Related papers: Solving Rubik's Cube via Quantum Mechanics and Dee…
Rubik's Cube (RC) is a well-known and computationally challenging puzzle that has motivated AI researchers to explore efficient alternative representations and problem-solving methods. The ideal situation for planning here is that a problem…
The Quadratic Unconstrained Binary Optimization (QUBO) model has gained prominence in recent years with the discovery that it unifies a rich variety of combinatorial optimization problems. By its association with the Ising problem in…
The development of quantum computational techniques has advanced greatly in recent years, parallel to the advancements in techniques for deep reinforcement learning. This work explores the potential for quantum computing to facilitate…
Combinatorial problems are formulated to find optimal designs within a fixed set of constraints. They are commonly found across diverse engineering and scientific domains. Understanding how to best use quantum computers for combinatorial…
This study combines the quantum Rubik's Cube matrix with the Benalcazar Bernevig Hughes model, defines a matrix algorithm based on the reverse process of convolution, and constructs an expression for the quantum Rubik's Cube matrix and…
The diameter of the Cayley graph of the Rubik's Cube group is the fewest number of turns needed to solve the Cube from the hardest initial configuration. For the 2$\times$2$\times$2 Cube, the diameter is 11 in the half-turn metric, 14 in…
We propose and evaluate a quantum-inspired algorithm for solving Quadratic Unconstrained Binary Optimization (QUBO) problems, which are mathematically equivalent to finding ground states of Ising spin-glass Hamiltonians. The algorithm…
Quantum algorithm, as compared to classical algorithm, plays a notable role in solving linear systems of equations with an exponential speedup. Here, we demonstrate a method for solving a particular system of equations by using the concept…
When working in a proof assistant, automation is key to discharging routine proof goals such as equations between algebraic expressions. Homotopy type theory allows the user to reason about higher structures, such as topological spaces,…
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
We consider quantum algorithms for the unique sink orientation problem on cubes. This problem is widely considered to be of intermediate computational complexity. This is because there no known polynomial algorithm (classical or quantum)…
Given two elements of a vector space acted on by a reductive group, we ask whether they lie in the same orbit, and if not, whether one lies in the orbit closure of the other. We develop techniques to optimize the orbit and orbit closure…
In the era of quantum computing, the emergence of quantum computers and subsequent advancements have led to the development of various quantum algorithms capable of solving linear equations and eigenvalues, surpassing the pace of classical…
The quantum guesswork quantifies the minimum number of queries needed to guess the state of a quantum ensemble if one is allowed to query only one state at a time. Previous approaches to the computation of the guesswork were based on…
The architecture of circuital quantum computers requires computing layers devoted to compiling high-level quantum algorithms into lower-level circuits of quantum gates. The general problem of quantum compiling is to approximate any unitary…
Quantum computing holds immense potential for solving classically intractable problems by leveraging the unique properties of quantum mechanics. The scalability of quantum architectures remains a significant challenge. Multi-core quantum…
A cube is an 8-rep-tile: it is the union of eight smaller copies of itself. Is there a set with a hole which has this property? The computer found an interesting and complicated solution, which then could be simplified. We discuss some…
As a cornerstone of automated reasoning, equational reasoning finds equivalences between symbolic expressions and fuels advances across scientific disciplines. Yet, its potential remains limited by the exponential growth of equivalent…
Quantum computing offers significant potential for solving NP-hard combinatorial (optimization) problems that are beyond the reach of classical computers. One way to tap into this potential is by reformulating combinatorial problems as a…
We present a decentralized model for autonomous reconfiguration of homogeneous pivoting cube modular robots in two dimensions. Each cube in the ensemble is controlled by a neural network that only gains information from other cubes in its…