Pareto-Efficient Quantum Circuit Simulation Using Tensor Contraction Deferral

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 circuits of such and larger sizes is a fundamental step to assess both the correctness, performance, and scaling behavior of quantum algorithms and the fidelities of quantum devices. However, resource requirements for such calculations on classical computers grow exponentially. We show that deferring tensor contractions can extend the boundaries of what can be computed on classical systems. To demonstrate this technique, 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 approaches 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 resource requirements.