Academy

Quantum Annealing

Quantum annealing is a specialized computational approach designed to solve complex optimization problems by exploiting quantum mechanical principles. Unlike classical algorithms that use thermal fluctuations to escape local minima, quantum annealers harness quantum tunneling to traverse energy barriers more directly. This makes them particularly suited for combinatorial problems such as feature selection in machine learning, where one seeks the best subset of inputs out of many possibilities.

How Quantum Annealing Works

1. Problem Encoding: The optimization task is formulated as a QUBO (Quadratic Unconstrained Binary Optimization) or equivalent Ising model. Variables are binary (0 or 1) and represent choices such as whether to include a pixel as a feature.
2. Hamiltonian Construction: Two Hamiltonians are defined: an initial “driver” Hamiltonian promoting superposition across all states, and a “problem” Hamiltonian encoding the cost function to minimize.
3. Annealing Schedule: A time-dependent parameter s(t) transitions the system from the driver Hamiltonian (s=0) to the problem Hamiltonian (s=1). The quantum system ideally remains in its ground state according to the adiabatic theorem.
4. Measurement: At the end of the schedule, qubits collapse to classical values that approximate the optimal solution. Many runs produce a distribution of low-energy states, from which the best solution is selected.

Key Components of a QUBO

• Linear Terms (hᵢ): Weights on individual variables reflecting their standalone importance (e.g., mutual information with class labels).
• Quadratic Terms (Jᵢⱼ): Couplings between pairs of variables capturing redundancy or interaction penalties.
• Penalty Functions: Additional terms enforce constraints such as selecting exactly k features. Sparse penalties preserve hardware embeddability.

Applications in Feature Selection

In machine learning for medical imaging, high-resolution images can have hundreds of thousands of pixels as potential features. Quantum annealing enables selecting a small informative subset by encoding a mutual-information-based objective into the QUBO. Subsampling and coupling thresholding reduce problem size and connectivity, making it feasible on current hardware like the D-Wave Pegasus topology.

Advantages and Challenges

• Pros: Potentially faster exploration of large solution spaces and direct hardware implementation.
• Cons: Limited qubit counts, sparse connectivity requiring embedding overhead, and noise in NISQ devices may yield suboptimal solutions.

Relevance to Digital Technologies and Longevity Science

Efficient feature selection in medical imaging supports streamlined data processing and reduced storage needs, which can accelerate diagnostic workflows. As longevity science increasingly relies on large-scale imaging data to monitor age-related changes and therapeutic effects, quantum-assisted workflows could help manage complexity and improve interpretability in imaging biomarkers.