Standard quantum mechanics has been formulated with complex-valued Schrodinger equations, wave functions, operators, and Hilbert spaces. However, previous work has shown possible to simulate quantum systems using only real numbers by adding extra qubits and exploiting an enlarged Hilbert space. A fundamental question arises: are the complex numbers really necessary for the quantum mechanical description of nature? To answer this question, a non-local game has been developed to reveal a contradiction between a multiqubit quantum experiment and a player using only real numbers. Here, based on deterministic and high-fidelity entanglement swapping with superconducting qubits, we experimentally implement the Bell-like game and observe a quantum score of 8.09(1), which beats the real number bound of 7.66 by 43 standard deviations. Our results disprove the real-number description of nature and establish the indispensable role of complex numbers in quantum mechanics.
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