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Attested & literatureAlgorithmsVariational quantum eigensolver

Quantum subspace expansion

Measured response operators around a VQE state define a generalized eigenproblem for excitations and mitigation.

VQEvariational algorithmquantum subspace expansion

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Measured response operators around a VQE state define a generalized eigenproblem for excitations and mitigation. This record separates the reusable method idea from any one molecule, Hamiltonian, optimizer, or device.

Circuit & simulation
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:

  • Quantum subspace expansion Method

    Takes A Hermitian H reachable as a sum of terms that can be measured separately; a statement of which state is wanted — an index k, a symmetry sector, or a target energy to sit nearest; for most of the methods here, the ground state already solved, and for the deflation route every lower state as well; a target additive error and a shot budget. Returns A scalar estimate — of that eigenvalue, or of the gap between it and the ground state — together with the run budget it consumed. Some methods return a whole low-energy subspace at once and others return one state per run, and that difference is a cost, not a convenience.

How it works

Measured response operators around a VQE state define a generalized eigenproblem for excitations and mitigation. In a complete experiment, the method must be paired with a defined qubit Hamiltonian, reference state, parameterized circuit, measurement grouping, classical optimizer, stopping rule, and error analysis. The catalog therefore treats it as a literature-backed algorithm record rather than pretending that one generic snippet is the paper's implementation. Use the cited source to recover assumptions and compare energy error, variance, circuit resources, measurement cost, optimizer evaluations, and robustness under the same instance and budget.

Implementation
Unsupported
vqe-quantum-subspace-expansion.txt
METHOD: Quantum subspace expansion
SCOPE: Measured response operators around a VQE state define a generalized eigenproblem for excitations and mitigation.

This is a literature method record, not a fixed circuit.
Supply: Hamiltonian, reference state, ansatz, optimizer, measurement plan, and stopping rule.

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 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

Nobody has reviewed this record for gaps yet.

Literature & references
Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States2016 · Jarrod R. McClean, Mollie E. Schwartz, Jonathan Carter, Wibe A. de Jong

Primary or survey context for Quantum subspace expansion; consult the paper for assumptions and implementation details.

arxiv.org/abs/1603.05681