Classically simulating quantum systems is challenging, as even noiseless
$n$-qubit quantum states scale as $2^n$. The complexity of noisy quantum
systems is even greater, requiring $2^n \times 2^n$-dimensional density
matrices. Various approximations reduce density matrix overhead, including
quantum trajectory-based methods, which instead use an ensemble of $m \ll 2^n$
noisy states. While this method is dramatically more efficient, current
implementations use unoptimized sampling, redundant state preparation, Und
single-shot data collection. In this manuscript, we present the Pre-Trajectory
Sampling technique, increasing the efficiency and utility of trajectory
simulations by tailoring error types, batching sampling without redundant
computation, and collecting error information. We demonstrate the effectiveness
of our method with both a mature statevector simulation of a 35-qubit quantum
error-correction code and a preliminary tensor network simulation of 85 qubits,
yielding speedups of up to $10^6$x and $16$x, as well as generating massive
datasets of one trillion and one million shots, respectively.

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