Fig 1.
(a) Example mapping of each possible codon for the amino acid Glycine (gray oval labeled “G”) to qubits. Gray boxes represent qubits labeled q0…q3, and the codon assigned to each qubit is shown next to the qubit label. (b) A penalty matrix is constructed to add infinite energy to cases where more than one codon is in the “1” state. In this example, qubit q2 is in the “1” state and the rest are in the “0” state, which returns an energetic penalty equal to 0. (c) Example mapping of codons for protein sequence GSK… to qubits. One codon is selected for each position in the sequence, highlighted in orange.
Fig 2.
Eigenvalues measured by QA vs GA scores.
Lower scores indicate higher probability of expression. Dashed line represents y = x. Error bars represent the standard deviation of 20 trials and are shown in blue.
Fig 3.
QA vs GA for 10 full-length proteins.
Dashed line represents y = x. Lower scores indicate higher probability of expression. Point labels indicate number of amino acids.
Fig 4.
(a) QAOA simulated scores vs exact scores. Each point represents a single run of the simulator for each peptide fragment. Lower scores indicate higher quality results. Trials that returned solutions with invalid mapping between codons and amino acids were excluded. Inset shows a histogram of the QAOA score to exact score ratios where it can be seen that the majority of the ratios are close to 1. (b) Number of qubits required to simulate each of the 313 peptide fragments of length 4.
Table 1.
Constants used in Eq (15).