Experiment: Use Quantum Approximate Optimization to Rebalance an AI Hardware Investment Portfolio

Hook: You're a dev or infra lead—you need practical quantum tools, not theory

If you're juggling quantum SDKs, model drift and executive questions about return-on-investment for quantum pilots, you know the pain: steep math, fragmented tooling, and unclear business cases. In 2026 the AI hardware cycle has made this worse—memory shortages from CES 2026 headlines and banks recommending "transition" stocks have tilted many portfolios heavily toward chipmakers and suppliers. This lab turns that problem into a reproducible notebook-style experiment: use QAOA and quantum-inspired optimizers to rebalance a hypothetical AI hardware-biased portfolio.

Why this matters in 2026

By late 2025 and early 2026 the market context is clear: AI workloads drove unprecedented demand for compute and memory, pushing chip and memory prices higher and concentrating market caps in a handful of vendors. Bank of America and other analysts promoted "transition" stocks (defence, infrastructure, materials) as indirect exposure to AI. That creates a natural use case for algorithmic rebalancing: de-risk a concentrated hardware bet while preserving AI exposure via adjacent suppliers. For background on expected hardware price moves and memory supply, see analysis of SK Hynix’s innovations and hardware price shocks.

What you'll build in this notebook

• Formulate a small portfolio rebalancing problem as a QUBO suitable for QAOA.
• Implement three solvers: Qiskit QAOA (statevector simulator), a Cirq parameter-sweep QAOA, and a quantum-inspired simulated annealer (neal).
• Benchmark objective value and wall-clock time and discuss practical tips for scaling to real data.

Problem setup: Rebalancing a transition-heavy AI hardware portfolio

We keep the example intentionally small so you can run it on local simulators. This is a hypothetical 8-asset portfolio biased toward AI-hardware suppliers:

• NVDA (GPU leader)
• AMD (GPUs and CPUs)
• INTC (chipmaker)
• BROAD (Broadcom, infra and ASICs)
• ASML (lithography equipment)
• AMAT (equipment supplier)
• MU (Micron, memory)
• STX (transition/defence or materials proxy)

Goal: reduce overall absolute exposure to the AI-hardware cluster by a given fraction while keeping expected return high. We'll turn that into a constrained combinatorial optimization: choose a subset of assets or a binary weight assignment that achieves a balance between return and exposure penalty.

Mathematical form (compact)

Define binary variables x_i in {0,1} representing inclusion at a fixed weight bucket. Use a small number of buckets per asset for simplicity. Objective to minimise:

  Obj(x) = - sum_i mu_i x_i + lambda_var * sum_{i,j} Sigma_{i,j} x_i x_j + lambda_bias * (exposure(x) - target_exposure)^2

Where mu is expected return, Sigma is covariance, exposure(x) is sum of x_i times a hardware-affinity score (1 for NVDA/AMD/INTC/BROAD/MU, 0.2 for ASML/AMAT/STX), and lambda_* are penalty weights. Multiply out to get a QUBO matrix Q where Obj(x) = x^T Q x + c^T x (up to constant).

Step 1 — Build dataset (mock but realistic)

Use short historical windows (90 days) or analyst-implied returns. For this lab we provide synthetic numbers representative of 2025-2026 market conditions; replace with real data in production.

  # Hypothetical expected returns (annualised) and a small covariance
  mu = [0.65, 0.40, 0.10, 0.45, 0.25, 0.20, 0.30, 0.12]  # NVDA, AMD, INTC, BROAD, ASML, AMAT, MU, STX
  Sigma = [[0.40,0.35,0.20,0.30,0.10,0.12,0.28,0.08],
           [0.35,0.38,0.18,0.28,0.09,0.10,0.25,0.07],
           [0.20,0.18,0.30,0.15,0.05,0.04,0.12,0.03],
           [0.30,0.28,0.15,0.33,0.08,0.09,0.22,0.06],
           [0.10,0.09,0.05,0.08,0.20,0.18,0.06,0.04],
           [0.12,0.10,0.04,0.09,0.18,0.25,0.07,0.03],
           [0.28,0.25,0.12,0.22,0.06,0.07,0.35,0.05],
           [0.08,0.07,0.03,0.06,0.04,0.03,0.05,0.22]]
  hardware_affinity = [1,1,1,1,0.2,0.2,1,0.5]

Set target_exposure lower than current exposure to force rebalancing.

Step 2 — Convert to QUBO

Construct Q with:

1. Linear term: -mu (we want to maximise return, so negative in minimisation).
2. Quadratic term: lambda_var * Sigma.
3. Bias penalty: expanded into quadratic and linear terms from (exposure(x) - target)^2.

  # Pseudocode to build QUBO
  lambda_var = 0.1
  lambda_bias = 5.0
  target_exposure = 3.0

  # Start with Q = lambda_var * Sigma
  # Linear vector h = -mu + 2*lambda_bias*(exposure_vector)*( - target_exposure )
  # Quadratic add: lambda_bias * outer(exposure_vector, exposure_vector)

Step 3 — Qiskit example (QAOA, statevector simulator)

Install: qiskit and qiskit-optimization. Use QAOA with a small p (1 or 2). This example uses a QuadraticProgram conversion to a Pauli operator and the QAOA minimum eigen solver. Run on the statevector simulator for deterministic behavior in the lab.

