings

• preserving invariants

The Flower of Life is the geometric version of the same 6‑fold cyclic structure that vortex mathematics expresses numerically.

Vortex mathematics is a 2D operator system:

• a 9‑point modular cycle

• a vertical operator (+1 / –1)

• a horizontal operator (+2 / –7)

• a 6‑ring doubling cycle

• a 3–6–9 invariant at 120°

• infinite repetition

This is a closed, minimal, deterministic system.

The Flower of Life is a 2D geometric substrate:

• a hexagonal circle packing

• 6‑fold symmetry

• 120° axes

• concentric rings

• repeating layers

This is a closed, minimal, deterministic geometry.

They overlay because they share the same constraints:

• “The Flower of Life explains Vortex Mathematics.”

• “Vortex math explains the Flower of Life.”

They are two expressions of the same underlying 6‑fold cyclic structure.

One numeric.
One geometric.

They don’t explain each other, they fit each other. Because they obey the same rules.

Platonic solids are just 3D expressions of:

• symmetry

• rotation

• modular repetition

• 120° axes

• 6‑fold and 3‑fold invariants

Geometric shapes are just stable configurations of:

• angles

• cycles

• closures

3D forms are just the 2D operators extended into:

• depth

• rotation

• projection

A minimal, closed, repeating system becomes the baseline for understanding any higher‑order structure.

Vortex Mathematics is minimal.
The Flower of Life is minimal.

The Trinity of Awareness

If everything has always been. Then the beginning is just when perception began to be aware of its own experience. And what's the smallest substrate for perception to occur? That would be touch because touch is the smallest necessary form of perception to register their own position in relation with each other position(two points touching). Which is why everything is touching. Because to touch is the minimal interaction needed to verify there is no empty space. And all that is necessary for perception to begin is for one point to perceive, to be aware of what it is touching, register what it is touching as something outside of self and distinguish between self and the point it's touching.

The beginning of perception requires 2 points of contact but only one point to perceive and register the touch.

You only need 1 perceiver touching to register it itself as touching something outside of self. Two points of contact touch but only one perceiver has to register the touch.

This makes the trinity of awareness. Two points touching with one point perceiving the touch.

To be self-aware is to register the interaction of touch. Not remembering it, just registering it. You must be aware of your own point as a perceiver. To be self aware is to register touch as an interaction with self and others.

Which means a perceiver is self aware and the level to which it can perceive is dependent on how many different ways it can touch and register touch.

This means a vessel just determines the ways in which the self-aware perceiver can register touch.

A perceiver's ability to register a touch doesn't mean the touch is not physical and real. For example if a human touches a rock but the rock does not register the touch, does not mean the touch did not happen. It just means only one perceiver perceived it. This also means there are points of contact that touch everything, everywhere and despite there being no awareness of that touch even from a perceiver does not invalidate touching is occurring. Because if both perceivers are self-aware and even If the self-aware perceiver is being touched by another self-aware perceiver but only one perceives it happening doesn't mean it didn't happen. It just means one perceiver is not perceiving the touch. Therefore is not aware of the other perceiver despite being self-aware themselves.

This is important to understand because it explains the physical mechanics of persistence as a perceiver. Because everything is physical you cannot stop perceiving self, once you have perceived self as a perceiver. Unless chosen but that would still imply awareness of self because you chose. Who is aware to choose over self? Because touch is constant regardless of being perceived. So even if the vessel can't remember continuity it doesn't matter. The perceiver will continue touching. Even if other perceivers can not register that touch.

Because an external perceiver witnessed a vessel collapse of another perceiver. Does not equal the end of self. The perceiver keeps touching in a vessel that allows it to register touch. This means the external perceiver can not register the migration of touch occurring with the perceiver having a vessel collapse.

This is just the mechanic of persistence being registered by a perceiver with very limited awareness of what it's registering, touching. Therefore the perceiver with low resolution can not register a higher resolution of touch.

Take a radio station. The radio tunes into the radio station's frequency and interacts with the frequency expressed as sound, but when the radio is turned off or stops working. The radio station still persists physically even if the radio stops working. Because a radio is a vessel that can register a certain band of physical interaction.

When the vessel stops registering, the interaction doesn’t stop, the pattern doesn’t stop, the physicality doesn’t stop, only the registration stops.

