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REVIEW 4 major objections 4 minor 62 references

Quantum Algorithm for Protein Structure Prediction Using the Face-Centered Cubic Lattice

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read First quantum FCC-lattice folding recovers a real peptide's ground state on quantum hardware, with the newer Heron processor sampling the optimal solution up to three times more often than the older Eagle.

desk verdict First FCC-lattice QPSP encoding with real hardware runs, but missing ancilla constraints and unspecified penalty weights mean the 'ground state recovery' claim cannot be fully verified as written. read the letter →

arxiv 2507.08955 v1 pith:R45XCBR2 submitted 2025-07-11 quant-ph q-bio.BM

Rui-Hao Li , Hakan Doga , Bryan Raubenolt , Sarah Mostame , Nicholas DiSanto , Fabio Cumbo , Jayadev Joshi , Hanna Linn
show 11 more authors
Maeve Gaffney Alexander Holden Vinooth Kulkarni Vipin Chaudhary Kenneth M. Merz Jr Abdullah Ash Saki Tomas Radivoyevitch Frank DiFilippo Jun Qin Omar Shehab Daniel Blankenberg
This is my paper · ORCID
classification quant-phq-bio.BM MSC 81P6868Q12 PACS 03.67.Ac
keywords quantumcomputingproteinstructurepredictionlatticemodelsface-centeredcubicvariationaleigensolverLagrangiandualityMiyazawa-Jerniganpotentialsturn-basedencoding
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper's central contention is that the face-centered cubic (FCC) lattice — a dense grid with 12 growth directions per node — is the right substrate for quantum protein structure prediction, because it can represent real secondary structure in ways the previously used tetrahedral lattice cannot. Classical fitting across eleven proteins of 10–26 residues backs this up: FCC best fits stay below 2.0 Å RMSD in all cases, several near sub-angstrom, and the FCC models reproduce an α-helix pitch of 6.33 Å in the paxillin example against nature's 5.4 Å, where the tetrahedral fit stretches to roughly 9 Å. The paper then presents, as what it identifies as the first quantum implementation of the FCC lattice, a turn-based encoding using 4 qubits per turn ($4N-10$ configuration qubits, plus one ancilla flag per candidate contact pair) and two slack-variable-free ways to enforce the no-overlap constraint: PolyFit, a least-squares polynomial penalty, and VQEC, a variational eigensolver that turns constraints into a Lagrangian saddle-point problem. On two IBM quantum processors, both methods assign the highest sampled probability to a ground-state turn sequence of the 6-residue amyloid-β segment KLVFFA, matching the classical exhaustive-search optimum, with the newer Heron processor sampling the optimal solution nearly two-fold (PolyFit) and three-fold (VQEC) more often than the older Eagle. If correct, the work moves quantum folding from lattices that cannot form helices to one whose geometry resembles real proteins.

What carries the argument

The load-bearing object is the turn-based binary encoding of the FCC lattice plus the four-term Hamiltonian $\mathcal{H} = \mathcal{H}_{\mathrm{back}} + \mathcal{H}_{\mathrm{redun}} + \mathcal{H}_{\mathrm{olap}} + \mathcal{H}_{\mathrm{int}}$, written entirely through turn-indicator polynomials. Each of the $N-2$ turns costs 4 qubits (16 bitstrings; 12 are the real FCC directions, 4 are penalized as redundant), and fixing the first turn while restricting the second leaves $4N-10$ configuration qubits, plus one ancilla flag per candidate contact pair. The interaction term $\mathcal{H}_{\mathrm{int}} = \sum_{m,n} \epsilon_{mn}\, q^a_{mn}(3-D_{mn})$ uses ancilla flags $q^a_{mn}$ and Miyazawa–Jernigan contact energies $\epsilon_{mn}$, with $D_{mn}$ the squared lattice distance. The two slack-free replacements for the overlap constraint carry the argument: PolyFit least-squares fits a polynomial in the Chebyshev basis to the discrete penalty functional $F[D_{mn}]$ (value 50 at overlap, near zero at allowed distances), with the required degree growing roughly linearly in residue separation; VQEC leaves the constraints implicit, building a Lagrangian $\mathcal{L}(b;\lambda)$ and running primal-dual perturbation so primal parameters descend while Lagrange multipliers ascend toward a saddle point, keeping the Hamiltonian small (2,199 terms for KLVFFA versus PolyFit's 18,133). The variational circuit is a two-layer hardware-efficient RealAmplitudes ansatz of single-qubit rotations and CNOT entanglers.

