Coarse-grained variational quantum eigensolver for intermolecular interactions
Determine the ground state of weakly-interacting, non-covalently bonded molecules — the weakly-bound intermolecular regime that variational quantum algorithms applied to strongly-bound, covalently-bonded systems with full molecular-orbital bases had left largely unexplored — using a coarse-grained representation of the electronic response suited to a VQA.
variational quantum eigensolvercoarse grainingintermolecular interactionsvan der waalsdispersion energy
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Determine the ground state of weakly-interacting, non-covalently bonded molecules — the weakly-bound intermolecular regime that variational quantum algorithms applied to strongly-bound, covalently-bonded systems with full molecular-orbital bases had left largely unexplored — using a coarse-grained representation of the electronic response suited to a VQA. Anderson, Kiffner, Barkoutsos, Tavernelli, Crain and Jaksch develop a coarse-grained representation of the electronic response that they state is ideally suited for determining the ground state of weakly interacting molecules using a variational quantum algorithm. Their construction requires qubit numbers that grow linearly with the number of molecules, and they derive scaling behaviour for the number of circuits and measurements required, stating that this compares favourably to traditional variational quantum eigensolver methods — the abstract attaches this favourable comparison to circuits and measurements specifically, separately from the linear qubit count. The authors demonstrate the method on IBM superconducting quantum processors, showing its capability to resolve the dispersion energy as a function of separation for a pair of non-polar molecules, and state that this establishes a means by which quantum computers can model Van der Waals interactions directly from zero-point quantum fluctuations. Within this coarse-grained approximation, they conclude that current-generation quantum hardware is capable of probing energies in this weakly bound but chemically ubiquitous and biologically important regime. They also report performing experiments on simulated and real quantum computers for systems of three, four and five oscillators, and for oscillators with anharmonic onsite binding potentials, stating that the consequences of the latter are unexamined in large systems by classical computational methods but can be incorporated here with low computational overhead.
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What this takes and returns
TakesNothingWhat joins here
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ReturnsNothingWhat joins here
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TakesA 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 ε and a confidence 1−δ.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
Anderson, Kiffner, Barkoutsos, Tavernelli, Crain and Jaksch develop a coarse-grained representation of the electronic response that they state is ideally suited for determining the ground state of weakly interacting molecules using a variational quantum algorithm. Their construction requires qubit numbers that grow linearly with the number of molecules, and they derive scaling behaviour for the number of circuits and measurements required, stating that this compares favourably to traditional variational quantum eigensolver methods — the abstract attaches this favourable comparison to circuits and measurements specifically, separately from the linear qubit count. The authors demonstrate the method on IBM superconducting quantum processors, showing its capability to resolve the dispersion energy as a function of separation for a pair of non-polar molecules, and state that this establishes a means by which quantum computers can model Van der Waals interactions directly from zero-point quantum fluctuations. Within this coarse-grained approximation, they conclude that current-generation quantum hardware is capable of probing energies in this weakly bound but chemically ubiquitous and biologically important regime. They also report performing experiments on simulated and real quantum computers for systems of three, four and five oscillators, and for oscillators with anharmonic onsite binding potentials, stating that the consequences of the latter are unexamined in large systems by classical computational methods but can be incorporated here with low computational overhead. The Classiq library carries this subject under applications · chemistry. Reported cost: Qubit numbers that grow linearly with the number of molecules. Separately, the abstract states that scaling behaviour for the number of circuits and the number of measurements required is derived and compares favourably to traditional variational quantum eigensolver methods, but it gives no explicit function of either quantity and no exponent or constant for the qubit scaling beyond linearly..
ALGORITHM: Coarse-grained variational quantum eigensolver for intermolecular interactions
PROBLEM: Determine the ground state of weakly-interacting, non-covalently bonded molecules — the weakly-bound intermolecular regime that variational quantum algorithms applied to strongly-bound, covalently-bonded systems with full molecular-orbital bases had left largely unexplored — using a coarse-grained representation of the electronic response suited to a VQA.
IDEA: Anderson, Kiffner, Barkoutsos, Tavernelli, Crain and Jaksch develop a coarse-grained representation of the electronic response that they state is ideally suited for determining the ground state of weakly interacting molecules using a variational quantum algorithm. Their construction requires qubit numbers that grow linearly with the number of molecules, and they derive scaling behaviour for the number of circuits and measurements required, stating that this compares favourably to traditional variational quantum eigensolver methods — the abstract attaches this favourable comparison to circuits and measurements specifically, separately from the linear qubit count. The authors demonstrate the method on IBM superconducting quantum processors, showing its capability to resolve the dispersion energy as a function of separation for a pair of non-polar molecules, and state that this establishes a means by which quantum computers can model Van der Waals interactions directly from zero-point quantum fluctuations. Within this coarse-grained approximation, they conclude that current-generation quantum hardware is capable of probing energies in this weakly bound but chemically ubiquitous and biologically important regime. They also report performing experiments on simulated and real quantum computers for systems of three, four and five oscillators, and for oscillators with anharmonic onsite binding potentials, stating that the consequences of the latter are unexamined in large systems by classical computational methods but can be incorporated here with low computational overhead.
REPORTED COST: Qubit numbers that grow linearly with the number of molecules. Separately, the abstract states that scaling behaviour for the number of circuits and the number of measurements required is derived and compares favourably to traditional variational quantum eigensolver methods, but it gives no explicit function of either quantity and no exponent or constant for the qubit scaling beyond linearly.
BASIS: The abstract of arXiv:2110.00968 states two separate scaling claims, each attached to a different resource. On qubits: "We require qubit numbers that grow linearly with the number of molecules". On a different pair of resources, scaling is derived but not given as an explicit function: "and derive scaling behaviour for the number of circuits and measurements required, which compare favourably to traditional variational quantum eigensolver methods." No exponent, big-O expression, or constant accompanies either claim, and compare favourably states a direction of comparison, not a bound: what the number of circuits or measurements actually is, as a function of system size, is not given. The Classiq index entry this record covers, applications/chemistry/quantum_drude_oscillator, gives a directory path and a file list and states no bound. Those are the only sources read for this field.
DEMONSTRATED BY: the Classiq library entry applications/chemistry/quantum_drude_oscillator
PRIMARY SOURCE: Lewis W. Anderson, Martin Kiffner, Panagiotis Kl. Barkoutsos, Ivano Tavernelli, Jason Crain, Dieter Jaksch (2021), Coarse grained intermolecular interactions on quantum processors — https://arxiv.org/abs/2110.00968
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Quantum vs classical
Classical baseline
Compare Variational quantum eigensolver 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
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Literature & references
Coarse grained intermolecular interactions on quantum processors2021 · Lewis W. Anderson, Martin Kiffner, Panagiotis Kl. Barkoutsos, Ivano Tavernelli, Jason Crain, Dieter Jaksch
Primary source: it develops the coarse-grained electronic-response representation for weakly-interacting molecules, states the linear qubit scaling with the number of molecules and the derived, favourably-compared scaling for circuits and measurements, and reports the IBM superconducting-processor demonstration resolving the dispersion energy of a pair of non-polar molecules and further experiments on systems of three to five oscillators and on anharmonic oscillators. Consult it for the explicit circuit- and measurement-scaling functions, the coarse-grained model's construction, and the accuracy of the reported dispersion energies, none of which the abstract states.