Q-TESTING
Run real quantum experiments on IBM Quantum hardware
Hello World - Bell State
Create a Bell state (maximally entangled state) and measure expectation values of 6 Pauli observables (IZ, IX, ZI, XI, ZZ, XX). This demonstrates quantum entanglement where individual qubits show no correlation, but joint measurements reveal perfect correlation.
CHSH Inequality
Demonstrate violation of Bell's inequality using the CHSH test. Classical physics predicts |S| ≤ 2, but quantum mechanics allows |S| ≤ 2√2 ≈ 2.83. This proves quantum mechanics is incompatible with local hidden variable theories.
ADVANCED EXPERIMENTS
IBM Quantum tutorials - Chemistry, Optimization, and Lattice Models
Quantum Diagonalization (Chemistry)
Sample-based quantum diagonalization of a chemistry Hamiltonian using the H2 molecule. Demonstrates finding ground state energy of molecular systems using quantum computing.
Krylov Diagonalization (Lattice)
Sample-based Krylov quantum diagonalization of a 2-site Fermi-Hubbard model. Explores strongly correlated electron systems on a lattice.
QAOA - MaxCut
Quantum Approximate Optimization Algorithm solving the MaxCut problem on a small graph. Demonstrates hybrid quantum-classical optimization for combinatorial problems.
Advanced QAOA
Advanced techniques for QAOA including warm-starting, parameter schedules, and custom mixer operators for improved optimization performance.
Pauli Correlation Encoding
Pauli correlation encoding technique to reduce measurement requirements (Mascut). Shows how correlation-aware encoding reduces quantum resource overhead.
About These Experiments
Bell States are the simplest examples of quantum entanglement. When two qubits are in a Bell state, measuring one qubit instantaneously determines the state of the other, regardless of distance. This "spooky action at a distance" puzzled Einstein but has been experimentally verified countless times.
CHSH Inequality provides a mathematical test to distinguish quantum mechanics from classical hidden variable theories. The 2022 Nobel Prize in Physics was awarded to Aspect, Clauser, and Zeilinger for experiments demonstrating Bell inequality violations, confirming the non-local nature of quantum mechanics.
Quantum Diagonalization (Chemistry) calculates the ground state energy of an H2 molecule across different bond distances. Using PySCF and Jordan-Wigner mapping, we transform the molecular Hamiltonian into qubit operators and find the equilibrium bond length (~0.735 Angstroms) where energy is minimized.
Krylov Diagonalization (Lattice) simulates a 2-site Fermi-Hubbard model, a fundamental model for studying electron correlations in materials. The energy spectrum reveals how onsite Coulomb repulsion (U=4) and hopping (t=-1) compete, relevant to understanding superconductivity and magnetism.
QAOA (MaxCut) uses the Quantum Approximate Optimization Algorithm to solve the MaxCut graph partitioning problem. This hybrid quantum-classical algorithm demonstrates quantum advantage potential for combinatorial optimization problems found in logistics, circuit design, and machine learning.
Advanced QAOA compares standard QAOA with warm-starting techniques. Warm-starting uses classical solutions as initial parameters, often achieving faster convergence and better results - a practical technique for near-term quantum devices.
Pauli Correlation Encoding analyzes how correlated Pauli measurements can reduce the number of circuit executions needed. This measurement optimization is crucial for running quantum chemistry on real hardware with limited coherence time.
Simulator vs Real Hardware: The simulator runs locally and is fast, but doesn't capture real-world noise. Real IBM Quantum hardware shows decoherence effects but proves these phenomena on actual quantum processors.
Testing History
Your IBM Quantum experiments are saved here (10 min limit on real hardware)