Quantum simulation of the Lindblad equation using a unitary decomposition of operators

Assisted quantum simulation of open quantum systems

“…Based on the quantum-assisted quantum algorithm and VQSP, we investigate its application in quantum simulation of open quantum systems (OQS). Our simulation approach integrates three important components: a Choi–Jamiolkowski isomorphism technique 49 , 50 , 51 , 52 , 53 which maps the Lindblad master equation into a stochastic Schr dinger equation with a non-Hermitian Hamiltonian, a variational quantum state preparation (VQSP) subroutine (introduced in subsection variational quantum state preparation ) for the ancillary state preparation, and a method presented by works 54 , 55 to implement the block diagonal unitary.…”

“…Here, we assume a local Lindblad equation such that both and are written as the sums of the tensor products of at most a few local degrees of freedom of the system. 58 Under the Choi–Jamiolkowski isomorphism 49 , 50 , 51 , 52 , 53 (see method details ), the Equation 21 can be rewritten in form of stochastic Schrodinger equation, with a non-Hermitian Hamiltonian in a doubled Hilbert space where and denote the complex conjugate and transpose of operator , is a identity.…”

“…To exhibit our algorithms, we consider the dynamics given by a two-level system with an amplitude damping channel and an open version of the dissipative transverse field Ising model (DTFIM) on two sites. 52 …”

Simulating noisy quantum channels via quantum state preparation algorithms

“…Therefore, the state described by O ′ , to be prepared in the circuit-based quantum computer using state preparation algorithms, is given by Figure 6. Theoretical, simulated, and experimental results of the l 1 -norm quantum coherence of the spin state given by equation (35) under the action of the Wigner rotations implemented using the quantum state preparation-based protocol.…”

“…There are also many works in the literature that deal with the simulation of open system dynamics, with a variety of techniques applied. But as it is not our objective to make a complete review of the subject here, we refer the interested reader to [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40].…”