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https://github.com/quantumjim/Quantum-Computation-course-Basel.git
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add ex 1
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quantumjim
247
exercises/tests1.py
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247
exercises/tests1.py
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from qiskit import QuantumCircuit, transpile
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from qiskit_ibm_runtime.fake_provider import FakeYorktownV2
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import numpy as np
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def test_xor(XOR):
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# Test XOR gate outputs using assert statements
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expected_outputs = {
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('0', '0'): '0',
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('0', '1'): '1',
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('1', '0'): '1',
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('1', '1'): '0'
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}
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for inp1 in ['0', '1']:
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for inp2 in ['0', '1']:
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_, output = XOR(inp1, inp2)
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assert output == expected_outputs[(inp1, inp2)], f"❌ XOR({inp1}, {inp2}) = {output}, expected {expected_outputs[(inp1, inp2)]}"
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print("✅ All XOR gate tests passed.")
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def test_and(AND):
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# Test AND gate outputs using assert statements
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expected_outputs = {
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('0', '0'): '0',
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('0', '1'): '0',
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('1', '0'): '0',
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('1', '1'): '1'
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}
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for inp1 in ['0', '1']:
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for inp2 in ['0', '1']:
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_, output = AND(inp1, inp2)
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assert output == expected_outputs[(inp1, inp2)], f"❌ AND({inp1}, {inp2}) = {output}, expected {expected_outputs[(inp1, inp2)]}"
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print("✅ All AND gate tests passed.")
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def test_nand(NAND):
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# Test NAND gate outputs using assert statements
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expected_outputs = {
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('0', '0'): '1',
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('0', '1'): '1',
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('1', '0'): '1',
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('1', '1'): '0'
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}
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for inp1 in ['0', '1']:
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for inp2 in ['0', '1']:
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_, output = NAND(inp1, inp2)
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assert output == expected_outputs[(inp1, inp2)], f"❌ NAND({inp1}, {inp2}) = {output}, expected {expected_outputs[(inp1, inp2)]}"
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print("✅ All NAND gate tests passed.")
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def test_or(OR):
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# Test OR gate outputs using assert statements
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expected_outputs = {
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('0', '0'): '0',
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('0', '1'): '1',
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('1', '0'): '1',
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('1', '1'): '1'
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}
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for inp1 in ['0', '1']:
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for inp2 in ['0', '1']:
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_, output = OR(inp1, inp2)
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assert output == expected_outputs[(inp1, inp2)], f"❌ OR({inp1}, {inp2}) = {output}, expected {expected_outputs[(inp1, inp2)]}"
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print("✅ All OR gate tests passed.")
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def test_compilation(layout):
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backend = FakeYorktownV2()
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def AND(inp1, inp2, backend, layout):
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qc = QuantumCircuit(3, 1)
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qc.reset(range(3))
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if inp1=='1':
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qc.x(0)
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if inp2=='1':
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qc.x(1)
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qc.barrier()
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qc.ccx(0, 1, 2)
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qc.barrier()
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qc.measure(2, 0)
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qc_trans = transpile(qc, backend, initial_layout=layout, optimization_level=3)
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return qc_trans
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for input1 in ['0','1']:
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for input2 in ['0','1']:
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qc_trans1 = AND(input1, input2, backend, layout)
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num_gates = qc_trans1.num_nonlocal_gates()
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print('For input '+input1+input2)
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assert num_gates==6, f"❌ Toffoli transpiled to {num_gates} two qubit gates rather than 6."
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print("✅ Ideal transpilation acheived.")
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def test_alt(
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find_orthogonal_state,
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find_mutually_unbiased_basis_plus,
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find_mutually_unbiased_basis_minus
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):
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ket_0 = np.array([[1], [0]], dtype=complex)
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ket_1 = np.array([[0], [1]], dtype=complex)
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# (a) Test for orthogonality
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theta = np.pi / 4
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ket_zero_bar = np.cos(theta) * ket_0 + np.sin(theta) * ket_1
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ket_one_bar = find_orthogonal_state(ket_zero_bar, theta)
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# Check if the inner product is close to zero
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inner_product_orthogonal = np.vdot(ket_zero_bar, ket_one_bar)
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assert np.isclose(inner_product_orthogonal, 0), "❌ Test (a) failed: The states |ψ0⟩ and |ψ1⟩ are not orthogonal."
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print("✅ Test (a) passed: |ψ0⟩ and |ψ1⟩ are orthogonal.")
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# (b) Test for mutually unbiased bases
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ket_plus_bar = find_mutually_unbiased_basis_plus(ket_zero_bar, ket_one_bar)
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ket_minus_bar = find_mutually_unbiased_basis_minus(ket_zero_bar, ket_one_bar)
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# Check orthogonality of the MUB states
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inner_product_mub = np.vdot(ket_plus_bar, ket_minus_bar)
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assert np.isclose(inner_product_mub, 0), "❌ Test (b) failed: The states |ψ+⟩ and |ψ-⟩ are not orthogonal."
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# Check the unbiased condition
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inner_product_plus_zero = np.abs(np.vdot(ket_plus_bar, ket_zero_bar))**2
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inner_product_plus_one = np.abs(np.vdot(ket_plus_bar, ket_one_bar))**2
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inner_product_minus_zero = np.abs(np.vdot(ket_minus_bar, ket_zero_bar))**2
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inner_product_minus_one = np.abs(np.vdot(ket_minus_bar, ket_one_bar))**2
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assert np.isclose(inner_product_plus_zero, 0.5), "❌ Test (b) failed: The bases are not mutually unbiased for |<ψ+|ψ0>|^2."
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assert np.isclose(inner_product_plus_one, 0.5), "❌ Test (b) failed: The bases are not mutually unbiased for |<ψ+|ψ1>|^2."
