VQE & QAOA — The Two Algorithms Powering Quantum Applications
VQE — Variational Quantum Eigensolver
VQE is a hybrid quantum-classical algorithm designed to find the lowest energy state (ground state) of a quantum system. It is the workhorse of quantum chemistry and drug discovery.
The core idea: prepare a trial quantum state (ansatz) on the quantum hardware, measure its energy expectation value, then use a classical optimiser to tune the ansatz parameters. Repeat until convergence.
Q-MUMMA VQE Results. We have run VQE on IBM ibm_marrakesh 156Q with verified results: OPTIMIZER −1.5479H, Vaccinae 0.3918H, BIO_VACCINAE_CHEM −0.9479H. These are real hardware executions — not classical simulations.
Why VQE Matters for Drug Discovery
Classical computers use Density Functional Theory (DFT) for molecular simulation. DFT scales as O(N³) to O(N⁷) with molecule size — it fails catastrophically for large drug candidate molecules like those targeting NSCLC, Nipah, and HIV. VQE on quantum hardware scales polynomially for these problems, enabling simulations that are physically impossible classically.
UCCSD Ansatz
The Unitary Coupled Cluster Singles and Doubles (UCCSD) ansatz is the gold standard for molecular VQE. It captures electron correlation effects that simpler ansatze miss. Q-MUMMA uses UCCSD by default for molecular simulation jobs.
QAOA — Quantum Approximate Optimisation Algorithm
QAOA is designed for combinatorial optimisation problems — scheduling, routing, portfolio construction, grid dispatch. These are problems where you need to find the best solution out of an astronomically large number of possibilities.
QAOA alternates between two types of quantum gates: a "cost" unitary encoding the problem, and a "mixer" unitary exploring the solution space. As the number of layers p increases, the solution quality improves — approaching the optimal solution.
QAOA Applications in Q-MUMMA
- Portfolio Optimisation: Select optimal assets from 50–100 choices with cardinality, sector, and risk constraints — simultaneously, in one quantum circuit.
- BESS Grid Dispatch: Minimise energy dispatch cost across multi-battery fleets while maintaining grid stability SLAs.
- Vehicle Routing: Multi-vehicle, multi-depot routing with time windows — verified advantage over classical heuristics above 30 vehicles.
- EV Battery Q-BMS: Quantum-optimised charge scheduling based on predicted degradation curves. 56+ hardware runs on ibm_heron_r2.
Grover's Algorithm — Quantum Search
Grover's algorithm provides √N speedup for unstructured search. Classical search through N items: O(N). Grover's: O(√N). For 2^256 items, this is the difference between impossible and merely very hard.
Q-MUMMA uses Grover's oracle search as a component in several AI+Quantum hybrid algorithms — it is the quantum subroutine powering quantum-enhanced ML feature selection.