A Novel Tensor Network Algorithm for Simulating Large Quantum Circuits

Simulations of quantum circuits often involve an exponential number of
resources, suffering from the so called "curse of dimensionality."
Because of this, obtaining measurement information from states output by
high-depth circuits is challenging. To overcome this limitation, we
employ a novel tensor network methodology to compute expectation values
that resembles the Keldysh formalism. This algorithm, which we term ICD (Iterative Contraction Decomposition), iteratively alternates between sequences of tensor contractions
and global sweeps of tensor pair Schmidt decompositions. We
demonstrate our algorithm's ability to determine measurement outcomes
for random circuits of up to 40 qubits with circuit depths of 80 steps.