from qiskit import QuantumCircuit from qiskit_aer import AerSimulator import numpy as np import random simulator = AerSimulator() SHOTS = 200000 # ===================================== # CIRCUIT # ===================================== def create_ghz_circuit(measure_q0=False,pre=False): # 5 qubits, 5 classical bits circuit = QuantumCircuit(5, 5) # current test circuit circuit.x(0) circuit.x(3) circuit.h(1) circuit.h(2) #circuit.h(3) #circuit.h(4) circuit.cx(1, 0) circuit.cx(1, 3) circuit.ccx(1, 2, 4) circuit.cx(2, 3) circuit.cx(2, 0) circuit.barrier() return circuit # ===================================== # CHSH BASIS # ===================================== def measure_in_basis(circuit, qubit, angle): circuit.ry(-2 * angle, qubit) # ===================================== # SPLIT q0 # ===================================== def split_counts_by_q0(counts): q0_0 = {} q0_1 = {} for key, value in counts.items(): # qiskit order: c4 c3 c2 c1 c0 q2q1 = key[2:4] # c2 c1 q0 = key[4] # c0 if q0 == "0": q0_0[q2q1] = q0_0.get(q2q1, 0) + value else: q0_1[q2q1] = q0_1.get(q2q1, 0) + value return q0_0, q0_1 # ===================================== # CORRELATION # ===================================== def calculate_correlation(counts): total = sum(counts.values()) if total == 0: return 0 corr = 0 for key, value in counts.items(): q2 = key[0] q1 = key[1] if q1 == q2: corr += value else: corr -= value return corr / total # ===================================== # TABLE # ===================================== def print_table(rows): print("\n") print("=" * 110) print( f"{'TEST':8}" f"{'q0':5}" f"{'00':7}" f"{'01':7}" f"{'10':7}" f"{'11':7}" f"{'N':8}" f"{'E(q1,q2)':12}" ) print("-" * 110) for r in rows: print( f"{r['test']:8}" f"{r['q0']:5}" f"{r['00']:7}" f"{r['01']:7}" f"{r['10']:7}" f"{r['11']:7}" f"{r['N']:8}" f"{r['corr']:12.6f}" ) print("=" * 110) # ===================================== # CHSH SETTINGS # ===================================== bases = [ ("A0B0", 0, np.pi / 8), ("A0B1", 0, -np.pi / 8), ("A1B0", np.pi / 4, np.pi / 8), ("A1B1", np.pi / 4, -np.pi / 8) ] # ===================================== # RUN # ===================================== def run_chsh(measure_q0, pre): results_all = [] results_q0_0 = [] results_q0_1 = [] table = [] print("\n") print("=" * 40) if measure_q0: print("q0 MEASURED") else: print("q0 NOT MEASURED") print("=" * 40) for name, a, b in bases: circuit = create_ghz_circuit(measure_q0, pre) meas = measure_q0 # measure the new ancillas q3 and q4 (optional, for checking) if pre: circuit.measure(3, 3) # measure q0 if requested if meas: circuit.measure(0, 0) circuit.measure(4, 4) circuit.barrier() # measurement bases on q1 and q2 measure_in_basis(circuit, 1, a) measure_in_basis(circuit, 2, b) circuit.barrier() # measure q1 and q2 circuit.measure(1, 1) circuit.barrier() circuit.measure(2, 2) circuit.barrier() # measure the