Attested & literatureAlgorithmsVariational quantum algorithm2026-08-12

Protein folding on a tetrahedral lattice by a variational quantum algorithm

protein foldingvariationallattice modelchemistrynisq

Atlas stars stay in the public catalog. Saving this entry to your workspace starts an unstarred private copy.

Predict the three-dimensional structure a protein takes from its primary sequence of amino acids, posed here on the model Hamiltonian the paper defines for a chain of N monomers placed on a tetrahedral lattice. The paper presents a model Hamiltonian with O(N⁴) scaling, together with a corresponding quantum variational algorithm, for the folding of a polymer chain with N monomers on a tetrahedral lattice. The abstract states that the model reflects many physico-chemical properties of the protein, reducing the gap between coarse-grained representations and mere lattice models. The optimisation scheme, which the authors describe as robust and versatile, brings together variational quantum algorithms specifically adapted to classical cost functions and evolutionary strategies (genetic algorithms). The paper reports simulating the folding of the 10 amino acid Angiotensin peptide on 22 qubits, and applying the same method to the folding of a 7 amino acid neuropeptide using 9 qubits on an IBM Q 20-qubit quantum computer.

Circuit & simulation

problem

encodetransform

algorithm

transformmeasure

readout

measure

What this takes and returns

TakesNothingWhat joins here

No input port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.

Nothing in the Atlas meets this end.

ReturnsNothingWhat joins here

No output port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.

Nothing in the Atlas meets this end.

This record publishes no gate sequence and no register, so there is nothing here to read an interface off. Absent rather than empty. See all 152 →

Where this sits

This record is named by the layer graph at:

Estimate a Hamiltonian's ground-state energy Slot
Takes A Hermitian $H$ reachable as a sum of terms, as sparse-access oracles or as a block-encoding; a way to prepare trial states, and — for the methods that need it — a trial state whose overlap with the ground state is not negligible; a target additive error $\varepsilon$ and a confidence $1-\delta$ . Returns A scalar estimate of the lowest eigenvalue with a stated additive-error guarantee, plus the run or query budget it consumed. Whether that estimate is also a rigorous upper bound is a property of the method and is not promised by the slot.

How it works

The paper presents a model Hamiltonian with O(N⁴) scaling, together with a corresponding quantum variational algorithm, for the folding of a polymer chain with N monomers on a tetrahedral lattice. The abstract states that the model reflects many physico-chemical properties of the protein, reducing the gap between coarse-grained representations and mere lattice models. The optimisation scheme, which the authors describe as robust and versatile, brings together variational quantum algorithms specifically adapted to classical cost functions and evolutionary strategies (genetic algorithms). The paper reports simulating the folding of the 10 amino acid Angiotensin peptide on 22 qubits, and applying the same method to the folding of a 7 amino acid neuropeptide using 9 qubits on an IBM Q 20-qubit quantum computer. The Classiq library carries this subject under applications · chemistry/protein_folding. Reported cost: O(N⁴) scaling for the model Hamiltonian of a polymer chain with N monomers on a tetrahedral lattice. The abstract states no running time for the variational algorithm, no query or gate count, and no speed-up factor against classical folding methods; its only concrete figures are qubit counts for two named instances, 22 qubits for the 10 amino acid Angiotensin peptide and 9 qubits for a 7 amino acid neuropeptide on an IBM Q 20-qubit quantum computer. On the classical side it states that the problem is intrinsically NP-hard even reduced to its simplest Hydrophobic-Polar model, while classical algorithms provide practical solutions by sampling the conformation space of small proteins..

