Unitary Quantum Electron Dynamics. II

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.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.

arXiv:2207.07112Jul 14, 20224 citations

Quantum Particle Dynamics

Ciaran P. Ryan

Philosophical StudiesJan 1, 195912 citations

Non-unitary scattering and capture. II. Quantum dynamical semigroup theory

E. B. Davies

Jan 1, 19803 citations

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.