Deterministic Realization of Classical Dissipation on Quantum Computers

• URL: http://arxiv.org/abs/2604.25429v1
• Date: Tue, 28 Apr 2026 09:36:40 GMT
• Title: Deterministic Realization of Classical Dissipation on Quantum Computers
• Abstract summary: Lattice Boltzmann (LB) on quantum devices must reconcile unitary gate evolution with the dissipative emph collide step.<n>In the multiple-relaxation-time (MRT) class, we work in the common setting of emphmodewise diagonal moment relaxation, $m_r'=_r,m_r$ with $_rin[-1,1]$.<n>The main result is the dissipative MRT block; construction of the equilibrium moment vector$mmathrmeq=Mfmathrm
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Lattice Boltzmann (LB) on quantum devices must reconcile unitary gate evolution with the dissipative \emph{collision} step. In the multiple-relaxation-time (MRT) class, we work in the common setting of \emph{modewise diagonal} moment relaxation, $δm_r'=λ_r\,δm_r$ with $λ_r\in[-1,1]$ (overrelaxation if $λ_r<0$). Embedding that contraction in a unitary by block encoding or a linear combination of unitaries (LCU) typically yields subunitary success probability that decays multiplicatively across modes, sites, and time, a key bottleneck for quantum LB. \emph{For the dissipative MRT block alone} we give a \emph{block-encoding-free} construction: a signed \emph{two-rail} population encoding, then a completely positive trace-preserving (CPTP) map (per-rail amplitude damping with survival $|λ_r|$ and, if $λ_r<0$, a rail SWAP) so that, after the decode, the map agrees with classical MRT relaxation exactly (expectations of the rail number operators, common encoding--decode scale). Trace preservation gives success probability $1$ for that substage. The main result is the dissipative MRT block; construction of the equilibrium moment vector~$m^{\mathrm{eq}}=Mf^{\mathrm{eq}}$ (prescribed~$f^{\mathrm{eq}}$, host moment matrix~$M$; notation as in Section~\ref{subsec:generic-mrt}), moment transforms, streaming, and boundaries are composed with it as in a standard host pipeline and lie outside the scope of the formal theorem. Hybrid and fully coherent encodings, adaptive scales, Carleman-based context, and a one-rail no-go in the same nonnegative population framework are in the main text. Audits of the open-channel map on a long LBM collide-stream simulation and on stencil-free inputs both match the target to machine precision.

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