new ancillas q3 and q4 (optional, for checking) if not pre: circuit.measure(3, 3) # measure q0 if requested if meas: circuit.measure(0, 0) print("\n", name) print(circuit.draw()) result = simulator.run(circuit, shots=SHOTS).result() counts = result.get_counts() # ===================================== # CHECK q0=1 AND q3=1 # ===================================== q0_q3_11 = 0 total_shots = 0 for key, value in counts.items(): q0 = key[4] q3 = key[1] if q0 == "1": total_shots += value if q3 == "1": q0_q3_11 += value if total_shots > 0: print( f"q0=1 -> q3=1: {q0_q3_11} / {total_shots}" f" ({100*q0_q3_11/total_shots:.4f}%)" ) else: print("\nq0 ALWAYS 0") print("\nCOUNTS") print(counts) # --- total correlation on q1,q2 --- clean = {} for k, v in counts.items(): # take only bits of q2 and q1 (positions 2 and 1 in the 5-bit string) q2q1 = k[2:4] clean[q2q1] = clean.get(q2q1, 0) + v corr = calculate_correlation(clean) results_all.append(corr) if not meas: table.append({ "test": name, "q0": "--", "00": clean.get("00", 0), "01": clean.get("01", 0), "10": clean.get("10", 0), "11": clean.get("11", 0), "N": sum(clean.values()), "corr": corr }) if meas: c0, c1 = split_counts_by_q0(counts) corr0 = calculate_correlation(c0) corr1 = calculate_correlation(c1) results_q0_0.append(corr0) results_q0_1.append(corr1) for label, c in [("0", c0), ("1", c1)]: table.append({ "test": name, "q0": label, "00": c.get("00", 0), "01": c.get("01", 0), "10": c.get("10", 0), "11": c.get("11", 0), "N": sum(c.values()), "corr": calculate_correlation(c) }) print_table(table) # Total CHSH S = results_all[0] + results_all[1] + results_all[2] - results_all[3] print("\nTotal CHSH =", S) if measure_q0: S0 = results_q0_0[0] + results_q0_0[1] + results_q0_0[2] - results_q0_0[3] S1 = results_q0_1[0] + results_q0_1[1] + results_q0_1[2] - results_q0_1[3] print("\nConditional CHSH") print("q0=0 :", S0) print("q0=1 :", S1) S0_alt = -results_q0_0[0] - results_q0_0[1] + results_q0_0[2] - results_q0_0[3] print("\nAlternative CHSH q0=0") print("S0_alt =", S0_alt) print("2*sqrt(2) =", 2 * np.sqrt(2)) # ===================================== # MAIN # ===================================== run_chsh(False, True) run_chsh(True, True) run_chsh(False, False) run_chsh(True, False) ========================= = PYTHON CODE OUTPUT = ========================= ======================================== q0 NOT MEASURED ======================================== A0B0 ┌───┐┌───┐ ┌───┐ ░ ░ ░ ░ ░ q_0: ┤ X ├┤ X ├───────────────┤ X ├─░────────░──────────────░─────░─────░─ ├───┤└─┬─┘ └─┬─┘ ░ ░ ┌───────┐ ░ ┌─┐ ░ ░ q_1: ┤ H ├──■────■────■─────────┼───░────────░──┤ Ry(0) ├───░─┤M├─░─────░─ ├───┤ │ │ │ ░ ░ ┌┴───────┴─┐ ░ └╥┘ ░ ┌─┐ ░ q_2: ┤ H ├───────┼────■────■────■───░────────░─┤ Ry(-π/4) ├─░──╫──░─┤M├─░─ ├───┤ ┌─┴─┐ │ ┌─┴─┐ ░ ┌─┐ ░ └──────────┘ ░ ║ ░ └╥┘ ░ q_3: ┤ X ├─────┤ X ├──┼──┤ X ├──────░─┤M├────░──────────────░──╫──░──╫──░─ └───┘ └───┘┌─┴─┐└───┘ ░ └╥┘┌─┐ ░ ░ ║ ░ ║ ░ q_4: ───────────────┤ X ├───────────░──╫─┤M├─░──────────────░──╫──░──╫──░─ └───┘ ░ ║ └╥┘ ░ ░ ║ ░ ║ ░ c: 5/══════════════════════════════════╩══╩════════════════════╩═════╩════ 3 4 1 2 q0 ALWAYS 0 COUNTS {'00110': 7326, '11110': 42871, '11010': 7275, '00100': 42717, '00000': 7313, '00010': 42514, '01100': 7268, '01000': 42716} A0B1 ┌───┐┌───┐ ┌───┐ ░ ░ ░ ░ ░ q_0: ┤ X ├┤ X ├───────────────┤ X ├─░────────░─────────────░─────░─────░─ ├───┤└─┬─┘ └─┬─┘ ░ ░ ┌───────┐ ░ ┌─┐ ░ ░ q_1: ┤ H ├──■────■────■─────────┼───░────────░──┤ Ry(0) ├──░─┤M├─░─────░─ ├───┤ │ │ │ ░ ░ ┌┴───────┴┐ ░ └╥┘ ░ ┌─┐ ░ q_2: ┤ H ├───────┼────■────■────■───░────────░─┤ Ry(π/4) ├─░──╫──░─┤M├─░─ ├───┤ ┌─┴─┐ │ ┌─┴─┐ ░ ┌─┐ ░ └─────────┘ ░ ║ ░ └╥┘ ░ q_3: ┤ X ├─────┤ X ├──┼──┤ X ├──────░─┤M├────░─────────────░──╫──░──╫──░─ └───┘ └───┘┌─┴─┐└───┘ ░ └╥┘┌─┐ ░ ░ ║ ░ ║ ░ q_4: ───────────────┤ X ├───────────░──╫─┤M├─░─────────────░──╫──░──╫──░─ └───┘ ░ ║ └╥┘ ░ ░ ║ ░ ║ ░ c: 5/══════════════════════════════════╩══╩═══════════════════╩═════╩════ 3 4 1 2 q0 ALWAYS 0 COUNTS {'00110': 7393, '00100': 42871, '11010': 7457, '01100': 7264, '01000': 42280, '00000': 7287, '00010': 42788, '11110': 42660} A1B0 ┌───┐┌───┐ ┌───┐ ░ ░ ░ ░ ░ q_0: ┤ X ├┤ X ├───────────────┤ X ├─░────────░──────────────░─────░─────░─ ├───┤└─┬─┘ └─┬─┘ ░ ░ ┌──────────┐ ░ ┌─┐ ░ ░ q_1: ┤ H ├──■────■────■─────────┼───░────────░─┤ Ry(-π/2) ├─░─┤M├─░─────░─ ├───┤ │ │ │ ░ ░ ├──────────┤ ░ └╥┘ ░ ┌─┐ ░ q_2: ┤ H ├───────┼────■────■────■───░────────░─┤ Ry(-π/4) ├─░──╫──░─┤M├─░─ ├───┤ ┌─┴─┐ │ ┌─┴─┐ ░ ┌─┐ ░ └──────────┘ ░ ║ ░ └╥┘ ░ q_3: ┤ X ├─────┤ X ├──┼──┤ X ├──────░─┤M├────░──────────────░──╫──░──╫──░─ └───┘ └───┘┌─┴─┐└───┘ ░ └╥┘┌─┐ ░ ░ ║ ░ ║ ░ q_4: ───────────────┤ X ├───────────░──╫─┤M├─░──────────────░──╫──░──╫──░─ └───┘ ░ ║ └╥┘ ░ ░ ║ ░ ║ ░ c: 5/══════════════════════════════════╩══╩════════════════════╩═════╩════ 3 4 1 2 q0 ALWAYS 0 COUNTS {'00100': 7253, '11010': 3615, '11000': 3668, '11100': 21477, '01010': 21565, '01110': 3669, '00110': 42312, '11110': 21498, '01000': 21325, '01100': 3754, '00010': 7362, '00000': 42502} A1B1 ┌───┐┌───┐ ┌───┐ ░ ░ ░ ░ ░ q_0: ┤ X ├┤ X ├───────────────┤ X ├─░────────░──────────────░─────░─────░─ ├───┤└─┬─┘ └─┬─┘ ░ ░ ┌──────────┐ ░ ┌─┐ ░ ░ q_1: ┤ H ├──■────■────■─────────┼───░────────░─┤ Ry(-π/2) ├─░─┤M├─░─────░─ ├───┤ │ │ │ ░ ░ ├─────────┬┘ ░ └╥┘ ░ ┌─┐ ░ q_2: ┤ H ├───────┼────■────■────■───░────────░─┤ Ry(π/4) ├──░──╫──░─┤M├─░─ ├───┤ ┌─┴─┐ │ ┌─┴─┐ ░ ┌─┐ ░ └─────────┘ ░ ║ ░ └╥┘ ░ q_3: ┤ X ├─────┤ X ├──┼──┤ X ├──────░─┤M├────░──────────────░──╫──░──╫──░─ └───┘ └───┘┌─┴─┐└───┘ ░ └╥┘┌─┐ ░ ░ ║ ░ ║ ░ q_4: ───────────────┤ X ├───────────░──╫─┤M├─░──────────────░──╫──░──╫──░─ └───┘ ░ ║ └╥┘ ░ ░ ║ ░ ║ ░ c: 5/══════════════════════════════════╩══╩════════════════════╩═════╩════ 3 4 1 2 q0 ALWAYS 0 COUNTS {'11010': 3708, '01110': 