Implementation

FrameworkUnsupported

protein-folding-variational.txt

ALGORITHM: Protein folding on a tetrahedral lattice by a variational quantum algorithm
PROBLEM: Predict the three-dimensional structure a protein takes from its primary sequence of amino acids, posed here on the model Hamiltonian the paper defines for a chain of N monomers placed on a tetrahedral lattice.
IDEA: The paper presents a model Hamiltonian with O(N⁴) scaling, together with a corresponding quantum variational algorithm, for the folding of a polymer chain with N monomers on a tetrahedral lattice. The abstract states that the model reflects many physico-chemical properties of the protein, reducing the gap between coarse-grained representations and mere lattice models. The optimisation scheme, which the authors describe as robust and versatile, brings together variational quantum algorithms specifically adapted to classical cost functions and evolutionary strategies (genetic algorithms). The paper reports simulating the folding of the 10 amino acid Angiotensin peptide on 22 qubits, and applying the same method to the folding of a 7 amino acid neuropeptide using 9 qubits on an IBM Q 20-qubit quantum computer.
REPORTED COST: O(N⁴) scaling for the model Hamiltonian of a polymer chain with N monomers on a tetrahedral lattice. The abstract states no running time for the variational algorithm, no query or gate count, and no speed-up factor against classical folding methods; its only concrete figures are qubit counts for two named instances, 22 qubits for the 10 amino acid Angiotensin peptide and 9 qubits for a 7 amino acid neuropeptide on an IBM Q 20-qubit quantum computer. On the classical side it states that the problem is intrinsically NP-hard even reduced to its simplest Hydrophobic-Polar model, while classical algorithms provide practical solutions by sampling the conformation space of small proteins.
BASIS: abstract of arXiv:1908.02163 (TeX rendered into Unicode: the abstract's script-O written O, its exponent as a superscript, and its italic N as plain N): "we present a model Hamiltonian with O(N⁴) scaling and a corresponding quantum variational algorithm for the folding of a polymer chain with N monomers on a tetrahedral lattice". The qubit figures are from the same abstract: "to simulate the folding of the 10 amino acid Angiotensin peptide on 22 qubits", and "The same method is also successfully applied to the study of the folding of a 7 amino acid neuropeptide using 9 qubits on an IBM Q 20-qubit quantum computer". The classical statements are from "Although classical algorithms provide practical solutions, sampling the conformation space of small proteins, they cannot tackle the intrinsic NP-hard complexity of the problem, even reduced to its simplest Hydrophobic-Polar model". The abstract states no running time and no comparison of running times, so none is recorded here.
DEMONSTRATED BY: the Classiq library entry applications/chemistry/protein_folding/protein_folding_with_qaoa
PRIMARY SOURCE: Anton Robert, Panagiotis Kl. Barkoutsos, Stefan Woerner, Ivano Tavernelli (2019), Resource-Efficient Quantum Algorithm for Protein Folding — https://arxiv.org/abs/1908.02163

This is a literature reference record, not an executable circuit.

A reference record, not runnable source. Leona cannot execute it, so it cannot be saved to your Library as a circuit.

Quantum vs classical

Classical baseline

Compare Variational quantum algorithm with the strongest classical method for the same instance, input budget, and output metric.

Quantum claim

This reference exposes a quantum circuit pattern; it does not imply an application-level speedup without a matched benchmark.

How to compare

Report input loading, circuit depth, repetitions, classical preprocessing, post-processing, and wall-clock time together.

Declared gaps

Nobody has reviewed this record for gaps yet.

Literature & references

Resource-Efficient Quantum Algorithm for Protein Folding2019 · Anton Robert, Panagiotis Kl. Barkoutsos, Stefan Woerner, Ivano Tavernelli

Primary source: it states the O(N⁴) model Hamiltonian for a polymer chain of N monomers on a tetrahedral lattice, the corresponding quantum variational algorithm, and the optimisation scheme that combines variational quantum algorithms adapted to classical cost functions with evolutionary strategies. It also reports the two experiments quoted here, the 10 amino acid Angiotensin peptide on 22 qubits and the 7 amino acid neuropeptide on 9 qubits of an IBM Q 20-qubit machine. Consult it for the encoding of a conformation into qubits, the ansatz and optimiser settings, the platform the 22-qubit result was obtained on, and the accuracy of the reported folds, none of which the abstract states.

