What is Quantum-Inspired Optimisation?
Quantum-inspired optimisation uses algorithms that mimic the behavior of quantum systems to solve complex optimisation problems. Unlike true quantum computing, these algorithms run on classical computers but borrow concepts from quantum mechanics.
Our system uses quantum annealing techniques to explore the vast solution space of possible portfolio allocations, finding optimal combinations that maximize risk-adjusted returns while avoiding local optima that trap classical algorithms.
Quantum Annealing
A process that finds optimal solutions by gradually "cooling" from a high-energy state, similar to how metals form crystals when cooled slowly.
Quantum Tunneling
In optimisation, this allows the algorithm to escape local optima by "tunneling" through barriers to find better solutions.
Temperature Scheduling
Controls exploration vs exploitation: high temperatures allow broad exploration, while low temperatures focus on refining the best solutions.
Metropolis-Hastings
An acceptance criterion that sometimes accepts worse solutions, preventing premature convergence to suboptimal results.
Modern Portfolio Theory
Modern Portfolio Theory (MPT), developed by Harry Markowitz in 1952, is a framework for constructing portfolios to maximize expected return for a given level of risk.
Core Principles:
- Diversification: Spreading investments across different assets reduces overall portfolio risk without sacrificing expected returns.
- Risk-Return Tradeoff: Higher potential returns typically come with higher risk. The goal is to optimise this tradeoff.
- Efficient Frontier: The set of optimal portfolios that offer the highest expected return for a defined level of risk.
- Correlation: Assets that don't move together (low correlation) provide better diversification benefits.
Risk Management Concepts
Understanding and managing risk is crucial for long-term investment success. Here are key risk metrics:
| Metric | Description | Interpretation |
|---|---|---|
| Volatility | Standard deviation of returns | Lower is generally better (less uncertainty) |
| Max Drawdown | Largest peak-to-trough decline | Shows worst-case historical loss |
| VaR (95%) | Value at Risk at 95% confidence | Maximum expected loss 95% of the time |
| Beta | Sensitivity to market movements | >1 means more volatile than market |
QAOA: Quantum Approximate Optimization Algorithm
QAOA is the core algorithm powering QuantumFira's portfolio optimisation. Developed by Farhi, Goldstone, and Gutmann in 2014, it's designed to find approximate solutions to combinatorial optimisation problems.
How QAOA Works
QAOA alternates between two operations: a "cost" layer that encodes the optimisation objective, and a "mixer" layer that explores different solutions. The depth (p) controls solution quality vs. computation time.
Variational Parameters
QAOA uses classical optimisation to tune quantum gate angles (γ and β). These parameters control how much the cost function influences the state and how much mixing occurs.
Cost Hamiltonian
For portfolio optimisation, the cost encodes the Sharpe ratio (or other objectives). Higher Sharpe ratios correspond to lower energy states that the algorithm seeks.
Measurement & Sampling
After applying QAOA layers, we measure the qubits multiple times. The most frequently observed states typically correspond to good portfolio allocations.
Understanding Qubits
Unlike classical bits (0 or 1), qubits can exist in superposition, representing multiple portfolio weights simultaneously until measured.
Superposition
A qubit can be in a combination of |0⟩ and |1⟩ states. This allows exploring many portfolio combinations in parallel before collapsing to a single answer.
Entanglement
Qubits can be correlated so measuring one affects others. This encodes relationships between assets, like how tech stocks tend to move together.
Quantum Interference
Probability amplitudes can add (constructive) or cancel (destructive). QAOA uses this to amplify good solutions and suppress bad ones.
Decoherence
Real quantum hardware suffers from noise that degrades qubits over time. Circuit depth must balance solution quality against error accumulation.
Investment Strategies
Understanding different investment approaches helps you make informed decisions about portfolio construction and optimisation objectives.
Portfolio Construction Approaches
Mean-Variance Optimisation
The classic Markowitz approach: maximise expected return for a given risk level. Forms the basis of Modern Portfolio Theory and the efficient frontier.
Risk Parity
Allocate so each asset contributes equally to portfolio risk. Often results in higher bond allocations than traditional 60/40 portfolios.
Maximum Sharpe Ratio
Find the portfolio with the highest risk-adjusted return. This is QuantumFira's default objective, as it balances return and risk optimally.
Minimum Variance
Minimise portfolio volatility regardless of return. Useful for conservative investors or uncertain market conditions.
Black-Litterman Model
Combines market equilibrium with investor views. Allows you to tilt the portfolio based on your beliefs while staying diversified.
Factor Investing
Target specific return drivers like value, momentum, quality, or low volatility. Factors have historically provided excess returns over market cap weighting.
Rebalancing Strategies
| Strategy | Description | Best For |
|---|---|---|
| Calendar | Rebalance on fixed schedule (monthly, quarterly) | Simplicity, low monitoring |
| Threshold | Rebalance when weights drift beyond tolerance (e.g., ±5%) | Volatile markets, tax efficiency |
| Tactical | Adjust based on market conditions or signals | Active management, momentum |
| Buy-and-Hold | No rebalancing, let winners run | Tax-sensitive accounts, long horizons |
Backtesting & Validation
Backtesting applies a strategy to historical data to evaluate how it would have performed. It's essential for validating optimisation results before real deployment.