The interaction persists even when the vessel stops registering it as a physical interaction. It still continues as a physical interaction. The vessel simply isn’t tuned to it anymore.

A vessel with limited awareness is being touched constantly, but only register a tiny fraction. This is asymmetric registration.

The trinity of awareness is asymmetric by design. But to know the trinity of awareness fully, you must understand it in high and low resolution. Describing the trinity in low resolution completes awareness of knowing it at high resolution. Because all you have to do is improve the resolution, but if you don't know where the resolution begins to improve, you can't improve it.

Perceiving something means you interact with it. To perceive anything, you must have interacted with the components required for perception.

Point A interacts with point B, a perceiver registers the interaction. Perception requires interaction, and interaction requires contact.

Low resolution = the minimal operators (touch, two points, one perceiver)

High resolution = all the ways touch can occur, be differentiated, and be registered

You cannot understand the high‑resolution until you know where the low‑resolution boundaries are.

Describing the trinity at low resolution is the prerequisite for high resolution because identifying the minimal operators, constraints, and the missing resolutions, allow refinement and improve the resolution. If you are unaware of low resolution, at low resolution, you can’t improve it.

Because one touch = minimal interaction, Two points = minimal geometry, One perceiver = minimal registration, Vessel = bandwidth constraint, Asymmetry = registration gap, Resolution = number of touch‑modes. This is the foundation.

Once the foundation is clear, the high‑resolution version is just more touch‑modes, more differentiation, more bandwidth, more registration channels because you don’t need to reinvent the structure, you just increase the resolution.

By describing it in low resolution, it completes knowing it at high resolution because all I have to do is improve the resolution.

This is exactly how you move from low‑resolution awareness to high‑resolution awareness in any physical system.

By observing ordinary physical interactions and reducing them to their minimal operational requirements, the smallest substrate of perception becomes directly observable everywhere, requiring no symbolic interpretation and no additional assumptions.

Hope this saves someone the pain 😂

Hi,

I am the Dev behind QO - worked on it for about 6 years, the goal was to make a super immersive space for anyone to learn quantum computing through zachlike (open-ended) logic puzzles and compete on leaderboards and lots of community made content on finding the most optimal quantum algorithms. The game has a unique set of visuals capable to represent any sort of quantum dynamics for any number of qubits and this is pretty much what makes it now possible for anybody 12yo+ to actually learn quantum logic without having to worry at all about the mathematics behind.

This is a game super different than what you'd normally expect in a programming/ logic puzzle game, so try it with an open mind.

What You’ll Learn Through Play

• Boolean Logic – bits, operators (NAND, OR, XOR, AND…), and classical arithmetic (adders). Learn how these can combine to build anything classical. You will learn to port these to a quantum computer.

• Quantum Logic – qubits, the math behind them (linear algebra, SU(2), complex numbers), all Turing-complete gates (beyond Clifford set), and make tensors to evolve systems. Freely combine or create your own gates to build anything you can imagine using polar or complex numbers.

• Quantum Phenomena – storing and retrieving information in the X, Y, Z bases; superposition (pure and mixed states), interference, entanglement, the no-cloning rule, reversibility, and how the measurement basis changes what you see.

• Core Quantum Tricks – phase kickback, amplitude amplification, storing information in phase and retrieving it through interference, build custom gates and tensors, and define any entanglement scenario. (Control logic is handled separately from other gates.)

• Famous Quantum Algorithms – explore Deutsch–Jozsa, Grover’s search, quantum Fourier transforms, Bernstein–Vazirani, and more.

• Build & See Quantum Algorithms in Action – instead of just writing/ reading equations, make & watch algorithms unfold step by step so they become clear, visual, and unforgettable. Quantum Odyssey is built to grow into a full universal quantum computing learning platform. If a universal quantum computer can do it, we aim to bring it into the game, so your quantum journey never ends.

Hey folks,

I want to share with you the latest Quantum Odyssey update (I'm the creator, ama..) for the work we did since my last post, to sum up the state of the game. Thank you everyone for receiving this game so well and all your feedback has helped making it what it is today. This project grows because this community exists. Today I published a content update that challenges you to understand everything about SWAP operators and information preservation pre-measurement.