3677, '11000': 3651, '11110': 21292, '00110': 7226, '00010': 42639, '00000': 7383, '01100': 3535, '01000': 21279, '01010': 21436, '00100': 42768, '11100': 21406} ============================================================================================================== TEST q0 00 01 10 11 N E(q1,q2) -------------------------------------------------------------------------------------------------------------- A0B0 -- 50029 49789 49985 50197 200000 0.002260 A0B1 -- 49567 50245 50135 50053 200000 -0.003800 A1B0 -- 67495 32542 32484 67479 200000 0.349740 A1B1 -- 32313 67783 67709 32195 200000 -0.354920 ============================================================================================================== Total CHSH = 0.70312 ======================================== q0 MEASURED ======================================== A0B0 ┌───┐┌───┐ ┌───┐ ░ ┌─┐ ░ ░ ░ ░ q_0: ┤ X ├┤ X ├───────────────┤ X ├─░────┤M├────░──────────────░─────░─────░─ ├───┤└─┬─┘ └─┬─┘ ░ └╥┘ ░ ┌───────┐ ░ ┌─┐ ░ ░ q_1: ┤ H ├──■────■────■─────────┼───░─────╫─────░──┤ Ry(0) ├───░─┤M├─░─────░─ ├───┤ │ │ │ ░ ║ ░ ┌┴───────┴─┐ ░ └╥┘ ░ ┌─┐ ░ q_2: ┤ H ├───────┼────■────■────■───░─────╫─────░─┤ Ry(-π/4) ├─░──╫──░─┤M├─░─ ├───┤ ┌─┴─┐ │ ┌─┴─┐ ░ ┌─┐ ║ ░ └──────────┘ ░ ║ ░ └╥┘ ░ q_3: ┤ X ├─────┤ X ├──┼──┤ X ├──────░─┤M├─╫─────░──────────────░──╫──░──╫──░─ └───┘ └───┘┌─┴─┐└───┘ ░ └╥┘ ║ ┌─┐ ░ ░ ║ ░ ║ ░ q_4: ───────────────┤ X ├───────────░──╫──╫─┤M├─░──────────────░──╫──░──╫──░─ └───┘ ░ ║ ║ └╥┘ ░ ░ ║ ░ ║ ░ c: 5/══════════════════════════════════╩══╩══╩════════════════════╩═════╩════ 3 0 4 1 2 q0=1 -> q3=1: 100261 / 100261 (100.0000%) COUNTS {'00110': 7310, '01101': 7258, '01001': 42898, '11011': 7228, '11111': 42877, '00100': 42531, '00000': 7291, '00010': 42607} A0B1 ┌───┐┌───┐ ┌───┐ ░ ┌─┐ ░ ░ ░ ░ q_0: ┤ X ├┤ X ├───────────────┤ X ├─░────┤M├────░─────────────░─────░─────░─ ├───┤└─┬─┘ └─┬─┘ ░ └╥┘ ░ ┌───────┐ ░ ┌─┐ ░ ░ q_1: ┤ H ├──■────■────■─────────┼───░─────╫─────░──┤ Ry(0) ├──░─┤M├─░─────░─ ├───┤ │ │ │ ░ ║ ░ ┌┴───────┴┐ ░ └╥┘ ░ ┌─┐ ░ q_2: ┤ H ├───────┼────■────■────■───░─────╫─────░─┤ Ry(π/4) ├─░──╫──░─┤M├─░─ ├───┤ ┌─┴─┐ │ ┌─┴─┐ ░ ┌─┐ ║ ░ └─────────┘ ░ ║ ░ └╥┘ ░ q_3: ┤ X ├─────┤ X ├──┼──┤ X ├──────░─┤M├─╫─────░─────────────░──╫──░──╫──░─ └───┘ └───┘┌─┴─┐└───┘ ░ └╥┘ ║ ┌─┐ ░ ░ ║ ░ ║ ░ q_4: ───────────────┤ X ├───────────░──╫──╫─┤M├─░─────────────░──╫──░──╫──░─ └───┘ ░ ║ ║ └╥┘ ░ ░ ║ ░ ║ ░ c: 5/══════════════════════════════════╩══╩══╩═══════════════════╩═════╩════ 3 0 4 1 2 q0=1 -> q3=1: 99937 / 99937 (100.0000%) COUNTS {'01101': 7234, '00110': 7416, '11011': 7152, '11111': 42588, '00100': 42654, '01001': 42963, '00000': 7527, '00010': 42466} A1B0 ┌───┐┌───┐ ┌───┐ ░ ┌─┐ ░ ░ ░ ░ q_0: ┤ X ├┤ X ├───────────────┤ X ├─░────┤M├────░──────────────░─────░─────░─ ├───┤└─┬─┘ └─┬─┘ ░ └╥┘ ░ ┌──────────┐ ░ ┌─┐ ░ ░ q_1: ┤ H ├──■────■────■─────────┼───░─────╫─────░─┤ Ry(-π/2) ├─░─┤M├─░─────░─ ├───┤ │ │ │ ░ ║ ░ ├──────────┤ ░ └╥┘ ░ ┌─┐ ░ q_2: ┤ H ├───────┼────■────■────■───░─────╫─────░─┤ Ry(-π/4) ├─░──╫──░─┤M├─░─ ├───┤ ┌─┴─┐ │ ┌─┴─┐ ░ ┌─┐ ║ ░ └──────────┘ ░ ║ ░ └╥┘ ░ q_3: ┤ X ├─────┤ X ├──┼──┤ X ├──────░─┤M├─╫─────░──────────────░──╫──░──╫──░─ └───┘ └───┘┌─┴─┐└───┘ ░ └╥┘ ║ ┌─┐ ░ ░ ║ ░ ║ ░ q_4: ───────────────┤ X ├───────────░──╫──╫─┤M├─░──────────────░──╫──░──╫──░─ └───┘ ░ ║ ║ └╥┘ ░ ░ ║ ░ ║ ░ c: 5/══════════════════════════════════╩══╩══╩════════════════════╩═════╩════ 3 0 4 1 2 q0=1 -> q3=1: 99657 / 99657 (100.0000%) COUNTS {'11011': 3684, '11001': 3642, '01001': 21250, '00100': 7400, '11111': 21417, '01101': 3633, '00110': 42608, '01111': 3680, '00000': 43012, '00010': 7323, '11101': 21242, '01011': 21109} A1B1 ┌───┐┌───┐ ┌───┐ ░ ┌─┐ ░ ░ ░ ░ q_0: ┤ X ├┤ X ├───────────────┤ X ├─░────┤M├────░──────────────░─────░─────░─ ├───┤└─┬─┘ └─┬─┘ ░ └╥┘ ░ ┌──────────┐ ░ ┌─┐ ░ ░ q_1: ┤ H ├──■────■────■─────────┼───░─────╫─────░─┤ Ry(-π/2) ├─░─┤M├─░─────░─ ├───┤ │ │ │ ░ ║ ░ ├─────────┬┘ ░ └╥┘ ░ ┌─┐ ░ q_2: ┤ H ├───────┼────■────■────■───░─────╫─────░─┤ Ry(π/4) ├──░──╫──░─┤M├─░─ ├───┤ ┌─┴─┐ │ ┌─┴─┐ ░ ┌─┐ ║ ░ └─────────┘ ░ ║ ░ └╥┘ ░ q_3: ┤ X ├─────┤ X ├──┼──┤ X ├──────░─┤M├─╫─────░──────────────░──╫──░──╫──░─ └───┘ └───┘┌─┴─┐└───┘ ░ └╥┘ ║ ┌─┐ ░ ░ ║ ░ ║ ░ q_4: ───────────────┤ X ├───────────░──╫──╫─┤M├─░──────────────░──╫──░──╫──░─ └───┘ ░ ║ ║ └╥┘ ░ ░ ║ ░ ║ ░ c: 5/══════════════════════════════════╩══╩══╩════════════════════╩═════╩════ 3 0 4 1 2 q0=1 -> q3=1: 100000 / 100000 (100.0000%) COUNTS {'01101': 3766, '00110': 7288, '11011': 3644, '11001': 3661, '01001': 21438, '00010': 42846, '00000': 7305, '01111': 3557, '11101': 21240, '01011': 21452, '11111': 21242, '00100': 42561} ============================================================================================================== TEST q0 00 01 10 11 N E(q1,q2) -------------------------------------------------------------------------------------------------------------- A0B0 0 7291 42607 42531 7310 99739 -0.707216 A0B0 1 42898 7228 7258 42877 100261 0.711034 A0B1 0 7527 42466 42654 7416 100063 -0.701328 A0B1 1 42963 7152 7234 42588 99937 0.712099 A1B0 0 43012 7323 7400 42608 100343 0.706547 A1B0 1 24892 24793 24875 25097 99657 0.003221 A1B1 0 7305 42846 42561 7288 100000 -0.708140 A1B1 1 25099 25096 25006 24799 100000 -0.002040 ============================================================================================================== Total CHSH = 0.7198800000000001 Conditional CHSH q0=0 : 0.00614254876732534 q0=1 : 1.428393871063332 Alternative CHSH q0=0 S0_alt = 2.8232305419315775 2*sqrt(2) = 2.8284271247461903 ======================================== q0 NOT MEASURED ======================================== A0B0 ┌───┐┌───┐ ┌───┐ ░ ░ ░ ░ ░ q_0: ┤ X ├┤ X ├───────────────┤ X ├─░─────░──────────────░─────░─────░──── ├───┤└─┬─┘ └─┬─┘ ░ ░ ┌───────┐ ░ ┌─┐ ░ ░ q_1: ┤ H ├──■────■────■─────────┼───░─────░──┤ Ry(0) ├───░─┤M├─░─────░──── ├───┤ │ │ │ ░ ░ ┌┴───────┴─┐ ░ └╥┘ ░ ┌─┐ ░ q_2: ┤ H ├───────┼────■────■────■───░─────░─┤ Ry(-π/4) ├─░──╫──░─┤M├─░──── ├───┤ ┌─┴─┐ │ ┌─┴─┐ ░ ░ └──────────┘ ░ ║ ░ └╥┘ ░ ┌─┐ q_3: ┤ X ├─────┤ X ├──┼──┤ X ├──────░─────░──────────────░──╫──░──╫──░─┤M├ └───┘ └───┘┌─┴─┐└───┘ ░ ┌─┐ ░ ░ ║ ░ ║ ░ └╥┘ q_4: ───────────────┤ X ├───────────░─┤M├─░──────────────░──╫──░──╫──░──╫─ └───┘ ░ └╥┘ ░ ░ ║ ░ ║ ░ ║ c: 5/══════════════════════════════════╩════════════════════╩═════╩═════╩═ 4 1 2 3 q0 ALWAYS 0 COUNTS {'11010': 7451, '00110': 7169, '11110': 42792, '01100': 7321, '01000': 42443, '00100': 42538, '00000': 7350, '00010': 42936} A0B1 ┌───┐┌───┐ ┌───┐ ░ ░ ░ ░ ░ q_0: ┤ X ├┤ X ├───────────────┤ X ├─░─────░─────────────░─────░─────░──── ├───┤└─┬─┘ └─┬─┘ ░ ░ ┌───────┐ ░ ┌─┐ ░ ░ q_1: ┤ H ├──■────■────■─────────┼───░─────░──┤ Ry(0) ├──░─┤M├─░─────░──── ├───┤ │ │ │ ░ ░ ┌┴───────┴┐ ░ └╥┘ ░ ┌─┐ ░ q_2: ┤ H ├───────┼────■────■────■───░─────░─┤ Ry(π/4) ├─░──╫──░─┤M├─░──── ├───┤ ┌─┴─┐ │ ┌─┴─┐ ░ ░ └─────────┘ ░ ║ ░ └╥┘ ░ ┌─┐ q_3: ┤ X ├─────┤ X ├──┼──┤ X ├──────░─────░─────────────░──╫──░──╫──░─┤M├ └───┘ └───┘┌─┴─┐└───┘ ░ ┌─┐ ░ ░ ║ ░ ║ ░ └╥┘ q_4: ───────────────┤ X ├───────────░─┤M├─░─────────────░──╫──░──╫──░──╫─ └───┘ ░ └╥┘ ░ ░ ║ ░ ║ ░ ║ c: 5/══════════════════════════════════╩═══════════════════╩═════╩═════╩═ 4 1 2 3 q0 ALWAYS 0 COUNTS {'11010': 7316, '00110': 7250, '11110': 42629, '01100': 7201, '01000': 42776, '00100': 42883, '00000': 7358, '00010': 42587} A1B0 ┌───┐┌───┐ ┌───┐ ░ ░ ░ ░ ░ q_0: ┤ X ├┤ X ├───────────────┤ X ├─░─────░──────────────░─────░─────░──── ├───┤└─┬─┘ └─┬─┘ ░ ░ ┌──────────┐ ░ ┌─┐ ░ ░ q_1: ┤ H ├──■────■────■─────────┼───░─────░─┤ Ry(-π/2) ├─░─┤M├─░─────░──── ├───┤ │ │ │ ░ ░ ├──────────┤ ░ └╥┘ ░ ┌─┐ ░ q_2: ┤ H ├───────┼────■────■────■───░─────░─┤ Ry(-π/4) ├─░──╫──░─┤M├─░──── ├───┤ ┌─┴─┐ │ ┌─┴─┐ ░ ░ └──────────┘ ░ ║ ░ └╥┘ ░ ┌─┐ q_3: ┤ X ├─────┤ X ├──┼──┤ X ├──────░─────░──────────────░──╫──░──╫──░─┤M├ └───┘ └───┘┌─┴─┐└───┘ ░ ┌─┐ ░ ░ ║ ░ ║ ░ └╥┘ q_4: ───────────────┤ X ├───────────░─┤M├─░──────────────░──╫──░──╫──░──╫─ └───┘ ░ └╥┘ ░ ░ ║ ░ ║ ░ ║ c: 5/══════════════════════════════════╩════════════════════╩═════╩═════╩═ 4 1 2 3 q0 ALWAYS 0 COUNTS {'00100': 7394, '01110': 3695, '11010': 3726, '00110': 43022, '01010': 21309, '00010': 7299, '00000': 42670, '11100': 21342, '11000': 3673, '01100': 3597, '01000': 21027, '11110': 21246} A1B1 ┌───┐┌───┐ ┌───┐ ░ ░ ░ ░ ░ q_0: ┤ X ├┤ X ├───────────────┤ X ├─░─────░──────────────░─────░─────░──── ├───┤└─┬─┘ └─┬─┘ ░ ░ ┌──────────┐ ░ ┌─┐ ░ ░ q_1: ┤ H ├──■────■────■─────────┼───░─────░─┤ Ry(-π/2) ├─░─┤M├─░─────░──── ├───┤ │ │ │ ░ ░ ├─────────┬┘ ░ └╥┘ ░ ┌─┐ ░ q_2: ┤ H ├───────┼────■────■────■───░─────░─┤ Ry(π/4) ├──░──╫──░─┤M├─░──── ├───┤ ┌─┴─┐ │ ┌─┴─┐ ░ ░ └─────────┘ ░ ║ ░ └╥┘ ░ ┌─┐ q_3: ┤ X ├─────┤ X ├──┼──┤ X ├──────░─────░──────────────░──╫──░──╫──░─┤M├ └───┘ └───┘┌─┴─┐└───┘ ░ ┌─┐ ░ ░ ║ ░ ║ ░ └╥┘ q_4: ───────────────┤ X ├───────────░─┤M├─░──────────────░──╫──░──╫──░──╫─ └───┘ ░ └╥┘ ░ ░ ║ ░ ║ ░ ║ c: 5/══════════════════════════════════╩════════════════════╩═════╩═════╩═ 4 1 2 3 q0 ALWAYS 0 COUNTS {'01110': 3776, '11010': 3674, '00110': 7223, '01100': 3611, '01000': 21380, '11000': 3648, '00000': 7315, '00010': 42571, '01010': 21662, '00100': 42361, '11110': 21422, '11100': 21357} ============================================================================================================== TEST q0 00 01 10 11 N E(q1,q2) -------------------------------------------------------------------------------------------------------------- A0B0 -- 49793 50387 49859 49961 200000 -0.002460 A0B1 -- 50134 49903 50084 49879 200000 0.000130 A1B0 -- 67370 32334 32333 67963 200000 0.353330 A1B1 -- 32343 67907 67329 32421 200000 -0.352360 ============================================================================================================== Total CHSH = 0.70336 ======================================== q0 MEASURED ======================================== A0B0 ┌───┐┌───┐ ┌───┐ ░ ░ ░ ░ ░ ┌─┐ q_0: ┤ X ├┤ X ├───────────────┤ X ├─░─────░──────────────░─────░─────░────┤M├ ├───┤└─┬─┘ └─┬─┘ ░ ░ ┌───────┐ ░ ┌─┐ ░ ░ └╥┘ q_1: ┤ H ├──■────■────■─────────┼───░─────░──┤ Ry(0) ├───░─┤M├─░─────░─────╫─ ├───┤ │ │ │ ░ ░ ┌┴───────┴─┐ ░ └╥┘ ░ ┌─┐ ░ ║ q_2: ┤ H ├───────┼────■────■────■───░─────░─┤ Ry(-π/4) ├─░──╫──░─┤M├─░─────╫─ ├───┤ ┌─┴─┐ │ ┌─┴─┐ ░ ░ └──────────┘ ░ ║ ░ └╥┘ ░ ┌─┐ ║ q_3: ┤ X ├─────┤ X ├──┼──┤ X ├──────░─────░──────────────░──╫──░──╫──░─┤M├─╫─ └───┘ └───┘┌─┴─┐└───┘ ░ ┌─┐ ░ ░ ║ ░ ║ ░ └╥┘ ║ q_4: ───────────────┤ X ├───────────░─┤M├─░──────────────░──╫──░──╫──░──╫──╫─ └───┘ ░ └╥┘ ░ ░ ║ ░ ║ ░ ║ ║ c: 5/══════════════════════════════════╩════════════════════╩═════╩═════╩══╩═ 4 1 2 3 0 q0=1 -> q3=1: 100030 / 100030 (100.0000%) COUNTS {'11011': 7328, '01101': 7348, '00110': 7424, '00000': 7335, '00010': 42513, '00100': 42698, '11111': 42901, '01001': 42453} A0B1 ┌───┐┌───┐ ┌───┐ ░ ░ ░ ░ ░ ┌─┐ q_0: ┤ X ├┤ X ├───────────────┤ X ├─░─────░─────────────░─────░─────░────┤M├ ├───┤└─┬─┘ └─┬─┘ ░ ░ ┌───────┐ ░ ┌─┐ ░ ░ └╥┘ q_1: ┤ H ├──■────■────■─────────┼───░─────░──┤ Ry(0) ├──░─┤M├─░─────░─────╫─ ├───┤ │ │ │ ░ ░ ┌┴───────┴┐ ░ └╥┘ ░ ┌─┐ ░ ║ q_2: ┤ H ├───────┼────■────■────■───░─────░─┤ Ry(π/4) ├─░──╫──░─┤M├─░─────╫─ ├───┤ ┌─┴─┐ │ ┌─┴─┐ ░ ░ └─────────┘ ░ ║ ░ └╥┘ ░ ┌─┐ ║ q_3: ┤ X ├─────┤ X ├──┼──┤ X ├──────░─────░─────────────░──╫──░──╫──░─┤M├─╫─ └───┘ └───┘┌─┴─┐└───┘ ░ ┌─┐ ░ ░ ║ ░ ║ ░ └╥┘ ║ q_4: ───────────────┤ X ├───────────░─┤M├─░─────────────░──╫──░──╫──░──╫──╫─ └───┘ ░ └╥┘ ░ ░ ║ ░ ║ ░ ║ ║ c: 5/══════════════════════════════════╩═══════════════════╩═════╩═════╩══╩═ 4 1 2 3 0 q0=1 -> q3=1: 99609 / 99609 (100.0000%) COUNTS {'11011': 7280, '00000': 7432, '00010': 42712, '01001': 42593, '01101': 7331, '00110': 