arxiv.org/abs/1908.02163 ↗

Verification

Attested & literature

Peer-reviewed paper

Method: Curation only. The Classiq library publishes this subject as the directory `applications/chemistry/protein_folding/protein_folding_with_qaoa`, pinned in scripts/classiq-parity/classiq-index.json; this record documents the algorithm that entry demonstrates, not the demonstration. The primary reference's title, authors and submission year were read from its arXiv abs page, and the complexity claim taken from a clause of that paper's abstract (abstract of arXiv:1908.02163 (TeX rendered into Unicode: the abstract's script-O written O, its exponent as a superscript, and its italic N as plain N): "we present a model Hamiltonian with O(N⁴) scaling and a corresponding quantum variational algorithm for the folding of a polymer chain with N monomers on a tetrahedral lattice". The qubit figures are from the same abstract: "to simulate the folding of the 10 amino acid Angiotensin peptide on 22 qubits", and "The same method is also successfully applied to the study of the folding of a 7 amino acid neuropeptide using 9 qubits on an IBM Q 20-qubit quantum computer". The classical statements are from "Although classical algorithms provide practical solutions, sampling the conformation space of small proteins, they cannot tackle the intrinsic NP-hard complexity of the problem, even reduced to its simplest Hydrophobic-Polar model". The abstract states no running time and no comparison of running times, so none is recorded here.). No circuit was constructed, simulated or run, and no Qmod model was executed.
Result: Pass · the record's problem statement and primary reference agree with the sources named above.
Caveat: Nothing here was built, compiled, simulated or run, and no peptide structure was predicted: this record documents the algorithm as its paper states it and does not reproduce any implementation of it. The O(N⁴) figure is the scaling of the model Hamiltonian in the number of monomers, not a running time and not a speed-up, and the abstract does not say which quantity of the Hamiltonian grows that way — its number of terms, of qubits, or of couplings. The abstract gives no time complexity for the variational optimisation, no gate count, no circuit depth, no ansatz, no iteration count and no accuracy, and it claims no advantage over classical folding methods, so nothing here supports one. Its NP-hard remark is about the folding problem itself and about what classical algorithms cannot tackle; it does not say that this algorithm escapes that complexity, and nothing here claims it does. The 22-qubit folding of the Angiotensin peptide and the 9-qubit run on the IBM Q machine are the paper's own reported experiments, at 10 and 7 amino acids respectively, and neither was repeated or checked here; the abstract names hardware only for the 7 amino acid case, so this record does not say on what platform the 22-qubit result was obtained, and neither experiment establishes that the method reaches proteins of biological size. A lattice model Hamiltonian is a reduction of the folding problem, so solving it answers the model rather than the structure-prediction problem itself, and the claim that this model reflects many physico-chemical properties of the protein, reducing the gap between coarse-grained representations and mere lattice models, is the abstract's rather than anything checked here. The abstract calls the second application successful without stating a criterion, and it does not say how close either reported fold is to the true structure. The NISQ premise is stated in the abstract as evidence that such algorithms can accelerate energy optimization in frustrated systems, not as a proof, and no noise model, error rate or error-correction requirement is given anywhere in it.

Facts

Record type: Literature reference
Classiq library entry: protein_folding_with_qaoa
Reported cost: O(N⁴) scaling for the model Hamiltonian of a polymer chain with N monomers on a tetrahedral lattice. The abstract states no running time for the variational algorithm, no query or gate count, and no speed-up factor against classical folding methods; its only concrete figures are qubit counts for two named instances, 22 qubits for the 10 amino acid Angiotensin peptide and 9 qubits for a 7 amino acid neuropeptide on an IBM Q 20-qubit quantum computer. On the classical side it states that the problem is intrinsically NP-hard even reduced to its simplest Hydrophobic-Polar model, while classical algorithms provide practical solutions by sampling the conformation space of small proteins.
Classiq publication directory: applications/chemistry/protein_folding/protein_folding_with_qaoa
Classiq shelf: applications · chemistry/protein_folding
Complexity basis: abstract of arXiv:1908.02163 (TeX rendered into Unicode: the abstract's script-O written O, its exponent as a superscript, and its italic N as plain N): "we present a model Hamiltonian with O(N⁴) scaling and a corresponding quantum variational algorithm for the folding of a polymer chain with N monomers on a tetrahedral lattice". The qubit figures are from the same abstract: "to simulate the folding of the 10 amino acid Angiotensin peptide on 22 qubits", and "The same method is also successfully applied to the study of the folding of a 7 amino acid neuropeptide using 9 qubits on an IBM Q 20-qubit quantum computer". The classical statements are from "Although classical algorithms provide practical solutions, sampling the conformation space of small proteins, they cannot tackle the intrinsic NP-hard complexity of the problem, even reduced to its simplest Hydrophobic-Polar model". The abstract states no running time and no comparison of running times, so none is recorded here.
Circuit: Not supplied

Source

Resource-Efficient Quantum Algorithm for Protein Folding ↗

Kind: curated reference
Reviewed by: Leona Quantum curation pass
License: Citation metadata only; source publication terms apply