  Due to the unreliability and limited capacity of existing quantum computer
prototypes, quantum circuit simulation continues to be a vital tool for
validating next generation quantum computers and for studying variational
quantum algorithms, which are among the leading candidates for useful quantum
computation. Existing quantum circuit simulators do not address the common
traits of variational algorithms, namely: 1) their ability to work with noisy
qubits and operations, 2) their repeated execution of the same circuits but
with different parameters, and 3) the fact that they sample from circuit final
wavefunctions to drive a classical optimization routine. We present a quantum
circuit simulation toolchain based on logical abstractions targeted for
simulating variational algorithms. Our proposed toolchain encodes quantum
amplitudes and noise probabilities in a probabilistic graphical model, and it
compiles the circuits to logical formulas that support efficient repeated
simulation of and sampling from quantum circuits for different parameters.
Compared to state-of-the-art state vector and density matrix quantum circuit
simulators, our simulation approach offers greater performance when sampling
from noisy circuits with at least eight to 20 qubits and with around 12
operations on each qubit, making the approach ideal for simulating near-term
variational quantum algorithms. And for simulating noise-free shallow quantum
circuits with 32 qubits, our simulation approach offers a $66\times$ reduction
in sampling cost versus quantum circuit simulation techniques based on tensor
network contraction.