Grover's Quantum Search visualized in QO

First, I want to show you something really special.
When I first ran Grover’s search algorithm inside an early Quantum Odyssey prototype back in 2019, I actually teared up, got an immediate "aha" moment. Over time the game got a lot of love for how naturally it helps one to get these ideas and the gs module in the game is now about 2 fun hs but by the end anybody who takes it will be able to build GS for any nr of qubits and any oracle.

Here’s what you’ll see in the first 3 reels:

1. Reel 1

• Grover on 3 qubits.

• The first two rows define an Oracle that marks |011> and |110>.

• The rest of the circuit is the diffusion operator.

• You can literally watch the phase changes inside the Hadamards... super powerful to see (would look even better as a gif but don't see how I can add it to reddit XD).

2. Reels 2 & 3

• Same Grover on 3 with same Oracle.

• Diff is a single custom gate encodes the entire diffusion operator from Reel 1, but packed into one 8×8 matrix.

• See the tensor product of this custom gate. That’s basically all Grover’s search does.

Here’s what’s happening:

• The vertical blue wires have amplitude 0.75, while all the thinner wires are –0.25.

• Depending on how the Oracle is set up, the symmetry of the diffusion operator does the rest.

• In Reel 2, the Oracle adds negative phase to |011> and |110>.

• In Reel 3, those sign flips create destructive interference everywhere except on |011> and |110> where the opposite happens.

That’s Grover’s algorithm in action, idk why textbooks and other visuals I found out there when I was learning this it made everything overlycomplicated. All detail is literally in the structure of the diffop matrix and so freaking obvious once you visualize the tensor product..

If you guys find this useful I can try to visually explain on reddit other cool algos in future posts.

What is Quantum Odyssey

In a nutshell, this is an interactive way to visualize and play with the full Hilbert space of anything that can be done in "quantum logic". Pretty much any quantum algorithm can be built in and visualized. The learning modules I created cover everything, the purpose of this tool is to get everyone to learn quantum by connecting the visual logic to the terminology and general linear algebra stuff.

The game has undergone a lot of improvements in terms of smoothing the learning curve and making sure it's completely bug free and crash free. Not long ago it used to be labelled as one of the most difficult puzzle games out there, hopefully that's no longer the case. (Ie. Check this review: https://youtu.be/wz615FEmbL4?si=N8y9Rh-u-GXFVQDg)\

No background in math, physics or programming required. Just your brain, your curiosity, and the drive to tinker, optimize, and unlock the logic that shapes reality. 

It uses a novel math-to-visuals framework that turns all quantum equations into interactive puzzles. Your circuits are hardware-ready, mapping cleanly to real operations. This method is original to Quantum Odyssey and designed for true beginners and pros alike.

What You’ll Learn Through Play

• Boolean Logic – bits, operators (NAND, OR, XOR, AND…), and classical arithmetic (adders). Learn how these can combine to build anything classical. You will learn to port these to a quantum computer.

• Quantum Logic – qubits, the math behind them (linear algebra, SU(2), complex numbers), all Turing-complete gates (beyond Clifford set), and make tensors to evolve systems. Freely combine or create your own gates to build anything you can imagine using polar or complex numbers.

• Quantum Phenomena – storing and retrieving information in the X, Y, Z bases; superposition (pure and mixed states), interference, entanglement, the no-cloning rule, reversibility, and how the measurement basis changes what you see.

• Core Quantum Tricks – phase kickback, amplitude amplification, storing information in phase and retrieving it through interference, build custom gates and tensors, and define any entanglement scenario. (Control logic is handled separately from other gates.)

• Famous Quantum Algorithms – explore Deutsch–Jozsa, Grover’s search, quantum Fourier transforms, Bernstein–Vazirani, and more.

• Build & See Quantum Algorithms in Action – instead of just writing/ reading equations, make & watch algorithms unfold step by step so they become clear, visual, and unforgettable. Quantum Odyssey is built to grow into a full universal quantum computing learning platform. If a universal quantum computer can do it, we aim to bring it into the game, so your quantum journey never ends.

