Algorithms · Variational quantum eigensolver
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.
Attested & literatureUpdated
Open on the mapView frozen graph
- Record typeLiterature reference
- Reference implementationquantum_drude_oscillator
- Reported costQubit 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.
- Papers1
A part this method uses, worked through
This page says determining the ground state of weakly interacting molecules using a variational quantum algorithm
— here is a concrete, runnable instance of it.
VQE on a 2-qubit transverse-field Ising Hamiltonian
2 qubits, H = Z⊗Z + 0.5*(X⊗I + I⊗X), a stated toy Hamiltonian (not a molecule), minimised with a hardware-efficient ansatz.
Where it ends up
- 1043%
- 0143%
- 007%
- 117%
At these angles the ansatz's energy ⟨H⟩ reaches E0 = −√2, the Hamiltonian's exact ground energy; a real VQE run reaches these angles by repeating measure-the-energy then update-the-angles, not by a closed-form solution.
Open this part in StudioDetermine 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.
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 →
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..
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 →
- Record type
- Literature reference
- Reference implementation
- quantum_drude_oscillator
- 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.
- Complexity 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 demonstration this record covers states no complexity bound of its own. Those are the only sources read for this field.
- Circuit
- Not supplied
This record is not a concrete circuit.
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.
Nobody has reviewed this record for gaps yet.
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 demonstration this record covers states no complexity bound of its own. Those are the only sources read for this field.
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
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.
Where this sits
This record is named by the layer graph at:
- Estimate a Hamiltonian's ground-state energy Slot
Takes A Hermitian 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 and a confidence . 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.
Related entries
- Variational quantum eigensolver for ground-state energy
Algorithms
- Hardware-efficient VQE ansatz
Algorithms
- Measurement-grouped VQE
Algorithms
- Coulomb interaction operator
Operators
References
- Coarse grained intermolecular interactions on quantum processors
Lewis W. Anderson, Martin Kiffner, Panagiotis Kl. Barkoutsos, Ivano Tavernelli, Jason Crain, Dieter Jaksch · 2021
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.