We propose Q-BIOLAT, a framework for modeling and optimizing protein fitness landscapes in binary latent spaces. Starting from protein sequences, we leverage pretrained protein language models to obtain continuous embeddings, which are then transformed into compact binary latent representations. In this space, protein fitness is approximated using a quadratic unconstrained binary optimization (QUBO) model, enabling efficient combinatorial search via classical heuristics such as simulated annealing and genetic algorithms. On the ProteinGym benchmark, we demonstrate that Q-BIOLAT captures meaningful structure in protein fitness landscapes and enables the identification of high-fitness variants. Despite using a simple binarization scheme, our method consistently retrieves sequences whose nearest neighbors lie within the top fraction of the training fitness distribution, particularly under the strongest configurations. We further show that different optimization strategies exhibit distinct behaviors, with evolutionary search performing better in higher-dimensional latent spaces and local search remaining competitive in preserving realistic sequences. Beyond its empirical performance, Q-BIOLAT provides a natural bridge between protein representation learning and combinatorial optimization. By formulating protein fitness as a QUBO problem, our framework is directly compatible with emerging quantum annealing hardware, opening new directions for quantum-assisted protein engineering. Our implementation is publicly available at: https://github.com/HySonLab/Q-BIOLAT
Figures & tables
Figure 1. Overview of the Q-BioLat framework. Protein sequences are first encoded using a pretrained protein language model (ESM) to obtain continuous embeddings. These embeddings are transformed into binary latent representations through projection and binarization, enabling protein fitness to be modeled as a quadratic unconstrained binary optimization (QUBO) problem. The resulting latent fitness landscape can be explored using combinatorial optimization methods and is directly compatible with quantum annealing hardware. Optimized latent codes are mapped back to high-fitness protein sequences.
Samples
Dim=8
Dim=16
Dim=32
Dim=64
1000
0.175
0.291
0.168
0.196
2000
0.168
0.257
0.235
0.225
5000
0.236
0.287
0.338
0.332
10000
0.209
0.302
0.385
0.413
Table 1. Test Spearman correlation of the QUBO surrogate across dataset sizes and latent dimensions. Best-performing latent dimension for each dataset size is highlighted in bold.
Method
Improvement
NN True Fitness
NN Percentile
Simulated Annealing
1.529 ± 0.239
3.675 ± 0.192
84.65 ± 16.93
Genetic Algorithm
1.529 ± 0.239
3.675 ± 0.192
84.65 ± 16.93
Random Search
1.448 ± 0.276
3.602 ± 0.233
77.45 ± 19.95
Greedy Hill Climb
1.127 ± 0.510
3.723 ± 0.084
88.21 ± 8.68
Latent BO
-0.104 ± 0.523
3.216 ± 0.746
64.93 ± 21.54
Table 2. Multi-seed optimization results on the GFP benchmark using Q-BioLat with PCA-based binary latent representations (10,000 samples, 16 latent bits). Improvement denotes surrogate score gain relative to the starting point. NN True Fitness and NN Percentile are computed from the nearest retrieved training sequence to the optimized latent code. Best values in each column are highlighted in bold.
Figure 2. Effect of latent dimension on optimization and surrogate performance on the GFP benchmark. Each curve corresponds to a different dataset size. Moderate latent dimensions (e.g., 16–32) provide a favorable trade-off between predictive accuracy and optimization stability.
Representation
Spearman
NN True Fitness
NN Percentile
Random Projection
0.302
3.622 ± 0.123
74.76 ± 13.35
PCA Projection
0.302
3.675 ± 0.192
84.65 ± 16.93
Table 3. Comparison of latent representation methods on the GFP benchmark (10,000 samples, 16 latent bits). Although both methods achieve similar Spearman correlation, PCA yields improved optimization performance, highlighting the role of representation geometry in guiding combinatorial search.
Shanghai Artificial Intelligence Laboratory · Generative Symbolic Intelligence Lab (GenSI), Tsinghua University · Institute for AI Industry Research (AIR), Tsinghua University +1