Operators · VQE Hamiltonians and observables
Hamiltonian variance operator
Eigenstate diagnostic and alternative objective. Representative form: H² - ⟨H⟩².
Attested & literatureUpdated
- Representative formH² - ⟨H⟩²
- Record typeOperator definition
- Papers1
This record, used inside a worked example
This page says To use this record in VQE
— 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 that example in StudioHamiltonian variance operator is cataloged as an operator rather than a circuit. Eigenstate diagnostic and alternative objective.
TakesNothingWhat joins here
No input port, deliberately. You measure a state with this entry; you do not apply it and pass a register on.
Nothing in the Atlas meets this end.
ReturnsNothingWhat joins here
No output port, deliberately. An observable is measured with, never applied, so there is no register to hand on.
Nothing in the Atlas meets this end.
Not a stage. You measure a state with this; you do not apply it and pass a register on. It has a width and deliberately no ports. See all 60 →
Eigenstate diagnostic and alternative objective. A representative mathematical form is H² - ⟨H⟩². To use this record in VQE, an implementation must specify index ordering, coefficient values and units, basis conventions, fermion-to-qubit mapping where applicable, symmetry sector, and measurement grouping. Those choices can change resource counts and even the physical interpretation. The catalog therefore preserves this as a sourced operator definition and refuses to fabricate seven circuit variants for an object that is not itself an ordered gate program.
TakesNothingWhat joins here
No input port, deliberately. You measure a state with this entry; you do not apply it and pass a register on.
Nothing in the Atlas meets this end.
ReturnsNothingWhat joins here
No output port, deliberately. An observable is measured with, never applied, so there is no register to hand on.
Nothing in the Atlas meets this end.
Not a stage. You measure a state with this; you do not apply it and pass a register on. It has a width and deliberately no ports. See all 60 →
- Representative form
- H² - ⟨H⟩²
- Record type
- Operator definition
- Circuit
- Not supplied
- Instance data
- Required for execution
This record is not a concrete circuit.
Quantum vs classical
Classical baseline
Use a classical state-vector or matrix simulation at the same width, precision, and measurement objective.
Quantum claim
The quantum record demonstrates a state or operator behavior; it does not make classical simulation or communication costs disappear.
How to compare
Compare fidelity, samples, gate depth, noise, memory, and the cost of preparing and reading the state.
Nobody has reviewed this record for gaps yet.
OPERATOR: Hamiltonian variance operator
REPRESENTATIVE FORM: H² - ⟨H⟩²
ROLE: Eigenstate diagnostic and alternative objective.
This is a mathematical operator 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.
Related entries
- Variational quantum eigensolver for ground-state energy
Algorithms
- Pauli-X operator
Operators
References
- OpenFermion: The Electronic Structure Package for Quantum Computers
Jarrod R. McClean, Kevin J. Sung, Ian D. Kivlichan, Yudong Cao, Chengyu Dai, E. Schuyler Fried, Craig Gidney, Brendan Gimby, Pranav Gokhale, Thomas Häner, Tarini Hardikar, Vojtěch Havlíček, Oscar Higgott, Cupjin Huang, Josh Izaac, Zhang Jiang, Xinle Liu, Sam McArdle, Matthew Neeley, Thomas O'Brien, Bryan O'Gorman, Isil Ozfidan, Maxwell D. Radin, Jhonathan Romero, Nicholas Rubin, Nicolas P. D. Sawaya, Kanav Setia, Sukin Sim, Damian S. Steiger, Mark Steudtner, Qiming Sun, Wei Sun, Daochen Wang, Fang Zhang, Ryan Babbush · 2017
Provides open-source representations and transformations for fermionic and qubit operators used in quantum simulation.