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[!NOTE] Qter is currently an incomplete work-in-progress

Qter is a computer architecture that allows humans to perform computations by manipulating the Rubik's Cube (or any twisty puzzle) by hand. Following is an example executable program that accepts an index as user input and computes the corresponding Fibonacci number, written in our custom twisty puzzle file format named Q. It can be physically executed by a human without needing to know how computers work.

fib.q

Puzzles
A: 3x3

1 | input "Which Fibonacci number to calculate:"
           B2 U2 L F' R B L2 D2 B R' F L
           max-input 8
2 | solved-goto UFR 14
3 | D L' F L2 B L' F' L B' D' L'
4 | L' F' R B' D2 L2 B' R' F L' U2 B2
5 | solved-goto UFR 15
6 | repeat until DL DFL solved
            L U' B R' L B' L' U'
            L U R2 B R2 D2 R2 D'
7 | L' F' R B' D2 L2 B' R' F L' U2 B2
8 | solved-goto UFR 16
9 | repeat until FR DRF solved
            D' B' U2 B D' F' D L' D2
            F' R' D2 F2 R F2 R2 U' R'
10 | L' F' R B' D2 L2 B' R' F L' U2 B2
11 | solved-goto UFR 17
12 | repeat until UF solved
            B R2 D' R B D F2 U2 D'
            F' L2 F D2 F B2 D' L' U'
13 | goto 4
14 | halt "The number is: 0"
15 | halt until DL DFL solved
          "The number is"
          L D B L' F L B' L2 F' L D'
16 | halt until FR DRF solved
          "The number is"
          F2 L2 U2 D' R U' B L' B L' U'
17 | halt until UF solved
          "The number is"
          U L' R' F' U' F' L' F2 L U R

This was compiled from our custom high level programming language named QAT (Qter Assembly Text):

fib.qat

.registers {
    A, B, C, D <- 3x3 builtin (30, 18, 10, 9)
}

.macro fib-shuffle {
    // Let `fib(n)` be the nth fibonacci number
    // Expects $R1 = fib(n), $R2 = fib(n-1), $R3 = 0
    // Sets the registers to $R1 = 0, $R2 = fib(n+1), $R3 = fib(n) by adding $R1 to $R2 and $R3
    ($R1:reg $R2:reg $R3:reg $counter:reg) => {
        dec $counter
        if solved $counter {
            halt "The number is" $R1
        }
        while not-solved $R1 {
            dec $R1
            inc $R2
            inc $R3
        }
    }
}

input "Which Fibonacci number to calculate:" D
if solved D {
    halt "The number is 0"
}
inc B
loop {
    fib-shuffle B A C D
    fib-shuffle A C B D
    fib-shuffle C B A D
}

If you're hooked and want to learn more, you can read the book at [https://qter.dev]!

How does Qter work?

This repository hosts a suite of various twisty puzzle utilities to compile QAT programs to Q:

• cycle_combination_finder: Discover Qter architectures on a twisty puzzle
• cycle_combination_solver: Find short move sequences for the "add 1" operation for each register of an architecture
• movecount_coefficient_calculator: Rewrite of trangium's online tool to score twisty puzzle move sequences by how easy they are to physically perform
• compiler: Compile QAT code to the Q file format
• interpreter: Simulate a twisty puzzle to execute QAT or Q
• robot: Stepper motor control software for the Qter robot
• visualiser: Qter program execution visualiser tool

Some other repositories in the qter-project organization

• puzzle_theory
  • Contains generic code for analyzing twisty puzzles. If you're writing your own twisty puzzle code in Rust, consider using it as a library.
  • puzzle_geometry: Convert an arbitrary polyhedra and cutting planes into a twisty puzzle
• pog_ans: Implementation of tabled asymmetric numerical systems compression for use in pruning tables and compressing algorithm tables.
• qvis: Implementation of our computer vision system for the robot; it is designed to be general purpose so you can reuse it for your robot if you like.
• tree-sitter-q: Syntax highlighting for Q using tree-sitter

Refer to our paper for a technical breakdown of the mathematics and programming behind Qter.

About the Authors

• Arhan Chaudhary: Hi! I am a junior at Purdue University, and I have always been fascinated by Rubik's cubes since I learned how to solve them in middle school. I was greatly inspired by the Purdue Hackers community to begin this project, and have spent the better part of the entire school year working on it. Read more about my work at my website.
• Henry Rovnyak: Hello there! Like Arhan, I too am a junior at Purdue University. I'm interested in math and programming, and I met Arhan through this project and the Purdue Hackers community. I enjoy systems and scientific programming, but I also have a soft spot for theoretical work and frontend design. Arhan may or may not have gotten me addicted to cubes... You should consider checking out my website to see some of the other stuff I've been working on.
• Asher Gray: Hello! I'm a data analyst and youtuber from the PNW. I started off making videos about solving Rubik's cubes blindfolded, and now focus on math and fun ways to visualize it. Lately I've been studying the theory of abelian groups, including the abelian subgroups of the Rubik's cube. I'm excited to have joined this project, such an interesting application of these ideas! You can find me on YouTube or enjoy some interactive math visualizations on my website.

Acknowledgements

We extend our sincere thanks to Tomas Rokicki for personally providing us key insight into Rubik's Cube programming techniques. Qter would not have been possible without his guidance. We are immensely grateful for his time.

We also extend our gratitude to Ben Whitmore for helping ideate the initial design of the cycle_combination_solver.