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assert np.isclose(inner_product_minus_zero, 0.5), "❌ Test (b) failed: The bases are not mutually unbiased for |<ψ-|ψ0>|^2."
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assert np.isclose(inner_product_minus_one, 0.5), "❌ Test (b) failed: The bases are not mutually unbiased for |<ψ-|ψ1>|^2."
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print("✅ Test (b) passed: The bases are mutually unbiased.")
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print("\nCongratulations! All tests passed!")
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def test_paulis(
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I,
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X,
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Y,
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Z,
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test_square_to_identity,
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test_anticommutation,
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test_product_relation,
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get_eigenvalues_and_eigenvectors,
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):
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I = np.array([
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[1, 0],
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[0, 1]
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]) # Identity matrix
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paulis = {'X': X, 'Y': Y, 'Z': Z, 'I':I}
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assert all(p is not None for p in [X, Y, Z, I]), "❌ FAIL: At least one matrix is not defined."
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# (a)
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for i in paulis:
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assert np.allclose(test_square_to_identity(paulis[i]) , I), "❌ FAIL (a): Your function did not correctly verify that all Pauli matrices square to the identity."
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print("✅ PASS (a): Your function `test_square_to_identity` works correctly.")
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# (b)
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for i in ['X', 'Y', 'Z']:
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for j in ['X', 'Y', 'Z']:
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if i!=j:
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assert np.allclose(paulis[i]@paulis[j],test_anticommutation(paulis[i],paulis[j])), "❌ FAIL (b): Your function did not correctly verify the anticommutation relations."
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print("✅ PASS (b): Your function `test_anticommutation` works correctly.")
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# (c)
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assert np.allclose(np.array(test_product_relation()), np.array([X@Y,Y@Z,Z@X])), "❌ FAIL (c): Your function did not correctly verify the Pauli product relations."
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print("✅ PASS (c): Your function `test_product_relation` works correctly.")
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# (d)
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eigenvalues, eigenvectors = get_eigenvalues_and_eigenvectors()
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assert isinstance(eigenvalues, dict) and isinstance(eigenvectors, dict), "❌ FAIL (d): Function must return two dictionaries."
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assert all(k in eigenvalues for k in ['X', 'Y', 'Z']), "❌ FAIL (d): Eigenvalues dictionary is missing keys."
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assert all(k in eigenvectors for k in ['X', 'Y', 'Z']), "❌ FAIL (d): Eigenvectors dictionary is missing keys."
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print("✅ PASS (d): Your function `get_eigenvalues_and_eigenvectors` has the correct return type and keys.")
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for name in ['X', 'Y', 'Z']:
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# Check eigenvalues
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e_vals = eigenvalues[name]
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assert np.allclose(sorted(np.real(e_vals)), [-1, 1]), f"❌ FAIL (d): Eigenvalues for {name} are incorrect. Expected [-1, 1]."
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# Check eigenvector equation: P * v = lambda * v
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p_matrix = paulis[name]
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e_vecs = eigenvectors[name]
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for i in range(len(e_vals)):
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lambda_val = e_vals[i]
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v_vec = e_vecs[:, i].reshape(2, 1)
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assert np.allclose(p_matrix @ v_vec, lambda_val * v_vec), f"❌ FAIL (d): Eigenvector equation Pv=λv does not hold for {name}."
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print("✅ PASS (d): Eigenvalues and eigenvectors are correct for all Pauli matrices.")
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print("\nCongratulations! All tests passed!")
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def test_hadamard(
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H,
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get_hadamard_eigen_system,
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test_hadamard_squares_to_identity,
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test_hadamard_pauli_transformation
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):
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print("--- Running Verification ---")
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I = np.array([
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[1, 0],
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[0, 1]
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])
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# Check that matrices are defined before proceeding
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assert H is not None, "❌ FAIL: H matrix is not defined."
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# (a)
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eigen_system = get_hadamard_eigen_system()
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assert isinstance(eigen_system, tuple) and len(eigen_system) == 2, "❌ FAIL (a): Function must return a tuple of (eigenvalues, eigenvectors)."
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eigenvalues, eigenvectors = eigen_system
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# Check eigenvalues are correct (+1 and -1)
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assert np.allclose(sorted(np.real(eigenvalues)), [-1, 1]), f"❌ FAIL (a): Eigenvalues for H are incorrect. Expected [-1, 1]."
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# Check eigenvector equation H * v = lambda * v
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for i in range(len(eigenvalues)):
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lambda_val = eigenvalues[i]
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v_vec = eigenvectors[:, i].reshape(2, 1)
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assert np.allclose(H @ v_vec, lambda_val * v_vec), f"❌ FAIL (a): Eigenvector equation Hv=λv does not hold."
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print("✅ PASS (a): Your function `get_hadamard_eigen_system` works correctly.")
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# (b)
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assert np.allclose(test_hadamard_squares_to_identity() , I), "❌ FAIL (b): Your function did not correctly verify that H^2 = I."
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print("✅ PASS (b): Your function `test_hadamard_squares_to_identity` works correctly.")
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answers = ["Z", "-Y", "X"]
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X = np.array([[0, 1], [1, 0]], dtype=complex)
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Y = np.array([[0, -1j], [1j, 0]], dtype=complex)
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I = np.array([[1,0],[0,1]])
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Z = np.array([[1,0],[0,-1]])
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# (c)
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things = [ '1. H X H†',
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'2. H Y H†',
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'3. H Z H†']
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for i,val in enumerate(test_hadamard_pauli_transformation()):
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assert val == answers[i], f"❌ FAIL (c): Your function did not correctly verify the Hadamard-Pauli transformation {things[i]}."
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print("✅ PASS (c): Your answers are correct.")
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print("\nCongratulations! All tests passed!")
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