Quantum computing portfolio optimization
An IBM Qiskit function called the Quantum Portfolio Optimizer was introduced by the technology company Global Data Quantum. It uses quantum computing to optimize investment portfolios.
Here’s a thorough breakdown:
Quantum Portfolio Optimizer Purpose
In order to maximize investment performance while lowering transaction costs and risks, the Quantum Portfolio Optimizer was created. Finding the best investment plan over a number of time periods to maximize expected return and decrease risks, often while dealing with limitations like budget, transaction costs, or risk aversion, is the dynamic portfolio optimization problem that it tackles. In contrast to traditional portfolio optimization, which takes into account a single rebalancing period, the dynamic version adjusts assets in response to changing asset performance. Analysts, individual investors, and portfolio managers are all intended users of the program. In portfolio optimization, it makes it possible to backtest trading methods.
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Quantum Portfolio Optimizer Accessibility:
You may find the function in the IBM Qiskit Functions Catalogue. Currently in preview release state, this experimental functionality is exclusively accessible to users of the IBM Quantum Premium Plan and Flex Plan. To gain access to Global Data Quantum, users must submit a catalogue request.
Why Use Quantum Computing?
As the number of resources or constraints rises, traditional approaches encounter severe speed and efficiency limitations. Even on high-performance computing (HPC) resources, complicated problems that are difficult for classical solvers like CPLEX, Gurobi, or Pyscf to handle can be solved significantly more quickly and efficiently thanks to quantum computing’s ability to analyse several variables in parallel.
How Quantum Portfolio Optimizer Works?
Four steps make up the Quantum Portfolio Optimizer’s process:
- The prices of financial assets and user-specified investment conditions are among the inputs it gets.
- The classical input data is mapped to quantum circuits to transform this information into a problem designed for quantum resolution. In order to do this, the dynamic portfolio optimisation problem must be constructed using the Quadratic Unconstrained Binary Optimisation (QUBO) formulation and converted into a quantum operator (Ising Hamiltonian).
- The Variational Quantum Eigensolver (VQE) algorithm is taken into consideration. The VQE was created especially to find the best investment combinations in the entire solution area. In this hybrid quantum-classical approach, the cost function is estimated by the quantum circuit, and the classical optimisation is carried out via a classical optimisation technique (such as Differential Evolution).
- The system generates an optimal, reliable, and feasible recommendation by adjusting post-processing to reduce the noise characteristic of existing quantum devices. A noise-aware (SQD-based) post-processing is included of the system to maximise output quality.
Problem Formulation
Quadratic Unconstrained Binary Optimisation (QUBO), a multi-objective problem, is used to formulate the portfolio optimisation. The QUBO function seeks to optimise four goals at once:
- Increase the return function (F) to its maximum.
- Reduce the investment risk (R) and transaction expenses (C).
- Respect the limitations on investments (P). With γ representing the risk aversion coefficient and ρ the constraints reinforcement coefficient (Lagrange multiplier), the QUBO function is expressed as O = -F + (γ/2)R + C + ρP. A problem’s minimum qubit count is determined by the number of assets (na), time periods (nt), and bit resolution (nq) that is utilised to represent the investment (na * nt * nq).
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Input
The function needs a number of input parameters:
- Assets: Dates serve as secondary keys in a dictionary that contains asset prices. For the same dates, data must be consistent across all assets.
- Qubo_settings: A dictionary that allows you to configure the QUBO issue with parameters including the number of resolution qubits (nq), time window each step (dt), maximum investment per asset, risk aversion coefficient, transaction charge, and restriction coefficient.
- Optimizer_settings (Optional): Sets up the traditional optimisation procedure, including primitive settings (such as sampler_shots, estimator_shots) and differentiation_evolution algorithm parameters (such as num_generations, population_size).
- ansatz_settings (Optional): Configure the quantum circuit ansatz by choosing “optimized_real_amplitudes” or “tailored” and turning on multiple pass managers or dynamical decoupling, among other options.
- Backend (Optional): The QPU backend name to utilise, such as “ibm_torino.”
- previous_session_id (Optional): A list of past session IDs to resume execution or retrieve data is provided by the optional previous_session_id parameter.
- Apply_postprocess (Optional): A boolean representing the application of noise-aware SQD post-processing, with True as the default.
- Tags (optional): A string list used to label the experiment.
Output
“result” and “metadata” are the two dictionaries that are returned by the function.
- Result: Consists of the best optimization outcomes, such as the best investment strategy over time and the corresponding least objective cost. The overall amount invested is used to normalize the investment weights.
- Metadata: All outcomes obtained during the optimization process are detailed in the metadata. This covers counts, investment paths, objective costs, Sharpe ratios, returns, limitation violations, samples/states, and transaction costs. The session ID, asset order, QUBO matrix, and resource consumption summary are among the other details it contains. The optimal solution’s metadata includes important parameters like the return, Sharpe ratio, restriction deviation, and minimum objective cost.
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Qiskit Application Function Context
By abstracting away the complexity of the quantum workflow, application functions such as the Quantum Portfolio Optimiser offer a complete, pre-made quantum pipeline. It is simple to incorporate quantum methods into current application processes without the need for specialised understanding of quantum computing because they take standard classical inputs and return domain-familiar classical outputs.
Analysis of Performance and Benchmarks:
Various resolution qubit, ansatz circuit, and asset grouping configurations are used to verify the function. Benchmarks assess the quality of solutions using two primary metrics:
- Objective cost: In order to gauge the effectiveness of optimization, the objective cost compares the cost function value with the output of traditional solvers such as Gurobi (free version).
- Sharpe ratio: The Sharpe ratio measures the portfolio’s risk-adjusted return. According to benchmark data, the quantum optimizer successfully finds profitable investment plans. For instance, the Optimized Real Amplitudes ansatz produced an objective cost of -3.67 and a Sharpe ratio of 14.48 for a test using IBEX35 assets (Set 3, 4 time steps, 2-bit encoding, 56 qubits), while Gurobi produced a Sharpe ratio of 16.44 and an objective cost of -4.11. Comparing the quantum technique to random sampling, visual examination reveals that the cost distribution is significantly concentrated at lower costs.
