Quantum simulation of dissipation for Maxwell equations in dispersive media

• URL: http://arxiv.org/abs/2308.00056v2
• Date: Wed, 15 May 2024 12:23:18 GMT
• Title: Quantum simulation of dissipation for Maxwell equations in dispersive media
• Authors: Efstratios Koukoutsis, Kyriakos Hizanidis, Abhay K. Ram, George Vahala,
• Abstract summary: dissipation appears in the Schr"odinger representation of classical Maxwell equations as a sparse diagonal operator occupying an $r$-dimensional subspace. The unitary operators can be implemented through qubit lattice algorithm (QLA) on $n$ qubits. The non-unitary-dissipative part poses a challenge on how it should be implemented on a quantum computer.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In dispersive media, dissipation appears in the Schr\"odinger representation of classical Maxwell equations as a sparse diagonal operator occupying an $r$-dimensional subspace. A first order Suzuki-Trotter approximation for the evolution operator enables us to isolate the non-unitary operators (associated with dissipation) from the unitary operators (associated with lossless media). The unitary operators can be implemented through qubit lattice algorithm (QLA) on $n$ qubits. However, the non-unitary-dissipative part poses a challenge on how it should be implemented on a quantum computer. In this paper, two probabilistic dilation algorithms are considered for handling the dissipative operators. The first algorithm is based on treating the classical dissipation as a linear amplitude damping-type completely positive trace preserving (CPTP) quantum channel where the combined system-environment must undergo unitary evolution in the dilated space. The unspecified environment can be modeled by just one ancillary qubit, resulting in an implementation scaling of $\textit{O}(2^{n-1}n^2)$ elementary gates for the dilated unitary evolution operator. The second algorithm approximates the non-unitary operators by the Linear Combination of Unitaries (LCU). We obtain an optimized representation of the non-unitary part, which requires $\textit{O}(2^{n})$ elementary gates. Applying the LCU method for a simple dielectric medium with homogeneous dissipation rate, the implementation scaling can be further reduced into $\textit{O}[poly(n)]$ basic gates. For the particular case of weak dissipation we show that our proposed post-selective dilation algorithms can efficiently delve into the transient evolution dynamics of dissipative systems by calculating the respective implementation circuit depth. A connection of our results with the non-linear-in-normalization-only (NINO) quantum channels is also presented.

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