The Relativistic Quantum Search: A Paradoxical Slowdown in Grover's Algorithm

Grover's algorithm enables quantum computers (QCs) to achieve computational speedups by reducing search complexity to the square root of N. Special relativity (SR), which governs the behaviour of systems at high velocities, gives rise to phenomena such as time dilation that alter the perception of time and motion. Because quantum computers rely on precise timing, relativistic effects could influence how their computations are perceived across reference frames. This study examines whether the computational speed of a QC increases due to its relativistic motion to an external observer. Using Python, a quantum computer executing Grover's algorithm at near-light speeds was simulated. The simulation calculated and compared the computation time of the QC in its rest and observer frames, as determined by the Lorentz factor. The results reveal a relativistic slowdown paradox: computation time within the QC's proper frame remains constant, while to an observer it increases significantly with velocity. At v=0.999c, computation appears considerably slower. These findings indicate that relativistic motion offers no computational advantage. Quantum operations progress in accordance with the system's proper time. Moreover, the system requires an impossibly large kinetic energy. As a result, SR fortifies rather than alleviates the physical constraints on computation.