Xiyuan (Tommy) Guo · Quantum Error Correction

About

|Xīyuán⟩ = |希⟩ ⊗ |源⟩ ↦ |⟩ ⊗ |⟩ — the wellspring of hope.

I’m a Computer Science undergraduate at UVA working on quantum error correction and constrained optimization.

My work grew from constrained image reconstruction at Yale into quantum LDPC decoding. I’m interested in the guarantees and limits of optimization-based decoders under realistic noise.

AFK I do Muay Thai with my sheltie ∪･ω･∪

Selected research

Independent research · Jul 2026–present

qudec · Quantum LDPC decoding

LP and batched ADMM decoders for bivariate bicycle codes, evaluated against BP+OSD under increasingly realistic noise.

Methods & findings

Method: Parity-polytope relaxations, with two-slice projection for batched PyTorch ADMM. Small-code checks use exhaustive minimum-weight baselines and LP objective comparisons.
Evaluation: LP: [[144,12,12]] under code-capacity noise. ADMM: [[72,12,6]] with time-expanded detectors under phenomenological noise, followed by circuit-level sweeps.
Finding: LLR normalization and penalty tuning strongly affected performance. Weighted ADMM improved one primary test cell, but showed no consistent advantage over BP+OSD across the broader sweep.

qudec

Yale · Prof. Mengxia Liu’s group

Constrained image reconstruction

Recovering 81 spectral bands and four Stokes channels from a single lensless speckle image using physical constraints and sparsity priors.

Methods & findings

Method: A consensus ADMM solver in PyTorch, combining spectral-sparsity proximal updates with projection onto the physically admissible Stokes cone; executed on Rivanna GPUs.
Finding: The coherency matrix connects polarization constraints to positive semidefiniteness. This work shaped my interest in how physical structure constrains inference from incomplete measurements.

lensless-recon

UVA BAL Lab · Prof. Xin Cynthia Tong

Covariance-constrained imputation

PRISM adjusts missing-data imputations toward a model-implied covariance structure through constrained projection.

Methods & findings

Method: A C++17/RcppArmadillo solver with projected gradient updates and first-order stationarity diagnostics. Supported by a $5,000 Double Hoo Research Grant.
Finding: In a separate exploratory three-qubit tomography study, random-forest imputation offered no benefit over a linear baseline; density-matrix projection enforced positivity and unit trace.

prism