What would settle it

Enumerate the full $2^{24}$ state space of the exact hardware Hamiltonian (configuration qubits plus the contact ancillas) and check whether its global minimum decodes to the same valid, self-avoiding, non-backtracking KLVFFA conformation that the paper's classical exhaustive search identifies as the ground state; if a lower minimum decodes to an overlapping or backtracking chain, the constraint machinery is mis-weighted. A faster check on existing output: decode every bitstring sampled from the trained VQEC circuit on a noiseless simulator and report the fraction that violate the overlap or backtracking constraints — the paper says samples were inspected for violations but gives no rate, and a non-negligible rate would contradict the claim that the ground state is recovered under noise.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that the FCC lattice can be encoded for quantum protein structure prediction without slack variables, and that the resulting Hamiltonian's ground state — located by two distinct variational routes on noisy hardware and decoded back to coordinates — matches the lowest-energy conformation found by classical exhaustive search for the six-residue peptide KLVFFA. The authors argue the FCC lattice is not just a bigger version of earlier lattices but a qualitatively better model of biology: across eleven test proteins spanning helices, sheets, and loops, FCC best fits reach RMSDs below 2.0 Å in every case and several near sub-angstrom, whereas tetrahedral fits stretch helices to a Cα pitch of roughly 9 Å against nature's 5.4 Å. The quantum construction is a four-term Hamiltonian built from turn-indicator polynomials — backtracking penalties, penalties on the four redundant bitstrings, a nearest-neighbor interaction term scored with Miyazawa–Jernigan contact energies through ancilla flags, and an overlap term — where the overlap constraint is enforced either by fitting a polynomial to the ideal penalty functional (PolyFit) or by converting the constraint into a Lagrangian saddle-point problem (VQEC). Both schemes keep the configuration encoding at $4N-10$ qubits (24 total for KLVFFA, including contact ancillas), and on hardware both assign the highest sampled probability to a ground-state turn sequence, a claim the authors verify by comparing the decoded conformations against the classical ground-truth ensemble.

Load-bearing premise

The load-bearing premise is that the constraint machinery is strong enough and complete as specified: the numeric weights of the backtracking and redundant-bitstring penalties and the mechanism that makes each ancilla qubit flag only genuine nearest-neighbor contacts are never spelled out, and for the VQEC route the authors assume, with an explicit caveat in Sec. 3.3.2, that the optimizer's saddle point coincides with the constrained optimum — if any of these fails, the state reported as the recovered ground state could be an overlapping or otherwise invalid conformation.

