Bloch Cube Chess

Game Overview

• Players: 2 or 4 players (not 3)

• Board: 8x8 grid (like a chess board)

• Goal: Move one of your Bloch Cubes from your starting side to the opposite side of the board

Equipment

Each player gets 8 Bloch Cubes in their color (red, blue, green, or yellow). These cubes have special markings on each face showing quantum states labeled as |+x>, |-x>, |+y>, |-y>, |+z>, and |-z>.

Two Ways to Use Your Cubes

1. On the Board (as Qubits): When you place a cube on the board, it becomes a "qubit" that can move around

2. Off the Board (as Qugates): Cubes not on the board are "qugates" that you use to move or rotate your qubits

How to Play

Starting the Game

1. All players roll their cubes to randomize them

2. Determine who goes first by rolling cubes (specific method up to players)

3. Play continues counterclockwise in Northern Hemisphere, clockwise in Southern Hemisphere

On Your Turn

You can do ONE of these actions:

1. Place a new cube on the board from your starting side

   • You can choose which way the cube faces, but can't change its top face

2. Use one of your off-board cubes (qugate) to affect one of your on-board cubes (qubit)

   • After using a qugate, roll it randomly to prepare for your next turn

How Qugates Affect Qubits

When you use a qugate on your qubit, one of two things happens:

1. If the qugate and qubit show different faces: The qubit rolls one square forward, backward, left, or right

2. If the qugate and qubit show the same face: The qubit spins in place 90 degrees

In the standard version, rotations follow the right-hand rule. In the variant version, cubes can rotate either direction, e.g., +Z/-Z qugates have the same effect.

Special Rules

Stacking Cubes (Singlet States)

• Two cubes can share the same square only in a "singlet state"

• Bottom cube must show |+/-w> and top cube must show |-/+w> (e.g., top cube |+x>, bottom cube |-x>, or top cube |-y>, bottom cube |+y>)

• The top cube traps the bottom cube, preventing it from moving

• The player controlling the top cube can rotate both cubes together to switch between X, Y, and Z directions while maintaining the +/- relationship, e.g., switching from top cube |+x>, bottom cube |-x> to top cube |-z>, bottom cube |+z>

Optional Measurement Rule

Instead of using a qugate normally, you can use it to "measure" a qubit. The qugate's face determines the measurement direction W=X, Y, or Z:

1. If the qubit is in the |+w> or |-w> direction, nothing happens

2. Otherwise:

   • Roll the qugate

   • If it shows a positive value: Reorient the qubit to point in the |+w> direction

   • If it shows a negative value: Reorient the qubit to point in the |-w> direction

   • The qubit stays in its current square during measurement

Winning

The first player to move one of their qubits across the board and off the opposite side wins!

Strategy Tips

• Having more cubes on the board means fewer qugates to move them with

• Cubes can move off the board on their starting side, turning back into qugates

• Plan your moves carefully - sometimes spinning in place sets up better future moves