Quantum Circuit Betting Game

How to Play

Game Overview

Welcome to the Quantum Circuit Game! Test your understanding of quantum gates and their effects on qubit states through four different game modes:

  • Amplitude Game: Focus on predicting quantum state probabilities
  • Phase Game: Master both amplitude and phase predictions
  • Two-Qubit Game: Explore quantum entanglement and two-qubit operations
  • Sandbox Mode: Freely experiment with quantum gates

Basic Rules

  • Start with 100 credits in game modes
  • Each round presents a random sequence of quantum gates
  • Predict the resulting quantum state
  • Earn credits based on prediction accuracy
  • Use hints to guide your predictions

Game Modes

Amplitude Game

  • Predict probabilities of measuring |0⟩ and |1⟩ states
  • Use the probability slider to set your predictions
  • Visualize predictions through histograms

Phase Game

  • Predict both amplitudes and phases of quantum states
  • Use probability sliders for amplitudes
  • Use phase dials to predict quantum phases
  • Master the complete quantum state description

Two-Qubit Game

  • Predict probabilities for two-qubit states (|00⟩, |01⟩, |10⟩, |11⟩)
  • Work with entangling operations like CNOT and SWAP
  • Understand quantum correlations between qubits

Sandbox Mode

  • Freely apply quantum gates to explore their effects
  • No scoring - perfect for learning and experimentation
  • Real-time visualization of quantum state changes

Quantum Gates

H

Hadamard: Creates equal superposition

X

Pauli-X: Quantum NOT gate

Y

Pauli-Y: Complex rotation

Z

Pauli-Z: Phase flip

S

Phase Gate: π/2 phase rotation

T

T Gate: π/4 phase rotation

CNOT

Controlled-NOT: Two-qubit gate that flips target if control is |1⟩

SWAP

SWAP: Exchanges states of two qubits

Hints System

Purchase measurements to help guide your predictions:

  • 1 Shot (5 credits): Quick snapshot with high uncertainty
  • 100 Shots (15 credits): Better statistical sampling
  • ∞ Shots (30 credits): Perfect measurement, but costs more

Scoring

  • Closer predictions earn more credits
  • Perfect predictions can earn up to 40 credits
  • Poor predictions result in credit loss
  • Game ends if credits reach zero

Quantum Circuit Betting Game

Round: 0
Credits: 100
Score: 0
|0⟩
Get measurement hints (costs credits):
1.0 0.5 0.0
0.50
|0⟩
0.50
|1⟩

Quantum Circuit Sandbox

Available Gates

|0⟩
1.0 0.5 0.0
1.00
|0⟩
0.00
|1⟩
|0⟩ Phase
|1⟩ Phase

Current State:

|ψ⟩ = |0⟩

Quantum Phase Betting Game

Round: 0
Credits: 100
Score: 0
|0⟩
Get measurement hints (costs credits):

Amplitude Betting

1.0 0.5 0.0
0.50
|0⟩
0.50
|1⟩

Phase Betting

Two-Qubit Quantum Game

Round: 0
Credits: 100
Score: 0
|0⟩0
|0⟩1
Get measurement hints (costs credits):

State Probabilities

1.0 0.5 0.0
0.25
|00⟩
0.25
|01⟩
0.25
|10⟩
0.25
|11⟩