Fig 1.
Schematic representation of our circuits.
A) Different steps of Grover’s algorithm; B) Different sub-steps implemented in our Oracle. The parallel lines represent qubits. The blue lines show the n qubits and the red lines show the work qubits. In the oracle, if |k〉 is an answer state, f(k) = 1, otherwise it is 0.
Fig 2.
Schematic representations of protein models.
SP model with: a) Two designable sites; b) Three designable sites; c) Six designable sites with I) three, II) four, and III) five pair-wise interactions. MR model with: d) Two designable sites; e) Three designable sites. The designable sites are shown as circles with numbers. The red dashed lines represent the interactions among the designable sites. In a–c) the pattern of interactions between the sites are provided for each structure. The checkered circles are non-interacting residues. In this study, there are no geometrical differences between residues, and all are being treated as identical beads represented with circles. In d) and e) the is the corresponding distance reciprocal between designable sites i and j.
Fig 3.
Energy tables to represent the pair-wise interactions in our systems and the binary representation of residues.
Energy tables for: a) The SP model; b) The MR model. c) Binary representation of residues in the energy table. d) Energy table and the residue representations for the HP protein model. In a–c) H1 and H2 represent two types of hydrophobic residues, Pol1 and Pol2 represent two types of polar residues, Pos represents a positive residue, Neg represents a negative residue, and two types of “other” residues that do not fit in any of the previous categories are represented by X1 and X2. Note that all energies in our tables have qualitative values. In d) H represents hydrophobic and P represents polar residues.
Table 1.
A brief description of each circuit in this study.
Fig 4.
Histogram representations of the probability of finding each state (64 in total) in circuits with two designable sites.
Results for circuits in the SP model with: a) Eth = -3 and R = 1; b) Eth = -3 and R = Rmax = 4; c) Eth = -2 and R = 1; d) Eth = -2 and R = Rmax = 2. Results for circuits in the MR model with: e) Eth = 95%Emin and R = 1; f) Eth = 95%Emin and R = Rmax = 4; g) Eth = 85%Emin and R = 1; h) Eth = 85%Emin and R = Rmax = 3.
Fig 5.
Probability of finding answer states in different systems as a function of normalized number of iterations (R/Rmax).
Results for a) The SP model; b) The MR model; The inset in a), represents data for the first few R for systems with six designable sites.
Fig 6.
The maximum number of iterations (Rmax) values as a function of normalized number of states (N/M).
The circles represent the data for the SP model and the stars are the data for the MR model. The magenta dashed line shows the Rmax threshold for Grover’s algorithm, while the black dashed line is the threshold of the classic realm.
Fig 7.
Histogram representations of probabilities for each state in the IBM-SP model circuit.
a) Results of the circuit, using the ideal MPS quantum computer simulator. b) Results of the circuit using: I) gate fidelity, measurement fidelity, initialization fidelity and qubit mapping of ibmq_toronto in the simulator; II) Real ibm_toronto device averaged over 20 different runs. c) Results of the circuit using: I) gate fidelity, measurement fidelity, initialization fidelity and qubit mapping of ibmq_montreal in the simulator; II) Real ibm_montreal device averaged over 30 different runs. In b) and c), the data bars with different colours show results for five separate runs. The error bars represent the standard deviation from the mean value. The numbers on each set of bars show the average probability of the state. The number of samplings for all plots is set to 8,192 shots.