In-Sample vs Out-of-Sample
In-sample data trains the model; out-of-sample data tests it. Never evaluate performance on training data, as this overstates results.
Walk-Forward Analysis
Rolling window approach: optimise on past N months, test on next month, then roll forward. More realistic than single train/test split.
Transaction Costs
Real trading incurs costs: commissions, spreads, slippage. A backtest without costs overstates performance, especially for frequent rebalancing.
Survivorship Bias
Using only current stocks ignores delisted companies. This makes backtests look better than reality, as failures are excluded.
Key Backtest Metrics
| Metric | What It Measures | Watch Out For |
|---|---|---|
| CAGR | Compound annual growth rate | Can be skewed by start/end dates |
| Max Drawdown | Worst peak-to-trough decline | Single worst period may not recur |
| Calmar Ratio | CAGR divided by max drawdown | Combines return and tail risk |
| Win Rate | Percentage of profitable periods | Ignores magnitude of wins/losses |
| Profit Factor | Gross profits / gross losses | >1 needed to be profitable |
Glossary of Terms
Example: A Sharpe ratio of 1.5 means the portfolio earns 1.5 units of return for each unit of risk taken.
Good Value: Generally, above 1.0 is considered good, above 2.0 is very good.
Why it matters: Investors typically care more about downside risk than upside volatility.
Calculation: (Return - Target Return) / Downside Deviation
Example: An alpha of 2% means the portfolio outperformed its benchmark by 2%.
Note: Positive alpha suggests skill or superior strategy.
Usage: Essential for portfolio optimisation, helps identify diversification opportunities.
Reading it: High positive values indicate assets move together; negative values indicate inverse movement.
Visualization: Typically shown as a curve on a risk-return plot.
Goal: Portfolios below this curve are suboptimal.
Interpretation: Beta of 1.0 = moves with market. Beta > 1 = more volatile. Beta < 1 = less volatile. Beta < 0 = moves opposite to market.
Example: A stock with beta 1.5 tends to rise 15% when the market rises 10%.
Formula: (Portfolio Return - Risk-Free Rate) / Beta
Use case: Best for comparing portfolios that are part of a larger diversified portfolio.
Formula: (Portfolio Return - Benchmark Return) / Tracking Error
Interpretation: Higher is better. Above 0.5 is good, above 1.0 is excellent.
How it works: Alternates between quantum "cost" and "mixer" layers, with classical optimisation tuning the parameters.
Application: Ideal for portfolio optimisation as it naturally maps to QUBO problems.
Key property: Can exist in superposition of |0⟩ and |1⟩ states simultaneously.
Portfolio context: Each qubit can represent a binary decision (e.g., include asset or not).
Advantage: Allows exploring many portfolio combinations simultaneously before measurement collapses to one answer.
Analogy: Like spinning a coin that is both heads and tails until it lands.
Example: If portfolio goes from $100K to $70K then recovers to $120K, max drawdown is 30%.
Why it matters: Shows the worst historical loss an investor would have experienced.
Example: 95% VaR of $10,000 means there's a 5% chance of losing more than $10,000.
Limitation: Doesn't tell you how bad the loss could be in that 5% of cases.
Values: +1 = perfect positive correlation, 0 = no correlation, -1 = perfect negative correlation.
Diversification: Lower correlations between assets provide better diversification benefits.
Why needed: Asset price changes cause weights to drift from optimal levels.
Trade-off: More frequent rebalancing maintains targets but incurs transaction costs and taxes.
Examples: S&P 500 for US equities, Bloomberg Aggregate for bonds, 60/40 for balanced portfolios.
Purpose: Determines whether active management adds value vs. passive investing.
Interpretation: Higher tracking error = more deviation from benchmark. Low = closely follows benchmark.
Active vs Passive: Index funds target low tracking error; active managers accept higher for potential alpha.
Formula: (Ending Value / Beginning Value)^(1/years) - 1
Advantage: Accounts for compounding, making it easier to compare investments of different durations.
Usage: Baseline for calculating excess returns (Sharpe ratio, alpha, etc.).
Current: Varies with monetary policy; check current Treasury yields for accurate calculations.
QuantumFira runs portfolio optimisations across multiple quantum backends, automatically selecting the best option for each job.
IBM Quantum
Real superconducting quantum processors. Up to 156 qubits (ibm_fez). Used for production optimisations where real hardware validation matters.
Amazon Braket
Access to IonQ trapped-ion processors and Rigetti superconducting hardware, plus high-performance cloud simulators (SV1, DM1) for rapid prototyping.
MIMIQ (qPerfect)
Matrix Product State simulator optimised for deep variational circuits. Used for research-grade simulations where noise-free results are needed.
All backends use the same QAOA variational algorithm. Results are comparable across platforms, with differences arising from hardware noise profiles and qubit connectivity. The platform selects the optimal backend based on portfolio size, circuit depth, and account tier.