Data-Conditioned Variational Quantum Eigensolvers for Clinical Biomarker Discovery: Constructing Patient-Specific Hamiltonians from Medical Data

Abstract

The variational quantum eigensolver (VQE) was at
first designed as a hybrid quantum-classical method for finding
the ground-state energies of molecules on noisy intermediate-scale
quantum (NISQ) devices. Currently, however, there is a small
but emerging line of research that takes the opposite approach:
instead of minimizing the energy of a Hamiltonian which is
derived from physical principles, the quantum state is determined
according to an encoding of the patient’s clinical record, and the
algorithm searches for a Hamiltonian whose ground state most
closely matches that state. The resulting operator is regarded
as a sparse and interpretable biomarker, and the expectation
value of this operator is used as a calibrated clinical risk score.
In this article, we examine this data-conditioned, or inverse,
VQE approach. We begin by reiterating the standard VQE
formalism, then restate the inverse objective along with its
analytic solution for single-term Pauli Hamiltonians as given
in the source. Additionally, we analyze the encoding, coefficient
inference, measurement, and thresholding elements essential for
a complete pipeline. A recent multi-qubit study involving a cohort
with co-infection of HIV and tuberculosis is analyzed in detail as
the most advanced example of this approach. We compare it with
other related methods based on quantum kernels, variational
quantum classifiers, and quantum-enhanced feature selection,
and we place it within the current classification of quantum-
enhanced biomarker discovery, where it does not belong in any
of the existing categories. We then carry out a critical evaluation
of the paradigm. The classical eigenvalue calculation within
the search loop has an asymptotic scaling of O(8N), although
at the two qubits that are actually used it is negligible. By
restricting the search to single-term Pauli operators, it becomes
possible to classically simulate the quantum expectation values,
thereby nullifying the claims of quantum advantage while still
preserving interpretability. The benefits reported are based on
small, severely imbalanced, single-center cohorts and include no
external validation or actual implementation on real hardware.
Compared with the requirements that the quantum computing
community is now moving towards for benchmark definitions, the
published evaluation still does not yet satisfy most of the criteria
currently proposed for application-level benchmarking, mainly
because the classical and quantum contributions to the result
are never separated. We conclude with a roadmap that specifies
the particular conditions, from an evaluation-theoretic point of
view, under which data-conditioned Hamiltonian learning could
become a real application of quantum computing in precision
medicine, before turning to algorithmic aspects.