Dissipative preparation of injective tensor network states

• URL: http://arxiv.org/abs/2605.25089v1
• Date: Sun, 24 May 2026 14:09:33 GMT
• Title: Dissipative preparation of injective tensor network states
• Abstract summary: Preparation of tensor network states is a fundamental prerequisite for a wide range of quantum simulation tasks.<n>In this paper, we construct both continuous-time and discrete-time geometrically local dissipative processes whose steady state is a given injective tensor network state.<n>Our method prepares all injective matrix product states on $N$ sites to an error $varepsilon$ in $O(log (N/varepsilon)$ time, yielding an exponential improvement over previously known dissipative preparation schemes.
• Score: 0.09999629695552194
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The preparation of tensor network states is a fundamental prerequisite for a wide range of quantum simulation tasks. While many unitary protocols for preparing these states have been investigated, dissipative state preparation provides a powerful alternative since it can be robust to noise and initialization errors. In this paper, we construct both continuous-time and discrete-time geometrically local dissipative processes whose unique steady state is a given injective tensor network state. Our method prepares all injective matrix product states on $N$ sites to an error $\varepsilon$ in $O(\log (N/\varepsilon))$ time, yielding an exponential improvement over previously known dissipative preparation schemes. For two and higher-dimensional tensor network states, we prove that when the tensors of the state are \emph{highly injective}, the constructed dissipative processes are rapid-mixing i.e., they prepare a state $\varepsilon$-close to the $N$-site target state in $O( \log (N/\varepsilon))$ time. For these states, our approach provides a polynomial speedup over known unitary methods for states defined on lattices and an exponential speedup for states on general bounded-degree graphs. We corroborate our theoretical results with numerical studies that indicate that the dissipative protocol can rapidly prepares states outside the high-injectivity assumption.

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