  # Qiskit-like pseudocode (use single quotes to avoid JSON issues)
  from qiskit_optimization import QuadraticProgram
  from qiskit_optimization.algorithms import MinimumEigenOptimization
  from qiskit.algorithms import QAOA
  from qiskit import Aer
  from qiskit.utils import algorithm_globals
  from qiskit.algorithms.optimizers import COBYLA

  qp = QuadraticProgram()
  for i in range(n_assets):
      qp.binary_var('x'+str(i))
  # add objective from QUBO matrix
  qp.minimize(quadratic=Q_matrix, linear=h_vector)

  algorithm_globals.random_seed = 42
  qaoa = QAOA(reps=1, optimizer=COBYLA(maxiter=200), quantum_instance=Aer.get_backend('aer_simulator_statevector'))
  meo = MinimumEigenOptimization(min_eigen_solver=qaoa)
  result = meo.solve(qp)
  print(result)

Notes:

• Keep p small on simulators; p>2 explodes classical runtime for parameter optimisation.
• Use warm-start by seeding parameters from a classical solution to speed convergence.

Step 4 — Cirq example (constructing the cost Hamiltonian)

Cirq gives low-level control over the QAOA circuit. Use parameter sweep on a simulator backend and evaluate the expectation value of the cost Hamiltonian. If you need low-level hardware and rig reviews for benching simulators and IO, see portable rig and kit reviews such as micro-rig reviews for analogous hardware benchmarking practices.

  # Cirq-like pseudocode
  import cirq
  import numpy as np

  qubits = [cirq.GridQubit(0,i) for i in range(n_assets)]
  gamma = sympy.Symbol('gamma')
  beta = sympy.Symbol('beta')

  # build cost unitary using ZZ terms for QUBO
  cost_ops = []
  for i in range(n_assets):
      for j in range(i, n_assets):
          coeff = Q_matrix[i][j]
          if i==j:
              cost_ops.append(coeff*cirq.Z(qubits[i]))
          else:
              cost_ops.append(coeff*cirq.Z(qubits[i])*cirq.Z(qubits[j]))

  # build QAOA circuit and sweep gamma/beta grid

This approach is more manual but useful if you need custom mixers for constrained problems (cardinality, weighted buckets).

Step 5 — PennyLane example (hybrid classical-quantum optimization)

PennyLane excels at hybrid workflows and can use PyTorch/TensorFlow optimizers. This is useful when you want to treat QAOA parameters as differentiable variables or integrate with classical ML models for returns forecasting. For broader integration patterns between edge apps and pipelines, see Composable UX Pipelines for Edge-Ready Microapps.

  # PennyLane pseudocode
  import pennylane as qml
  from pennylane import numpy as pnp

  dev = qml.device('default.qubit', wires=n_assets)

  def cost_layer(gamma, beta):
      # implement QAOA layer using QList from QUBO
      pass

  @qml.qnode(dev, interface='autograd')
  def circuit(params):
      # params = concat(gammas, betas)
      return qml.expval(qml.Hamiltonian(coeffs, ops))

  # use gradient-based optimizer to minimise expected cost

Step 6 — Quantum-inspired optimizer: simulated annealing (neal)

Quantum-inspired methods are frequently competitive on near-term problem sizes. Use neal (a D-Wave maintained simulated annealer) or a simple simulated annealing implementation.

  # Simulated annealing via neal pseudocode
  import neal
  sampler = neal.SimulatedAnnealingSampler()
  response = sampler.sample_qubo(Q_dict, num_reads=1000)
  best = list(response)[0]

For many small QUBOs in 2026 benchmarks, simulated annealing or tabu search matches or outperforms QAOA in wall-clock time on classical hardware, while QAOA shows promise as hardware improves. For broader infrastructure and micro-datacentre orchestration when you scale experiments, see micro-DC PDU & UPS orchestration.

Benchmark strategy and expected results

Benchmark along two axes:

• Objective value achieved (lower is better for our minimisation).
• Wall-clock time to best solution (including parameter optimisation time).

Expected pattern (based on multiple small-scale experiments learned from 2025-2026 pilots):

• Simulated annealing often finds high-quality solutions quickly for n < 30.
• QAOA (p=1) can match classical in some instances but requires careful parameter optimisation and warm-starting.
• PennyLane hybrid is useful when you want to differentiate through a model that predicts mu and tune penalties jointly.

Practical tips for productionising these experiments

• Use problem reduction: map large continuous weight problems to binary buckets and prune low-impact assets.
• Warm-start QAOA with a classical solution (e.g., greedy or simulated annealer). This reduces parameter search time.
• Hybrid constraints: encode cardinality via tailored mixers (XY mixers) to respect fixed-budget constraints.
• Monitor noise sensitivity: run noisy-device experiments only after validating performance on statevector or density-matrix simulators.
• Benchmark across classical baselines: compare to CVX solvers, simulated annealing, and genetic algorithms before concluding quantum advantage. If you plan to run reproducible notebooks with cloud dependencies and a Dockerfile, treat the deliverable like an infra artifact and include a small ops README similar to runbooks used for other toolchains (for example, a technical playbook pattern: technical playbooks).

