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

With the current rate of progress in quantum computing technologies, systems with more than 50 qubits will soon become reality. Computing ideal quantum state amplitudes for devices of such and larger sizes is a fundamental step to assess their fidelity, but memory requirements for such calculations on classical computers grow exponentially. In this study, we present a new approach for this task that extends the boundaries of what can be computed on a classical system. We present 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, and 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. Combining our methodology with other decomposition techniques found in the literature, we show that we can simulate $7 \times 7$-qubit random circuits to arbitrary depth by leveraging secondary storage. These calculations were thought to be impossible due to memory requirements; our methodology requires memory within the limits of existing classical computers.