Attested & literatureOperatorsVQE Hamiltonians and observables2026-07-18

Bose–Hubbard Hamiltonian

Interacting lattice-boson model. Representative form: H = -tΣ⟨ij⟩(b†ᵢbⱼ+h.c.) + U/2Σᵢnᵢ(nᵢ-1).

VQE operatorHamiltonianbose–hubbard hamiltonian

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Bose–Hubbard Hamiltonian is cataloged as an operator rather than a circuit. Interacting lattice-boson model.

Circuit & simulation

definition

specifymap

mapping

mapgroup

measurement

group

What this takes and returns

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 →

Where the map uses this

This record is an instance of an object the map names, so these are the processes that consume or produce one. None of them is about this record in particular.

Hamiltonian you can query 4 of 33 processes

Graph-Laplacian finite differences hands one back
Recast a non-Hermitian generator as Hamiltonian evolution hands one back
Block-encode a matrix takes one
Simulate Hamiltonian evolution takes one

How it works

Interacting lattice-boson model. A representative mathematical form is H = -tΣ⟨ij⟩(b†ᵢbⱼ+h.c.) + U/2Σᵢnᵢ(nᵢ-1). 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.

Implementation

FrameworkUnsupported

operator-bose-hubbard.txt

OPERATOR: Bose–Hubbard Hamiltonian
REPRESENTATIVE FORM: H = -tΣ⟨ij⟩(b†ᵢbⱼ+h.c.) + U/2Σᵢnᵢ(nᵢ-1)
ROLE: Interacting lattice-boson model.

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.

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.

Declared gaps

Nobody has reviewed this record for gaps yet.

Literature & references

OpenFermion: The Electronic Structure Package for Quantum Computers2017 · 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

Provides open-source representations and transformations for fermionic and qubit operators used in quantum simulation.

arxiv.org/abs/1710.07629 ↗