Quantum state preparation and nonunitary evolution with diagonal operators

Exact Non-Markovian Quantum Dynamics on the NISQ Device Using Kraus Operators

“…Notwithstanding the advantage, one major concern of its quantum computing implementation is that M k ( t ) is not unitary, and therefore, additional steps are required to convert it to a unitary operation. Schemes for converting nonunitary operators to unitary ones exist, ,,,− and in Section , we will describe in detail the specific implementation used in this paper.…”

“…Specifically, .25ex2ex M k = U Σ V † where U and V are unitary matrices that can be directly implemented on a quantum computer. The ∑ matrix is a nonunitary diagonal and can be dilated to a unitary one in the following way . First, a unitary operator associated with the elements of ∑ is defined by .25ex2ex U normalΣ = ( .25ex2ex Σ + 0 0 Σ − ) where .25ex2ex normalΣ ± j = σ j ± i 1 − σ j 2 with σ j being the elements of ∑.…”

“…The circuit construction for the SVD is shown in Figure , where the ancilla qubit implements the Hadamard gates.…”

“…Since the insightful suggestion by Feynman and the pioneering demonstration by Lloyd, numerous studies have emerged in seeking efficient quantum algorithms for quantum simulations. − As for open quantum systems, although a wealth of literature exists for Markovian dynamics, including the construction of a universal set of semigroup generators , and the development of various techniques for efficient Lindblad dynamics simulation, − quantum algorithms for non-Markovian evolution are much less explored and are still in the nascent stage of advancement. Notable studies include Sweke et al who considered locally indivisible maps that are capable of describing non-Markovian systems and Head-Marden et al who used ensembles of Lindblad trajectories originating from different times to capture the non-Markovian behavior.…”

Quantum Simulation of the Radical Pair Dynamics of the Avian Compass

“…The interaction between the system and the bath is often too complex to be simulated exactly and thus requires approximations to average out the effects of the baththis results in the nonunitary dynamics of open quantum systems. Simulating the dynamics of quantum systems has been a main focus of quantum computing research, − yet relatively few quantum algorithms have been developed for simulating the dynamics of open quantum systems. − To this end, we have developed and demonstrated a general quantum algorithm for open quantum dynamics − that is capable of simulating general and complex physical systems. The quantum algorithm leverages the Sz.-Nagy unitary dilation approach to convert nonunitary time evolution operators into corresponding unitary operators, which can then be implemented on a quantum circuit.…”