OpenQASM Bernstein-Vazirani sample (#2403)

Co-authored-by: Dmitry Vasilevsky <dmitryv@microsoft.com>

Author: DmitryVasilevsky

samples/OpenQASM/BernsteinVazirani.qasm

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+// OpenQASM Bernstein-Vazirani sample
+//
+// This sample demonstrates the Bernstein-Vazirani algorithm,
+// which determines the value of a bit string encoded in a function.
+
+OPENQASM 3;
+include "stdgates.inc";
+
+// Define the number of qubits.
+const int nQubits = 5;
+// The secret bit string to be determined.
+const bit[nQubits] secretBitString = "10101";
+
+// Given bit string 𝑟⃗ = (r₀, …, rₙ₋₁), represented as an array of bits,
+// this operation applies a unitary 𝑈 that acts on 𝑛 + 1 qubits as:
+//     𝑈 |𝑥〉|𝑦〉 = |𝑥〉|𝑦 ⊕ 𝑓(𝑥)〉
+// where 𝑓(𝑥) = Σᵢ 𝑥ᵢ 𝑟ᵢ mod 2.
+def ApplyParityOperation(
+    bit[nQubits] bitStringAsBoolArray,
+    qubit[nQubits] xRegister,
+    qubit yQubit ) {
+
+    // Apply the quantum operations that encode the secret bit string.
+    for int i in [0:nQubits-1] {
+        if (bitStringAsBoolArray[i]) {
+            cx xRegister[i], yQubit;
+        }
+    }
+}
+
+// Applies parity operation for a particular secret bit string.
+def ParityOperationForSecretBitstring(qubit[nQubits] xRegister, qubit yQubit) {
+    ApplyParityOperation(secretBitString, xRegister, yQubit);
+}
+
+// Given a register in the all-zeros state, prepares a uniform
+// superposition over all basis states.
+def PrepareUniform(qubit[nQubits] q) {
+    for int i in [0:nQubits-1] {
+        h q[i];
+    }
+}
+
+// This operation implements the Bernstein-Vazirani quantum algorithm.
+// This algorithm computes for a given Boolean function that is promised to
+// be a parity 𝑓(𝑥₀, …, 𝑥ₙ₋₁) = Σᵢ 𝑟ᵢ 𝑥ᵢ a result in the form of a bit
+// vector (𝑟₀, …, 𝑟ₙ₋₁) corresponding to the parity function.
+// Note that it is promised that the function is actually a parity
+// function.
+def BernsteinVazirani(qubit[nQubits] queryRegister, qubit target) -> bit[nQubits] {
+    bit[nQubits] results;
+
+    // The target qubit needs to be flipped so that a relative phase is
+    // introduced when we apply a Hadamard gate and we can use
+    // phase kickback when parity operation is applied.
+    x target;
+    h target;
+
+    // Prepare the query register in a uniform superposition.
+    PrepareUniform(queryRegister);
+
+    // Apply the parity operation.
+    ParityOperationForSecretBitstring(queryRegister, target);
+
+    // Uncompute the preparation of the uniform superposition.
+    PrepareUniform(queryRegister);
+
+    // Measure the qubits
+    results = measure queryRegister;
+
+    // The string we are looking for is returned after execution.
+    return results;
+}
+
+// Main program
+
+// Initialize the qubits
+qubit[nQubits] queryRegister;
+qubit target;
+
+reset queryRegister;
+reset target;
+
+// This register will hold and return the bit string found by the algorithm.
+output bit[nQubits] results;
+
+// Call the Bernstein-Vazirani algorithm to find the secret bit string.
+results = BernsteinVazirani(queryRegister, target);