Add bell inequality example

examples/bell_inequalities.rs

@@ -0,0 +1,136 @@
+use qip::*;
+
+fn circuit1() -> Vec<f64> {
+    // build 2 qubits
+    let mut builder = OpBuilder::new();
+    let qubit1 = builder.qubit();
+    let qubit2 = builder.qubit();
+
+    // transform qubits from |0> to |1>
+    let qubit1 = builder.not(qubit1);
+    let qubit2 = builder.not(qubit2);
+
+    // apply hadamard and cnot
+    let qubit1 = builder.hadamard(qubit1);
+    let (qubit1, qubit2) = builder.cnot(qubit1, qubit2);
+
+    // apply rz to qubit2
+    let qubit2 = builder.rz(qubit2, std::f64::consts::FRAC_PI_3);
+
+    // apply hadamard to both qubits
+    let qubit1 = builder.hadamard(qubit1);
+    let qubit2 = builder.hadamard(qubit2);
+
+    // merge both qubits
+    let merged = builder.merge(vec![qubit1, qubit2]).unwrap();
+
+    // add a measurement of all possible states
+    let (merged, m_handle) = builder.stochastic_measure(merged);
+
+    // run and get probabilities
+    let (_, mut measured) = run_local::<f64>(&merged).unwrap();
+    let probabilities = measured.pop_stochastic_measurements(m_handle).unwrap();
+
+    probabilities
+}
+
+fn circuit2() -> Vec<f64> {
+    // build 2 qubits
+    let mut builder = OpBuilder::new();
+    let qubit1 = builder.qubit();
+    let qubit2 = builder.qubit();
+
+    // transform qubits from |0> to |1>
+    let qubit1 = builder.not(qubit1);
+    let qubit2 = builder.not(qubit2);
+
+    // apply hadamard and cnot
+    let qubit1 = builder.hadamard(qubit1);
+    let (qubit1, qubit2) = builder.cnot(qubit1, qubit2);
+
+    // apply rz to qubit2
+    let qubit2 = builder.rz(qubit2, 2.0 * std::f64::consts::FRAC_PI_3);
+
+    // apply hadamard to both qubits
+    let qubit1 = builder.hadamard(qubit1);
+    let qubit2 = builder.hadamard(qubit2);
+
+    // merge both qubits
+    let merged = builder.merge(vec![qubit1, qubit2]).unwrap();
+
+    // add a measurement of all possible states
+    let (merged, m_handle) = builder.stochastic_measure(merged);
+
+    // run and get probabilities
+    let (_, mut measured) = run_local::<f64>(&merged).unwrap();
+    let probabilities = measured.pop_stochastic_measurements(m_handle).unwrap();
+
+    probabilities
+}
+
+fn circuit3() -> Vec<f64> {
+    // build 2 qubits
+    let mut builder = OpBuilder::new();
+    let qubit1 = builder.qubit();
+    let qubit2 = builder.qubit();
+
+    // transform qubits from |0> to |1>
+    let qubit1 = builder.not(qubit1);
+    let qubit2 = builder.not(qubit2);
+
+    // apply hadamard and cnot
+    let qubit1 = builder.hadamard(qubit1);
+    let (qubit1, qubit2) = builder.cnot(qubit1, qubit2);
+
+    // apply rz to both qubits
+    let qubit1 = builder.rz(qubit1, std::f64::consts::FRAC_PI_3);
+    let qubit2 = builder.rz(qubit2, 2.0 * std::f64::consts::FRAC_PI_3);
+
+    // apply hadamard to both qubits
+    let qubit1 = builder.hadamard(qubit1);
+    let qubit2 = builder.hadamard(qubit2);
+
+    // merge both qubits
+    let merged = builder.merge(vec![qubit1, qubit2]).unwrap();
+
+    // add a measurement of all possible states
+    let (merged, m_handle) = builder.stochastic_measure(merged);
+
+    // run and get probabilities
+    let (_, mut measured) = run_local::<f64>(&merged).unwrap();
+    let probabilities = measured.pop_stochastic_measurements(m_handle).unwrap();
+
+    probabilities
+}
+
+/// Bell inequality:
+/// |P(a, b) - P(a, c)| - P(b, c) <= 1
+/// To get P(a, b), P(a, c) and P(b, c) we use the 3 circuits presented in:
+/// https://arxiv.org/pdf/1712.05642.pdf - II.IMPLEMENTED EXPERIMENTS -> 3. Bell's inequality
+///
+/// A violation of the inequality is expected in any quantum computer or simulator.
+fn main() -> Result<(), CircuitError> {
+    println!("Bell inequality: |P(a, b) - P(a, c)| - P(b, c) <= 1");
+
+    let a_b = circuit1();
+    let p_of_a_b = (a_b[0] + a_b[3]) - (a_b[1] + a_b[2]);
+    println!("P(a, b) = {:.2}", p_of_a_b);
+
+    let a_c = circuit2();
+    let p_of_a_c = (a_c[0] + a_c[3]) - (a_c[1] + a_c[2]);
+    println!("P(a, c) = {:.2}", p_of_a_c);
+
+    let b_c = circuit3();
+    let p_of_b_c = (b_c[0] + b_c[3]) - (b_c[1] + b_c[2]);
+    println!("P(b, c) = {:.2}", p_of_b_c);
+
+    let left_side = num::abs(p_of_a_b - p_of_a_c) - p_of_b_c;
+    println!(
+        "|{:.2} - {:.2}| - ({:.2}) = {:.2} IS NOT <= 1",
+        p_of_a_b, p_of_a_c, p_of_b_c, left_side
+    );
+
+    assert!(left_side > 1.0);
+
+    Ok(())
+}