Quantum risk analysis
By Stefan Woerner, Daniel J. Egger. npj Quantum Information, 2018
351 citations recorded by the source corpus.
We present a quantum algorithm that analyzes risk more efficiently than Monte Carlo simulations traditionally used on classical computers. We employ quantum amplitude estimation to price securities and evaluate risk measures such as Value at Risk and Conditional Value at Risk on a gate-based quantum computer. Additionally, we show how to implement this algorithm and how to trade-off the convergence rate of the algorithm and the circuit depth. The shortest possible circuit depth—growing polynomially in the number of qubits representing the uncertainty—leads to a convergence rate of O(M−2/3), where M is the number of samples. This is already faster than classical Monte Carlo simulations which converge at a rate of O(M−1/2). If we allow the circuit depth to grow faster, but still polynomially, the convergence rate quickly approaches the optimum of O(M−1). Thus, for slowly increasing circuit depths our algorithm provides a near quadratic speed-up compared to Monte Carlo methods. We demonstrate our algorithm using two toy models. In the first model we use real hardware, such as the IBM Q Experience, to price a Treasury-bill (T-bill) faced by a possible interest rate increase. In the second model, we simulate our algorithm to illustrate how a quantum computer can determine financial risk for a two-asset portfolio made up of government debt with different maturity dates. Both models confirm the improved convergence rate over Monte Carlo methods. Using simulations, we also evaluate the impact of cross-talk and energy relaxation errors.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/71822fa2acf8c74b12e49ac6105ef5432e38f49f
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In Artificial Intelligence
- Stefan Woerner
- Daniel J. Egger
- Christa Zoufal
- Aurélien Lucchi
- Samuel Mugel
- Enrique Lizaso
- Roman Orus
- Jakub Marecek
In Atomic and Molecular Physics, and Optics
- Stefan Woerner
- Christa Zoufal
- Aurélien Lucchi
- Samuel Mugel
- Enrique Lizaso
- Roman Orus
- Jakub Marecek
- Daniel J. Egger
Citations in the corpus
- Quantum Computing for Finance: State-of-the-Art and Future Prospects (2020, methodology): “, we will construct A such that a = P [L ≤ x] for a given x ≥ 0, and apply a bisection search to find the smallest xα ≥ 0 such that P [L ≤ xα] ≥ α, which implies xα = VaRα[L] [9].”
- Warm-starting quantum optimization (2020, background): “Gate-based quantum computers are expected to aid in solving problems such as quantum chemistry calculations [1–3], machine learning [4, 5], financial simulation [6–13] and combinatorial optimization [14, 15].”
- Quantum Generative Adversarial Networks for learning and loading random distributions (2019, methodology): “[28] S.”
- Amplitude estimation without phase estimation (2019, background): “, in chemistry [7, 8], finance [9, 10], and machine learning [11– 14].”
- Option Pricing using Quantum Computers (2019, methodology): “[17], also gives a formula that specifies which value of c to use to minimize the estimation error made when using AE.”
- Quantum computing for finance: Overview and prospects (2018, methodology): “Woerner and Egger pioneered the idea of adapting the core principles of quantumaccelerated Monte Carlo to efficiently estimate these variables [72].”