Quantum Algorithm for Dissipative Dynamics: An Application to Electromagnetic Wave Propagation in Collisional Plasma*

Quantum computers are suitable for closed quantum systems as they are adept in performing unitary, probability preserving, operations. However, in a dissipative system, the Hamiltonian describing the dynamics is not Hermitian; its anti-Hermitian part, associated with dissipation, is characterized by a non-unitary evolution operator. As such, it is not directly amenable to implementation on a quantum computer. Non-unitary operators arise in open quantum systems that interact with an external environment and lead to decoherence and dissipation. We put forth a theoretical description based on the Kraus representation of open quantum systems in which dissipation is formulated as a non-trace preserving quantum channel. This is combined with a probabilistic unitary dilation algorithm that can be applied to dissipative plasma. Consequently, we can study electromagnetic wave propagation in a cold magnetized plasma in which dissipation – the external “environment”– is characterized by a phenomenological collision frequency. The associated algorithm uses one ancilla qubit for the environment rendering the unitary dilation optimal. For a d-dimensional system with a r-dimensional subspace characterizing dissipation, a unitary evolution for the composite system can be implemented in r number of multiqubit rotations. This is an improvement in circuit depth by a factor of  r/d.