  Quantum circuit simulations are critical for evaluating quantum algorithms
and machines. However, the number of state amplitudes required for full
simulation increases exponentially with the number of qubits. In this study, we
leverage data compression to reduce memory requirements, trading computation
time and fidelity for memory space. Specifically, we develop a hybrid solution
by combining the lossless compression and our tailored lossy compression method
with adaptive error bounds at each timestep of the simulation. Our approach
optimizes for compression speed and makes sure that errors due to lossy
compression are uncorrelated, an important property for comparing simulation
output with physical machines. Experiments show that our approach reduces the
memory requirement of simulating the 61-qubit Grover's search algorithm from 32
exabytes to 768 terabytes of memory on Argonne's Theta supercomputer using
4,096 nodes. The results suggest that our techniques can increase the
simulation size by 2 to 16 qubits for general quantum circuits.
