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‎docs/poster/amat-dark.png‎

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‎docs/poster/bibliography.bib‎

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@article{Roffe2020,
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title={Decoding across the quantum LDPC code landscape},
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author={Roffe, Joschka and White, David R and Burton, Simon and Campbell, Earl},
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journal={Physical Review Research},
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volume={2},
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number={4},
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pages={043423},
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year={2020},
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publisher={APS},
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note={arXiv:2005.07016}
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}
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@article{Chen2024,
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title={Improved Belief Propagation Decoding Algorithms for Surface Codes},
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author={Chen, Kai-wen and others},
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journal={arXiv preprint arXiv:2407.11523},
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year={2024}
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}
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@article{Liu2025,
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title={Exact Decoding of Repetition Code under Circuit Level Noise},
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author={Liu, Jin-Guo and others},
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journal={arXiv preprint arXiv:2501.03582},
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year={2025}
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}
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@article{Liu2023,
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author = {Liu, Jin-Guo and Gao, Xun and Cain, Madelyn and Lukin, Mikhail D. and Wang, Sheng-Tao},
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title = {Computing Solution Space Properties of Combinatorial Optimization Problems Via Generic Tensor Networks},
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journal = {SIAM Journal on Scientific Computing},
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volume = {45},
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number = {3},
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pages = {A1239-A1270},
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year = {2023},
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eprint = {https://doi.org/10.1137/22M1501787}
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}
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@article{Higgott2023,
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title={Improved decoding of circuit noise and fragile boundaries of tailored surface codes},
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author={Higgott, Oscar and Breuckmann, Nikolas P},
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journal={Physical Review X},
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volume={13},
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number={3},
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pages={031007},
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year={2023},
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publisher={APS},
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note={arXiv:2303.15933}
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}
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@article{Dennis2002,
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title={Topological quantum memory},
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author={Dennis, Eric and Kitaev, Alexei and Landahl, Andrew and Preskill, John},
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journal={Journal of Mathematical Physics},
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volume={43},
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number={9},
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pages={4452--4505},
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year={2002},
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publisher={AIP}
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}

‎docs/poster/email.png‎

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‎docs/poster/github-dark.png‎