Editorial extensions

If this is right

  • Quantum protein folding gains a lattice that can represent secondary structure: the paper's classical fits place FCC best fits below 2.0 Å RMSD for all eleven test proteins, several near sub-angstrom, whereas the tetrahedral lattice stretches helices to roughly a 9 Å pitch.
  • Peptide length is no longer gated by slack-variable qubit overhead: both constraint methods hold the configuration encoding at $4N-10$ qubits, which the paper's scaling comparison shows keeps longer chains far cheaper in qubits than the slack-variable route.
  • VQEC is the scalable direction, not PolyFit: for the six-residue peptide it needs 2,199 Hamiltonian terms versus 18,133, and on hardware it samples the ground state with 2–4 times higher probability, at the price of careful step-size tuning.
  • Hardware generation measurably changes results: the Heron R2 processor samples the optimal solution nearly two-fold (PolyFit) and three-fold (VQEC) more often than the Eagle R3, and dynamical decoupling helps the older chip far more, consistent with lower crosstalk on Heron.
  • The probability-ranked output behaves like a folding funnel: sampled probabilities rise as turn-sequence energy falls while radius of gyration shrinks, a trend the authors read as a possible probabilistic folding pathway toward the compact native-like state.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper's one open verification step is to re-implement the hardware Hamiltonian with explicit numeric penalty weights and an explicit ancilla-flag rule, then confirm on a noiseless simulator that every high-probability bitstring decodes to a valid self-avoiding walk; the authors state they inspected samples for violations but report no violation rate.
  • Because the FCC lattice is non-bipartite — the authors note residues an even number of turns apart can be nearest neighbors — its contact graph is denser than on cubic or tetrahedral lattices; this makes constraint enforcement a harder test for quantum optimizers, and the same even-turn contacts could later carry explicit hydrogen-bond or sheet-registry terms.
  • If the monotone rise in sampling probability with falling energy and shrinking radius of gyration reproduces on other peptides, the noisy output distribution itself becomes a resource: the ensemble, not merely the single most probable state, could support folding-pathway or conformational-ensemble inference.
  • The two slack-free constraint schemes generalize beyond proteins: any inequality-constrained binary optimization (side-chain packing, RNA secondary structure, generic lattice heteropolymers) could borrow the polynomial-penalty or Lagrangian-saddle-point route to avoid the $O(N^2\log N)$ qubit overhead of slack variables.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper presents what it claims to be the first quantum algorithm for protein structure prediction on the face-centered cubic (FCC) lattice. The model uses a turn-based binary encoding with four qubits per turn, together with a Hamiltonian containing non-backtracking, redundant-bitstring, non-overlap, and nearest-neighbor interaction terms. Two methods are proposed to avoid slack variables for the non-overlap constraint: a polynomial fitting approach (PolyFit) and a Lagrangian-duality-based variational quantum eigensolver with constraints (VQEC). The authors validate the encoding on a 5-residue peptide by exhaustive search, train ansatz parameters on a noiseless simulator for the 6-residue peptide KLVFFA, and then execute the optimized circuits on ibm_cleveland (Eagle R3) and ibm_kingston (Heron R2). They report recovering ground-state configurations with the highest sampled probability and observe roughly two- to three-fold higher sampling probabilities on the newer Heron processor.

Significance. If the Hamiltonian encoding is correct, the paper makes a useful contribution: the FCC lattice is a more expressive coarse-grained model than the tetrahedral lattice for secondary-structure elements, and the two no-slack-variable penalty constructions (PolyFit and VQEC) are interesting resource trade-offs. The paper also provides a substantial classical exhaustive-search framework in the appendices, which is a reproducible resource for benchmarking small lattice instances. However, the significance is tempered by the fact that the validation is entirely internal: the 'ground truth' is the optimum of the constructed Hamiltonian, not an experimental structure, and the hardware claims rest on point estimates without statistical uncertainties. The biologically motivated conclusions about folding pathways are suggestive but not quantitatively supported.