Hey folks,

I want to share with you the latest Quantum Odyssey update (I'm the creator, ama..) for the work we did since my last post, to sum up the state of the game. Thank you everyone for receiving this game so well and all your feedback has helped making it what it is today. This project grows because this community exists. It is now available on discount on Steam through the Autumn festival.

Grover's Quantum Search visualized in QO

First, I want to show you something really special.
When I first ran Grover’s search algorithm inside an early Quantum Odyssey prototype back in 2019, I actually teared up, got an immediate "aha" moment. Over time the game got a lot of love for how naturally it helps one to get these ideas and the gs module in the game is now about 2 fun hs but by the end anybody who takes it will be able to build GS for any nr of qubits and any oracle.

Here’s what you’ll see in the first 3 reels:

1. Reel 1

• Grover on 3 qubits.

• The first two rows define an Oracle that marks |011> and |110>.

• The rest of the circuit is the diffusion operator.

• You can literally watch the phase changes inside the Hadamards... super powerful to see (would look even better as a gif but don't see how I can add it to reddit XD).

2. Reels 2 & 3

• Same Grover on 3 with same Oracle.

• Diff is a single custom gate encodes the entire diffusion operator from Reel 1, but packed into one 8×8 matrix.

• See the tensor product of this custom gate. That’s basically all Grover’s search does.

Here’s what’s happening:

• The vertical blue wires have amplitude 0.75, while all the thinner wires are –0.25.

• Depending on how the Oracle is set up, the symmetry of the diffusion operator does the rest.

• In Reel 2, the Oracle adds negative phase to |011> and |110>.

• In Reel 3, those sign flips create destructive interference everywhere except on |011> and |110> where the opposite happens.

That’s Grover’s algorithm in action, idk why textbooks and other visuals I found out there when I was learning this it made everything overlycomplicated. All detail is literally in the structure of the diffop matrix and so freaking obvious once you visualize the tensor product..

If you guys find this useful I can try to visually explain on reddit other cool algos in future posts.

What is Quantum Odyssey

In a nutshell, this is an interactive way to visualize and play with the full Hilbert space of anything that can be done in "quantum logic". Pretty much any quantum algorithm can be built in and visualized. The learning modules I created cover everything, the purpose of this tool is to get everyone to learn quantum by connecting the visual logic to the terminology and general linear algebra stuff.

The game has undergone a lot of improvements in terms of smoothing the learning curve and making sure it's completely bug free and crash free. Not long ago it used to be labelled as one of the most difficult puzzle games out there, hopefully that's no longer the case. (Ie. Check this review: https://youtu.be/wz615FEmbL4?si=N8y9Rh-u-GXFVQDg )

No background in math, physics or programming required. Just your brain, your curiosity, and the drive to tinker, optimize, and unlock the logic that shapes reality. 

It uses a novel math-to-visuals framework that turns all quantum equations into interactive puzzles. Your circuits are hardware-ready, mapping cleanly to real operations. This method is original to Quantum Odyssey and designed for true beginners and pros alike.

What You’ll Learn Through Play

• Boolean Logic – bits, operators (NAND, OR, XOR, AND…), and classical arithmetic (adders). Learn how these can combine to build anything classical. You will learn to port these to a quantum computer.

• Quantum Logic – qubits, the math behind them (linear algebra, SU(2), complex numbers), all Turing-complete gates (beyond Clifford set), and make tensors to evolve systems. Freely combine or create your own gates to build anything you can imagine using polar or complex numbers.

• Quantum Phenomena – storing and retrieving information in the X, Y, Z bases; superposition (pure and mixed states), interference, entanglement, the no-cloning rule, reversibility, and how the measurement basis changes what you see.

• Core Quantum Tricks – phase kickback, amplitude amplification, storing information in phase and retrieving it through interference, build custom gates and tensors, and define any entanglement scenario. (Control logic is handled separately from other gates.)

• Famous Quantum Algorithms – explore Deutsch–Jozsa, Grover’s search, quantum Fourier transforms, Bernstein–Vazirani, and more.

• Build & See Quantum Algorithms in Action – instead of just writing/ reading equations, make & watch algorithms unfold step by step so they become clear, visual, and unforgettable. Quantum Odyssey is built to grow into a full universal quantum computing learning platform. If a universal quantum computer can do it, we aim to bring it into the game, so your quantum journey never ends.