Related papers: Solving Rubik's Cube via Quantum Mechanics and Dee…
The Rubix Cube is a 3-dimensional single-player combination puzzle attracting attention in the reinforcement learning community. A Rubix Cube has six faces and twelve possible actions, leading to a small and unconstrained action space and a…
Since its first appearance, transformers have been successfully used in wide ranging domains from computer vision to natural language processing. Application of transformers in Reinforcement Learning by reformulating it as a sequence…
This work describes in detail how to learn and solve the Rubik's cube game (or puzzle) in the General Board Game (GBG) learning and playing framework. We cover the cube sizes 2x2x2 and 3x3x3. We describe in detail the cube's state…
Learning to solve a Rubik's Cube requires the learners to repeatedly practice a skill component, e.g., identifying a misplaced square and putting it back. However, for 3D physical tasks such as this, generating sufficient repeated practice…
The Rubik's Cube is perhaps the world's most famous and iconic puzzle, well-known to have a rich underlying mathematical structure (group theory). In this paper, we show that the Rubik's Cube also has a rich underlying algorithmic…
The Rubiks Cube, with its vast state space and sparse reward structure, presents a significant challenge for reinforcement learning (RL) due to the difficulty of reaching rewarded states. Previous research addressed this by propagating…
Rubik's Revenge, a 4x4x4 variant of the Rubik's puzzles, remains to date as an unsolved puzzle. That is to say, we do not have a method or successful categorization to optimally solve every one of its approximately $7.401 \times 10^{45}$…
Existing combinatorial search methods are often complex and require some level of expertise. This work introduces a simple and efficient deep learning method for solving combinatorial problems with a predefined goal, represented by Rubik's…
The Rubik's cube is a famous puzzle in which faces can be moved and the corresponding movement operations define a group. We consider here a generalization to any $3$-valent map. We prove an upper bound on the size of the corresponding…
Permutation puzzles, such as the Rubik's Cube and the 15 puzzle, are enjoyed by the general public and mathematicians alike. Here we introduce quantum versions of permutation puzzles where the pieces of the puzzles are replaced with…
We demonstrate that models trained only in simulation can be used to solve a manipulation problem of unprecedented complexity on a real robot. This is made possible by two key components: a novel algorithm, which we call automatic domain…
We introduce a reinforcement learning algorithm designed to identify the fixed points of a given quantum operation. The method iteratively constructs the unitary transformation that maps the computational basis onto the basis of fixed…
The first 2x2x2 twisty cube was created as a demonstration tool by Erno Rubik in 1974 to help his students understand the complexity of space and the movements in 3D. He fabricated a novel 3x3x3 mechanism where the 26 cubies were turning,…
The core mechanical system is built around three stepper motors for physical manipulation, a microcontroller for hardware control, a camera and YOLO detection model for real-time cube state detection. A significant software component is the…
The problem of decomposing an arbitrary Clifford element into a sequence of Clifford gates is known as Clifford synthesis. Drawing inspiration from similarities between this and the famous Rubik's Cube problem, we develop a machine learning…
We describe in details the nxnxn Rubik's Cube, namely a Rubik's Cube with n rotating slices in each face. Then we state and prove the "first law of Cubology", i.e. the solvability criterion, for it
Combinatorial optimization is considered a promising class of problems in which quantum computers can show significant advantages. However, problems of practical relevance typically have more variables than current or foreseeable quantum…
A kind of brand-new robot, quantum robot, is proposed through fusing quantum theory with robot technology. Quantum robot is essentially a complex quantum system and it is generally composed of three fundamental parts: MQCU (multi quantum…
This paper details our winning submission to Phase 1 of the 2021 Real Robot Challenge; a challenge in which a three-fingered robot must carry a cube along specified goal trajectories. To solve Phase 1, we use a pure reinforcement learning…
By using two different invariants for the Rubik's Magic puzzle, one of metric type, the other of topological type, we can dramatically reduce the universe of constructible configurations of the puzzle. Finding the set of actually…