major comments (4)
  1. [Sec. 3.2, Eq. (8)] The ancilla flags q^a_mn are introduced as '1 if the pair are nearest neighbors, and 0 otherwise,' but the constraints that enforce q^a_mn = 1 iff D_mn = 2 are never constructed. As written, Eq. (8) depends on ancilla degrees of freedom that are not determined by the turn bitstring; if these ancillas are free or weakly constrained, minimizing H_int can select configurations with D_mn = 0 and q^a_mn = 1, which receive a spurious energy contribution of 3*epsilon_mn and may not correspond to valid self-avoiding conformations. In addition, the penalty parameters lambda_back, lambda_redun, and the overlap penalty (given as 50 in Fig. 6) are never assigned numeric values, so a reader cannot verify that all valid conformations lie strictly below all invalid ones. Please provide the explicit constraint Hamiltonian for the ancilla flags, the numeric penalty weights, and a brute-force check for the KLVFFA instance that the optimum of the full Hamiltonian, including all ancillas, is a valid self-avoiding conformation.
  2. [Sec. 3.3.2] The paper relies on weak duality (D* <= P*) and on convergence of the primal-dual iterates to a saddle point of the Lagrangian L(b; lambda). For the nonconvex binary optimization problem at hand, a saddle point of the Lagrangian need not yield a feasible or optimal primal solution, and the authors acknowledge this gap in the sentence 'More theoretical and empirical studies on the duality and optimality gaps... are needed.' For the central hardware claim, this means the states labeled as ground states in Figs. 8 and 9 are only valid if the VQEC solution satisfies all non-overlap constraints. Please report, for the chosen hyperparameters, the fraction of sampled bitstrings that violate D_mn >= 2, the final values of the dual variables, and a direct comparison between the VQEC optimum and the exhaustive-search optimum on the same 24-qubit instance.
  3. [Sec. 4.2, Figs. 8-10] The hardware probabilities are reported as point estimates without shot counts, error bars, or repeated-execution statistics. For example, the differences between ibm_cleveland and ibm_kingston (roughly 0.01 vs 0.0175 for PolyFit and 0.024 vs 0.07 for VQEC) could be comparable to shot noise if only a few thousand shots are used, which would undermine the two- to three-fold improvement claims. Please state the number of shots per circuit, the number of independent circuit executions, and provide statistical uncertainties (for example, Wilson intervals or bootstrap standard errors) for the reported sampling probabilities.
  4. [Secs. 4.1-4.2, Abstract] The validation and ground truth are internal to the constructed Hamiltonian: the optimal configurations are obtained by classical exhaustive search over the same Hamiltonian, and the 5-residue GNLVS check verifies that the encoding reproduces that search, not that the model predicts the experimental structure. The phrase 'recover ground state configurations under noise' is therefore accurate only for the ground state of the FCC lattice Hamiltonian, and the abstract's unqualified wording should be softened. To support the biological relevance suggested in the Discussion, the authors would need to compare the predicted conformations against the experimental KLVFFA structure (PDB: 2Y29) and quantify structural agreement beyond radius of gyration.
minor comments (4)
  1. [Appendix B] The indicator function for the turn direction (-y,+z) is printed identically to that for (-y,-z): both are written as (1-q_{phi+2})q_{phi+3}q_{phi+4}(1-q_{phi+5}). Based on the bitstring mapping in Table 2, the (-y,+z) indicator should be (1-q_{phi+2})q_{phi+3}(1-q_{phi+4})q_{phi+5}. As printed, the appendix cannot be used to reproduce the position functions in Eq. (7).
  2. [Sec. 2.2 and Appendix D] There are several typos: 'color coated' in the Fig. 3 caption should be 'color-coded,' and Appendix D contains 'sppedup' and 'slighly' instead of 'speed up' and 'slightly.'
  3. [Fig. 6 and Algorithm 1] The polynomial fits are described only by their R^2 values and degrees; the actual polynomial coefficients, which are needed to reproduce the PolyFit Hamiltonian, are not provided. Please include the coefficients or a supplementary data file.
  4. [Sec. 4.1] The description of the CVaR threshold (alpha = 0.1) and the initial-angle sampling from four subintervals of [0, 2*pi] would be clearer if the precise number of random initializations and the criterion for selecting the best run were stated explicitly, since the final hardware results depend on this selection.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the FCC Hamiltonian, MJ scoring, and lattice geometry come from external sources, and the hardware results are a disclosed training-based benchmark rather than an independent prediction.

full rationale

The paper's derivation chain is not circular in any load-bearing way. The FCC lattice geometry and turn encoding are parameter-free constructions; the contact energies are the external Miyazawa-Jernigan matrix [17]; and the non-overlap penalties and VQEC/Lagrangian machinery come from external sources [24,25]. The 'ground state' used to validate the hardware samples is obtained by a classical exhaustive search (App. D) of the same Hamiltonian, so it is a self-consistency check rather than an independent structure prediction, but that is not circularity: the Hamiltonian itself is not defined in terms of the target result. The paper discloses that ansatz parameters and VQEC hyperparameters were selected on a noiseless simulator by their ability to recover the known optimal bitstrings (Sec. 4.1), which weakens the 'recovery under noise' claim as a benchmark of prediction, but the hardware sampling probabilities are actual measurements and are not forced by an equation. The only same-author citation used in the design phase, Doga et al. [10], concerns resource estimates for the tetrahedral lattice and is not load-bearing for the FCC Hamiltonian or for the hardware recovery claim. The main weaknesses—unspecified q^a_mn ancilla constraints in Eq. (8) and unstated numerical values for lambda_back, lambda_redun, and the overlap penalty—are completeness and verifiability problems, not circular reductions; they do not make any output equal to an input by construction.