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‎docs/poster/main.pdf‎

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‎docs/poster/main.typ‎

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#import "@preview/peace-of-posters:0.5.6" as pop
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#import "@preview/cetz:0.4.1": canvas, draw
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#import "@preview/qec-thrust:0.1.1": *
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#show link: set text(blue)
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#set page("a0", margin: 1cm)
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#pop.set-poster-layout(pop.layout-a0)
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#pop.set-theme(pop.uni-fr)
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#set text(size: pop.layout-a0.at("body-size"))
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#let box-spacing = 1.2em
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#set columns(gutter: box-spacing)
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#set block(spacing: box-spacing)
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#pop.update-poster-layout(spacing: box-spacing)
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#pop.title-box(
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"BPDecoderPlus: Circuit-Level Quantum Error Correction with Belief Propagation and Tropical Tensor Networks",
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authors: [Si-Yuan Chen$""^*$, Meng-Kun Liu$""^*$, Shen Yang$""^*$ and Jin-Guo Liu$""^*$],
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institutes: text(36pt)[
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],
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title-size: 1.3em,
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)
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#columns(2,[
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#pop.column-box(heading: "Abstract")[
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Quantum error correction (QEC) is essential for fault-tolerant quantum computing. We present *BPDecoderPlus*, a Python package implementing two complementary approaches for decoding surface codes under circuit-level noise:
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1. *BP+OSD Decoder*: Belief propagation with ordered statistics decoding post-processing, achieving near-optimal performance on quantum LDPC codes.
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2. *Tropical Tensor Networks*: Exact Most Probable Explanation (MPE) computation via tropical semiring contraction, providing optimal solutions for moderate-size instances.
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Our implementation correctly resolves the circuit-level error threshold at $approx 0.7%$ for rotated surface codes, validating against established literature. The package features GPU acceleration via PyTorch, comprehensive CLI tools, and integration with Google's Stim simulator.
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]
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#pop.column-box(heading: "Rotated Surface Code")[
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#grid(columns: 2, gutter: 20pt,
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canvas(length: 5cm, {
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import draw: *
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surface-code((0, 0), size: 2.5, 3, 3, name: "sc")
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}),
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box[
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*Detection events* (not raw syndromes):
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- Measurement errors flip syndrome values
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- Event = XOR of consecutive measurements
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- Localizes errors in space-time
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*Detector Error Model* (DEM):
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- Error probabilities per fault
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- Detector-error associations
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- Observable flip annotations
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]
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)
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#align(center)[
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#box(stroke: 2pt, inset: 12pt, radius: 5pt)[
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Detection Events $arrow.r$ *Decoder* $arrow.r$ Observable Flip Prediction
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]
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]
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]
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#let hba = pop.uni-fr.heading-box-args
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#hba.insert("stroke", (paint: gradient.linear(blue, purple, red), thickness: 10pt))
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#let bba = pop.uni-fr.body-box-args
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#bba.insert("inset", 30pt)
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#bba.insert("stroke", (paint: gradient.linear(blue, purple, red), thickness: 10pt))
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#pop.column-box(heading: "BP+OSD Decoder", stretch-to-next: true)[
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*Belief Propagation* iteratively passes messages on a factor graph to compute marginal probabilities. For QEC, the factor graph is derived from the parity check matrix $H$.
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#grid(columns: 2, gutter: 40pt,
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canvas(length: 1.2cm, {
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import draw: *
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// Variable nodes (circles)
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for (i, x) in ((0, -2), (1, 0), (2, 2)) {
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circle((x, 2), radius: 0.4, name: "v" + str(i), stroke: 2pt, fill: rgb("#e3f2fd"))
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content((x, 2), [$e_#i$])
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}
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// Factor nodes (squares)
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for (i, x) in ((0, -1), (1, 1)) {
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rect((x - 0.4, -0.4), (x + 0.4, 0.4), name: "f" + str(i), stroke: 2pt, fill: rgb("#fff3e0"))
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content((x, 0), [$d_#i$])
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}
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// Edges
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line("v0", "f0", stroke: 2pt)
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line("v1", "f0", stroke: 2pt)
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line("v1", "f1", stroke: 2pt)
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line("v2", "f1", stroke: 2pt)
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content((0, -1.5), [Factor Graph])
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}),
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box[
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*Message passing:*
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$ mu_(v arrow f) = product_(f' in N(v) \\ f) mu_(f' arrow v) $
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$ mu_(f arrow v) = sum_(bold(x): x_v = 0,1) psi_f (bold(x)) product_(v' in N(f) \\ v) mu_(v' arrow f) $
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]
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)
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*Ordered Statistics Decoding (OSD)* post-processes BP output:
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1. Sort variables by BP reliability
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2. Fix most reliable bits using Gaussian elimination
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3. Exhaustively search remaining bits (OSD-$w$ searches $w$ bits)
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#highlight[Key insight: BP provides soft information; OSD provides guaranteed valid codeword.]
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]
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#colbreak()
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#pop.column-box(heading: "Tropical Tensor Networks for MPE")[
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The *Most Probable Explanation* (MPE) problem finds the most likely error pattern given observations. We solve this exactly using tropical tensor networks.
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*Tropical Semiring:* $(RR union {-infinity}, max, +)$
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- Addition $arrow.r$ max operation
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- Multiplication $arrow.r$ standard addition
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#grid(columns: 2, gutter: 30pt,
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box[
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*Standard tensor contraction:*
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$ C_(i k) = sum_j A_(i j) dot B_(j k) $
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],
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box[
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*Tropical contraction:*
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$ C_(i k) = max_j (A_(i j) + B_(j k)) $
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]
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)
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For probabilistic graphical models in log-space:
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$ log P(bold(x)) = sum_f log psi_f (bold(x)_f) $
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#highlight[Tropical contraction computes $max_(bold(x)) log P(bold(x))$ exactly!]
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*Implementation highlights:*
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- Uses `omeco` for optimal contraction ordering
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- PyTorch backend with GPU support
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- Backtracking recovers the optimal assignment
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- Complexity: $O(2^(text("treewidth")))$
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]
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#pop.column-box(heading: "Threshold Results")[
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#align(center)[
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#image("threshold_comparison.png", width: 95%)
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]
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#table(
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columns: 4,
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align: center,
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stroke: 0.5pt,
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table.header([*Noise Model*], [*BP Only*], [*BP+OSD*], [*Optimal*]),
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[Code capacity], [N/A], [$approx 9.9%$], [$10.3%$],
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[Circuit-level], [N/A], [$approx 0.7%$], [$approx 1%$],
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)
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#grid(columns: 2, gutter: 20pt,
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box[
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*Configuration:*
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- BP: 60 iterations, min-sum
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- Damping: 0.2, OSD order: 10
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],
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box[
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*Validation:*
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- Matches ldpc library @Higgott2023
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- Curves cross at threshold
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]
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)
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]
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#pop.column-box(heading: "Software Architecture")[
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#align(center)[
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#box(stroke: 1pt, inset: 10pt, radius: 3pt)[
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Stim Circuit $arrow.r$ DEM $arrow.r$ Factor Graph $arrow.r$ BP/Tropical $arrow.r$ Prediction
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]
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]
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*Key features:*
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- *Stim integration*: Generate noisy circuits for rotated surface codes
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- *DEM parsing*: Two-stage processing (separator splitting + hyperedge merging)
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- *PyTorch backend*: GPU-accelerated batch inference
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- *CLI tools*: `generate-noisy-circuits` for dataset creation
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- *Modular design*: BP and Tropical modules are independent
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#highlight[Developed with *vibe coding*: human-AI collaboration using Claude Code accelerated development from concept to working threshold plots.]
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#link("https://github.com/TensorBFS/BPDecoderPlus")[github.com/TensorBFS/BPDecoderPlus]
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]
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#pop.column-box(heading: "References", stretch-to-next: true)[
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#bibliography("bibliography.bib", title: none)
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]
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])
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#pop.bottom-box()[
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#align(right, [#align(horizon, grid(columns: 5, column-gutter: 30pt, image("github-dark.png", width: 70pt), "TensorBFS/BPDecoderPlus", h(50pt), image("email.png", width: 70pt), "jinguoliu@hkust-gz.edu.cn"))])
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]

‎docs/poster/threshold_comparison.png‎

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