Breaking the 49-Qubit Barrier in the Simulation of Quantum Circuits

With the current rate of progress in quantum computing technologies, 50-qubit systems will soon become a reality. To assess, refine and advance the design and control of these devices, one needs a means to test and evaluate their fidelity. This in turn requires the capability of computing ideal quantum state amplitudes for devices of such sizes and larger. In this study, we present a new approach for this task that significantly extends the boundaries of what can be classically computed. We demonstrate our method by presenting results obtained from a calculation of the complete set of output amplitudes of a universal random circuit with depth 27 in a 2D lattice of $7 \times 7$ qubits. We further present results obtained by calculating an arbitrarily selected slice of $2^{37}$ amplitudes of a universal random circuit with depth 23 in a 2D lattice of $8 \times 7$ qubits. Such calculations were previously thought to be impossible due to impracticable memory requirements. Using the methods presented in this paper, the above simulations required 4.5 and 3.0 TB of memory, respectively, to store calculations, which is well within the limits of existing classical computers.