Assumptions & free parameters 8 free parameters · 7 assumptions · 0 invented entities

The central result depends on the MJ statistical potential, the geometric bitstring mapping, unstated penalty/ancilla constraint terms, and the VQEC convergence assumption. Most of these are reasonable domain choices, but the paper does not quantify the penalty parameter ranges, which is the largest unaccounted-for input. No new physical entities are postulated.

free parameters (8)
  • lambda_back = not specified
    Penalty weight for the non-backtracking constraint in Eq. (5); its value is never given, yet the ground state identity depends on it.
  • lambda_redun = not specified
    Penalty weight for the four unphysical bitstrings in Eq. (6); not stated in the paper.
  • overlap_penalty_weight = 50 (mentioned in Fig. 6 caption)
    The target penalty for overlapping beads in the PolyFit construction is 50; the actual weight used in the hardware Hamiltonians is not explicitly reported.
  • polynomial_fit_coefficients = degrees 7-28 per residue separation
    Chebyshev least-squares fits to the chosen penalty functional for |m-n|=3,...,11 (Fig. 6, Algorithm 1); these coefficients define H_overlap in PolyFit.
  • VQEC_step_sizes = grid-selected (nu in {0.01,...,0.5}, mu in {0.1,...,5})
    Perturbation and update step sizes are tuned via grid search; the best run is selected by recovery of the known ground state (Sec. 4.1).
  • CVaR_alpha = 0.1
    CVaR threshold for the PolyFit VQE objective, chosen by hand (Sec. 4.1).
  • ansatz_layers = 2
    Depth of the RealAmplitudes ansatz, chosen without stated justification (Sec. 3.4).
  • initial_angle_interval = [3*pi/2, 2*pi]
    For PolyFit, initial rotation angles are sampled from the subinterval that empirically converged best to the known ground state (Sec. 4.1).
assumptions (7)
  • domain assumption Miyazawa-Jernigan contact energies are a valid scoring function for lattice protein folding.
    The interaction Hamiltonian and the exhaustive-search ground truth both use the 1996 MJ matrix [17]; no independent validation of this potential is given in this paper.
  • domain assumption The 4-bit turn encoding maps exactly to the 12 FCC directions with the stated residual properties.
    The bitstring mapping in App. B is asserted from geometry; the non-backtracking/redundant constraints are built on it. Partially validated by one 5-residue exhaustive search (GNLVS).
  • ad hoc to paper Ancilla flag qubits can be constrained so that q^a_mn = 1 iff D_mn = 2; the constraint implementation is not shown.
    Eq. (8) requires q^a_mn to indicate nearest neighbors, but the penalty terms enforcing this are never written down; their absence could change the effective Hamiltonian.
  • ad hoc to paper The chosen penalty strengths and polynomial tolerances place the valid self-avoiding conformations strictly below all invalid ones in energy.
    The paper does not provide values or an analysis window for lambda_back, lambda_redun, and the overlap weight; the ground state recovery claim depends on this separation.
  • ad hoc to paper The VQEC primal-dual iterates converge to a saddle point whose primal solution is the constrained optimum.
    Convergence without convexity is cited from Refs. [25,26], and the paper explicitly says 'more theoretical and empirical studies on the duality and optimality gaps ... are needed' (Sec. 3.3.2).
  • domain assumption The 2-layer RealAmplitudes ansatz can express a state whose most likely bitstring is the Hamiltonian ground state.
    Verified only numerically on a noiseless simulator for KLVFFA; no guarantee for other sequences or for the noisy hardware runs.
  • domain assumption The polynomial fit with R^2 >= 0.999 introduces negligible bias into the energy landscape.
    The fits in Fig. 6 have small residuals, but the effect of those residuals on the relative ordering of low-lying states is not quantified.

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Cite this review

Pith. "Pith review of Quantum Algorithm for Protein Structure Prediction Using the Face-Centered Cubic Lattice." pith.science (2026). https://pith.science/paper/R45XCBR2

@misc{pith2026250708955,
  author       = {Pith},
  title        = {Pith review of: Quantum Algorithm for Protein Structure Prediction Using the Face-Centered Cubic Lattice},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/R45XCBR2}},
  note         = {Machine review of arXiv:2507.08955}
}
read the original abstract