7407, '11111': 42405, '00100': 42840} A1B0 ┌───┐┌───┐ ┌───┐ ░ ░ ░ ░ ░ ┌─┐ q_0: ┤ X ├┤ X ├───────────────┤ X ├─░─────░──────────────░─────░─────░────┤M├ ├───┤└─┬─┘ └─┬─┘ ░ ░ ┌──────────┐ ░ ┌─┐ ░ ░ └╥┘ q_1: ┤ H ├──■────■────■─────────┼───░─────░─┤ Ry(-π/2) ├─░─┤M├─░─────░─────╫─ ├───┤ │ │ │ ░ ░ ├──────────┤ ░ └╥┘ ░ ┌─┐ ░ ║ q_2: ┤ H ├───────┼────■────■────■───░─────░─┤ Ry(-π/4) ├─░──╫──░─┤M├─░─────╫─ ├───┤ ┌─┴─┐ │ ┌─┴─┐ ░ ░ └──────────┘ ░ ║ ░ └╥┘ ░ ┌─┐ ║ q_3: ┤ X ├─────┤ X ├──┼──┤ X ├──────░─────░──────────────░──╫──░──╫──░─┤M├─╫─ └───┘ └───┘┌─┴─┐└───┘ ░ ┌─┐ ░ ░ ║ ░ ║ ░ └╥┘ ║ q_4: ───────────────┤ X ├───────────░─┤M├─░──────────────░──╫──░──╫──░──╫──╫─ └───┘ ░ └╥┘ ░ ░ ║ ░ ║ ░ ║ ║ c: 5/══════════════════════════════════╩════════════════════╩═════╩═════╩══╩═ 4 1 2 3 0 q0=1 -> q3=1: 99491 / 99491 (100.0000%) COUNTS {'01111': 3489, '00010': 7230, '00000': 43110, '01011': 21316, '11101': 21212, '01001': 21255, '01101': 3593, '00110': 42864, '11001': 3718, '11011': 3575, '00100': 7305, '11111': 21333} A1B1 ┌───┐┌───┐ ┌───┐ ░ ░ ░ ░ ░ ┌─┐ q_0: ┤ X ├┤ X ├───────────────┤ X ├─░─────░──────────────░─────░─────░────┤M├ ├───┤└─┬─┘ └─┬─┘ ░ ░ ┌──────────┐ ░ ┌─┐ ░ ░ └╥┘ q_1: ┤ H ├──■────■────■─────────┼───░─────░─┤ Ry(-π/2) ├─░─┤M├─░─────░─────╫─ ├───┤ │ │ │ ░ ░ ├─────────┬┘ ░ └╥┘ ░ ┌─┐ ░ ║ q_2: ┤ H ├───────┼────■────■────■───░─────░─┤ Ry(π/4) ├──░──╫──░─┤M├─░─────╫─ ├───┤ ┌─┴─┐ │ ┌─┴─┐ ░ ░ └─────────┘ ░ ║ ░ └╥┘ ░ ┌─┐ ║ q_3: ┤ X ├─────┤ X ├──┼──┤ X ├──────░─────░──────────────░──╫──░──╫──░─┤M├─╫─ └───┘ └───┘┌─┴─┐└───┘ ░ ┌─┐ ░ ░ ║ ░ ║ ░ └╥┘ ║ q_4: ───────────────┤ X ├───────────░─┤M├─░──────────────░──╫──░──╫──░──╫──╫─ └───┘ ░ └╥┘ ░ ░ ║ ░ ║ ░ ║ ║ c: 5/══════════════════════════════════╩════════════════════╩═════╩═════╩══╩═ 4 1 2 3 0 q0=1 -> q3=1: 100023 / 100023 (100.0000%) COUNTS {'01111': 3642, '11001': 3699, '11011': 3622, '01001': 21213, '11101': 21516, '01011': 21290, '00000': 7206, '00010': 42424, '11111': 21446, '00100': 42964, '01101': 3595, '00110': 7383} ============================================================================================================== TEST q0 00 01 10 11 N E(q1,q2) -------------------------------------------------------------------------------------------------------------- A0B0 0 7335 42513 42698 7424 99970 -0.704731 A0B0 1 42453 7328 7348 42901 100030 0.706568 A0B1 0 7432 42712 42840 7407 100391 -0.704376 A0B1 1 42593 7280 7331 42405 99609 0.706633 A1B0 0 43110 7230 7305 42864 100509 0.710772 A1B0 1 24973 24891 24805 24822 99491 0.000995 A1B1 0 7206 42424 42964 7383 99977 -0.708153 A1B1 1 24912 24912 25111 25088 100023 -0.000230 ============================================================================================================== Total CHSH = 0.7113 Conditional CHSH q0=0 : 0.009817735122860105 q0=1 : 1.4144259763584974 Alternative CHSH q0=0 S0_alt = 2.828032354512611 2*sqrt(2) = 2.8284271247461903