  Electronic structure and transport in realistically-sized systems often
require an open quantum system (OQS) treatment, where the system is defined in
the context of an environment. As OQS evolution is non-unitary, implementation
on quantum computers -- limited to unitary operations -- is challenging. We
present a general framework for OQSs where the system's $d \times d$ density
matrix is recast as a $d^{2}$ wavefunction which can be evolved by unitary
transformations. This theory has two significant advantages over conventional
approaches: (i) the wavefunction requires only an $n$-qubit, compared to
$2n$-qubit, bath for an $n$-qubit system and (ii) the purification includes
dynamics of any pure-state universe. We demonstrate this method on a two-level
system in a zero temperature amplitude damping channel and a two-site quantum
Ising model. Quantum simulation and experimental-device results agree with
classical calculations, showing promise in simulating non-unitary operations on
NISQ quantum devices.