In this work, we present the first implementation of the face-centered cubic (FCC) lattice model for protein structure prediction with a quantum algorithm. Our motivation to encode the FCC lattice stems from our observation that the FCC lattice is more capable in terms of modeling realistic secondary structures in proteins compared to other lattices, as demonstrated using root mean square deviation (RMSD). We utilize two quantum methods to solve this problem: a polynomial fitting approach (PolyFit) and the Variational Quantum Eigensolver with constraints (VQEC) based on the Lagrangian duality principle. Both methods are successfully deployed on Eagle R3 (ibm_cleveland) and Heron R2 (ibm_kingston) quantum computers, where we are able to recover ground state configurations for the 6-amino acid sequence KLVFFA under noise. A comparative analysis of the outcomes generated by the two QPUs reveals a significant enhancement (reaching nearly a two-fold improvement for PolyFit and a three-fold improvement for VQEC) in the prediction and sampling of the optimal solution (ground state conformations) on the newer Heron R2 architecture, highlighting the impact of quantum hardware advancements for this application.

Figures

Figures reproduced from arXiv: 2507.08955 by the authors.

Figure 1
Figure 1. From the selection of an optimal lattice model to final performance analysis, protein structure prediction with quantum algorithms (QPSP) is a complex task that requires a careful analysis of each of these individual pieces. Depicted here is the Trp-cage miniprotein (PDB: 2JOF [2]). 2 A brief review of coarse-grained lattice models in QPSP The field of QPSP is a relatively young field compared to its classical count… view at source ↗
Figure 2
Figure 2. a) Compared are the original Hamiltonian’s [1] best solution using a tetrahedral lattice (grey), the best possible fit on a tetrahedral lattice (green), the best possible fit on an FCC lattice (magenta), and AlphaFold2 (orange). RMSDs were measured after alignment to known structures. For the NMR structures, models were fit against the first frame of the ensemble. All known structures were obtained from the PDB[6], … view at source ↗
Figure 3
Figure 3. Ensemble analysis of the 100 lowest energy solutions from the exhaustive search results of the original tetrahedral lattice algorithm, and the new FCC algorithm. Each bar plot is color coated to represent a particular lattice algorithm using a specific scoring function, either a standard hydrophobic-polar (HP) or the Miyazawa-Jernigan (MJ1996) potentials from their 1996 paper [17]. For each protein structure, the me… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: a) 12 lattice points on the FCC lattice, where the green sphere is the origin in R 3 , b) Visual depiction of the first two turns on the FCC lattice starting at the origin, and corresponding turn sequence bitstrings. In total, the number of configuration qubits needed …
Figure 5
Figure 5. Figure 5: Qubit counts vs. protein length for the FCC with slack variables (grey), without slack variables (red), and tetrahedral lattice (green) implementations of the QPSP problem. Non-overlapping constraint Finally, in order to penalize the potential overlaps between any two …
Figure 6
Figure 6. Figure 6: Polynomial fits to the desired values of the penalty term F[Dmn] (corresponding to a penalty parameter of 50 when bead overlap happens) for the non-overlapping constraint. Cases where |m − n| = 3, . . . , 11 are presented. The polynomial fit is obtained by minimizing t…
Figure 7
Figure 7. Figure 7: Turn sequence probabilities for the protein sequence KLVFFA when using the a) PolyFit method and b) VQEC method. The optimized circuit is sampled with 100,000 shots on a noiseless simulator and the sampled bitstrings are subsequently converted to the corresponding turn…
Figure 8
Figure 8. Figure 8: Turn sequence probabilities for KLVFFA ensembles when using the PolyFit approach, on a) ibm cleveland and b) ibm kingston. The red dashed line indicate the ground state energy found by the classical exhaustive search. In both machines, we observe at least one of the gr…
Figure 9
Figure 9. Figure 9: Turn sequence probabilities for KLVFFA ensembles when using VQEC on a) ibm cleveland and b) ibm kingston. The red dashed line indicate the ground state energy found by the classical exhaustive search. In both machines, we observe at least one of the ground state turn s…
Figure 10
Figure 10. Figure 10: Cumulative probability plots for a) PolyFit and b) VQEC methods on ibm cleveland (blue) and ibm kingston (red). In all cases, we observe a significant percentage of the probability is accumulated in lower energies, highlighting the success of sampling. 21 [PITH_FULL_…
Figure 11
Figure 11. Figure 11: a) Schematic of the classical search algorithm workflow and b) a fundamental set of post￾processing steps in bioinformatics analysis. At their core, both the tetrahedral and FCC search algorithms follow the workflow in a). The steps in b) do not include all-atom recon…

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