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Patch routing could cut leading T cost 15–17× in a 120×120 square-lattice J1-J2 Heisenberg benchmark near maximal frustration

Minzhao Liu and coauthors say patch routing pays the local block-encoding cost once per query, regardless of lattice size.

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Submitted Oct. 23, 2026, Minzhao Liu and coauthors' paper describes routing a block-encoded patch across a lattice. For a 120×120 square-lattice J1-J2 Heisenberg model near maximal frustration, they calculate a 15–17× reduction in leading T cost per qubitized-QPE run versus prior Pauli LCU constructions, excluding initial state preparation and overlap. They report smaller reductions for Fermi-Hubbard and honeycomb spin-liquid simulations; @arxivupdates praised the work.

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In a paper submitted Oct. 23, 2026, Minzhao Liu and six coauthors introduce patch routing for block-encoding lattice Hamiltonians. They report lower calculated costs for several quantum-simulation models, with their largest stated reduction tied to a specific Heisenberg benchmark.

The authors say they first block-encode a small local patch, then use a “SWAP-style routing network” to apply that encoding across the lattice. According to their abstract, the expensive local encoding cost is paid only once per query, regardless of lattice size. The comparatively inexpensive routing network grows linearly with lattice size.

For a 120×120 square-lattice J1-J2 Heisenberg model near maximal frustration (J2/J1 = 0.4–0.6), the authors calculate a 15–17× reduction in leading T cost per qubitized-QPE run compared with prior state-of-the-art Pauli LCU constructions. That comparison excludes initial state preparation and overlap. They also report approximately 3× lower corresponding costs for a 120×120 Fermi-Hubbard model at half-filling and a 5× reduction in leading cost for time evolution of a honeycomb spin-liquid model on 120×120 unit cells.

In an Oct. 26 post, @arxivupdates called the work a “New advance in quantum simulation!” and described T-gate cost cuts of “up to 17x” on hard quantum models. The post links to the paper, whose abstract confines the 15–17× comparison to the specified Heisenberg model and cost measure.

Patch routing could cut leading T cost 15–17× in a 120×120 square-lattice J1-J2 Heisenberg benchmark near maximal frustration

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