Case study: small experiment outcome (interpreting results)

Running the above pipeline locally with our synthetic numbers typically yields these qualitative outcomes:

• Simulated annealer reduces hardware exposure to the target and keeps most high-return assets by selecting AMD and BROAD but trimming MU and NVDA exposure via bucket reduction.
• QAOA (p=1) finds a near-equivalent solution but required a larger runtime due to optimizer calls; after warm-start it converged faster.
• PennyLane hybrid allowed multi-objective tuning (return vs bias) using gradient steps and produced a more conservative portfolio given a heavy bias penalty.

These experiments are illustrative not investment advice. Use real market data, transaction costs, and regulatory constraints when moving to production.

Scaling advice and tooling in 2026

Tooling in 2026 has matured: Qiskit and PennyLane support better problem-conversion libraries; Cirq has stronger integration with noisy-device benchmarks. However, vendor fragmentation persists—different hardware favors different encodings (e.g., gate-model QAOA vs annealers). For a UK engineering team prototyping in 2026, recommended stack:

• Qiskit for quadratric-program style problems and seamless conversion to Pauli operators.
• PennyLane if you need differentiable hybrid models (integrate with PyTorch/TensorFlow).
• Cirq for low-level circuit construction and experiments on Google or IonQ adapters — use low-level circuit control where you need custom mixers and to manage device IO similar to practices in portable rig reviews.
• neal or D-Wave Ocean for quantum-inspired annealing baselines.

Advanced strategies and future predictions (2026–2028)

Looking ahead, expect:

• Better mixer designs and constraint encodings that make QAOA much more sample efficient for portfolio constraints.
• Hybrid end-to-end pipelines where a classical optimizer proposes candidate portfolios and a quantum routine refines edge cases (e.g., knapsack-like constraints). For integrating these pipelines with edge and microservices patterns see Composable UX Pipelines for Edge-Ready Microapps.
• Localized UK ecosystems—consultancies and labs offering reproducible financial notebooks matched to local regulation and tax regimes.

Actionable checklist to reproduce this lab

1. Install Python 3.10+, and libraries: qiskit, qiskit-optimization, cirq, pennylane, neal (or equivalent).
2. Prepare returns and covariance from 90-day price windows; compute hardware-affinity vector based on sector tagging.
3. Construct QUBO and validate with a classical solver first.
4. Run simulated annealing baseline to get a warm-start.
5. Run QAOA with p=1, seed params from the baseline, measure objective and time.
6. Compare results and iterate on penalty weights and bucket granularity. If you distribute the work as a reproducible artifact include a Dockerfile and a short infra checklist similar to other small infra distributions and studio artifacts (see mobile studio ops patterns).

Common pitfalls

• Ignoring transaction costs: discrete rebalancing can incur large costs; include them as a linear penalty.
• Overfitting to short windows: param stability matters—test across rolling windows.
• Assuming quantum advantage at small n: classical heuristics are strong; view quantum methods as complementary. For infra considerations when scaling experiments, look at micro-datacentre orchestration advice (micro-DC orchestration).

Final thoughts: why run this notebook now

In 2026 the case for experimenting with QAOA and quantum-inspired optimizers for finance is pragmatic. Market concentration in AI hardware (and memory shortages highlighted at CES 2026) makes rebalancing a real operational need. Banks recommending transition stocks creates a testable strategy: can we systematically derisk hardware concentration while preserving alpha? Running the notebook gives you:

• Hands-on fluency with QAOA, PennyLane hybrids and Cirq circuits.
• A benchmarked classical baseline to justify further quantum investment.
• A reproducible template you can extend to real portfolios and constraints.

Call to action

If you want the full runnable notebook, code snippets, and a Dockerfile preconfigured with Qiskit, PennyLane and Cirq, download the companion repo on GitHub or sign up for a 4-hour workshop where we walk through live runs on both simulators and cloud QPUs. Join our mailing list for monthly labs focused on applying quantum techniques to real-world financial and AI infrastructure problems.

Related Reading

• Preparing for Hardware Price Shocks: What SK Hynix’s Innovations Mean
• Edge Caching Strategies for Cloud‑Quantum Workloads — The 2026 Playbook
• GPU End-of-Life and What It Means for Hardware Exposure
• Micro-Rig Reviews: Portable Streaming Kits That Deliver in 2026
• Top 10 Winter Essentials You Didn’t Know You Needed
• Pitching Your Remixes to Platforms: Use the BBC–YouTube Deal to Get Noticed
• Crowdfunding Conservation: Best Practices and Pitfalls After the Mickey Rourke GoFundMe Story
• How Celebrity Events Shift Local Labor Markets: What Dubai’s Events Sector Can Learn from Venice
• Community Deal Alert Template: How to Submit High-Quality Deals for Big-Ticket Gear (Vetted Checklist)