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tangled-adjudicate

Tangled is a game designed such that determining who wins is a problem where there is a claim of quantum supremacy. You can read about it here.

This repo contains what I call adjudicators, which are functions that take as input a Tangled game state and output information derived from it (see below for particulars), including the score and the outcome of the game (win/loss/draw) if the game state is a terminal state.

Three different adjudicators are provided:

  1. A Schrödinger Equation solver, which is only useful for tiny game graphs
  2. A Simulated Annealing solver, whose parameters are chosen to mimic D-Wave hardware, and
  3. A Quantum Annealing solver that uses D-Wave hardware

In addition to the adjudicators, I provide several utility functions that support the adjudication process.

Setup

Git clone the repo, create a virtual environment running Python 3.10, and install the package in editable mode into it, which links the repository directory directly:

# Clone the repository
git clone https://github.com/snowdropquantum/tangled-adjudicate.git

# Navigate into the project directory
cd <repository-directory>

# Install the package
pip install -e .

Once installed, you can import this package in your Python scripts:

import tangled_adjudicate

If you are going to use QC hardware, follow the D-Wave setup instructions. If not (for example you just want to use simulated annealing) you don't have to do this.

Tangled Game Graph Specification

A Tangled game graph is specified by a graph number, which label specific graphs included here. I've included ten graphs numbered 1 through 10. Each graph requires specification of vertex count (how many vertices the graph has) and an explicit edge list, which are included for these ten graphs. If you'd like to add a new graph, it's simple! Just add it to the GraphProperties class, found in the /utils/game_graph_properties.py file.

Tangled Game State Specification: Expected Input Format For Adjudicators

The expected input to the adjudicators in this repo are Tangled game states. These are dictionaries with the following keys:

  • 'num_nodes': an integer, the number of vertices in the game graph
  • 'edges': a list of 3-tuples of length edge_count where the first two elements are indices of the vertices that edge connects and the third element is: 0 if the edge is unselected; 1 if the edge is gray (no coupling, J=0); 2 if the edge is green (ferromagnetic coupling, J=-1); and 3 if the edge is purple (antiferromagnetic coupling, J=+1)
  • 'player1_id' and 'player2_id': strings, specifying the names of the agents
  • 'turn_count': an integer, the number of turns that have been played to obtain the game state
  • 'current_player_index': an integer, either 1 or 2, corresponding to whose turn it is
  • 'player1_node' and 'player2_node': integers, the vertices owned by the players; if none chosen yet, this is -1

Here's an example:

game_state = {'num_nodes': 6, 'edges': [(0, 1, 1), (0, 2, 1), (0, 3, 2), (0, 4, 3), (0, 5, 2), (1, 2, 1),
(1, 3, 2), (1, 4, 3), (1, 5, 3), (2, 3, 1), (2, 4, 2), (2, 5, 3), (3, 4, 2), (3, 5, 1), (4, 5, 2)],
'player1_id': 'player1', 'player2_id': 'player2', 'turn_count': 17, 'current_player_index': 1,
'player1_node': 1, 'player2_node': 3}

If you want to add a new game graph, it's easy to modify the game state dictionary corresponding to it -- just make sure the 'num_nodes' is your vertex count and 'edges' includes an entry for each edge in your graph.

Adjudication Output

Adjudicators output a dictionary with the following keys:

  • 'game_state': a copy of the input game_state dictionary
  • 'adjudicator': a string, one of 'simulated_annealing', 'quantum_annealing', 'schrodinger_equation'
  • 'winner': if both players have chosen vertices, a string, one of 'red', 'blue', 'draw', otherwise None
  • 'score': if both players have chosen vertices, the difference in influence scores as a real number, otherwise None
  • 'influence_vector': a vector of real numbers of length vertex_count (one real number per vertex in the game graph)
  • 'correlation_matrix': symmetric real-valued matrix of spin-spin correlations with zeros on diagonals
  • 'parameters': a copy of the parameters dictionary

Minimal Use Example

See /utils/how_to_adjudicate_states.py for minimal examples of use. For example, to use the simulated_annealing adjudicator (assuming graph 2, which this game state is defined on), you'd just do:

from tangled_adjudicate.adjudicators.adjudicate import Adjudicator
from tangled_adjudicate.utils.parameters import Params

params = Params()
adjudicator = Adjudicator(params)

game_state = {'num_nodes': 3, 'edges': [(0, 1, 2), (0, 2, 2), (1, 2, 2)],
              'player1_id': 'player1', 'player2_id': 'player2', 'turn_count': 5,
              'current_player_index': 1, 'player1_node': 1, 'player2_node': 2}

results = adjudicator.simulated_annealing(game_state)

print(results)