Quantum Risk Analysis

Abstract

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 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 $O(M^{-2/3})$. 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 measure the financial risk in 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.

12 pages, 12 figures

References in corpus (8)

• Quantum computing for finance: overview and prospects
• A new quantum ripple-carry addition circuit
• Quantum computational finance: Monte Carlo pricing of financial derivatives
• Creating superpositions that correspond to efficiently integrable probability distributions
• Entanglement generation in superconducting qubits using holonomic operations
• Quantum Analog-Digital Conversion
• Quantum Sub-Gaussian Mean Estimator
• Optimizing Quantum Circuits for Arithmetic

Cited by in corpus (103)

• Quantum Generative Adversarial Networks for Learning and Loading Random Distributions
• Quantum Computing for Finance: State of the Art and Future Prospects
• Quantum computing for finance
• Warm-starting quantum optimization
• Amplitude estimation without phase estimation
• Option Pricing using Quantum Computers
• Iterative Quantum Amplitude Estimation
• Grover Adaptive Search for Constrained Polynomial Binary Optimization
• Application-Oriented Performance Benchmarks for Quantum Computing
• IBM Quantum Computers: Evolution, Performance, and Future Directions
• Quantum computers as universal quantum simulators: state-of-art and perspectives
• Scaling of the quantum approximate optimization algorithm on superconducting qubit based hardware
• A Threshold for Quantum Advantage in Derivative Pricing
• Non-adiabatic molecular quantum dynamics with quantum computers
• Quantum-inspired algorithms for multivariate analysis: from interpolation to partial differential equations
• Towards Pricing Financial Derivatives with an IBM Quantum Computer
• Quantum Algorithms for Mixed Binary Optimization applied to Transaction Settlement
• Quantum walk-based portfolio optimisation
• Quantum unary approach to option pricing
• A hybrid quantum-classical approach to mitigating measurement errors
• Efficient State Preparation for Quantum Amplitude Estimation
• Enhancing the Quantum Linear Systems Algorithm using Richardson Extrapolation
• Faster Amplitude Estimation
• QASMBench: A Low-level QASM Benchmark Suite for NISQ Evaluation and Simulation
• Variational quantum amplitude estimation
• Prospects and challenges of quantum finance
• Amplitude estimation via maximum likelihood on noisy quantum computer
• Quantum Monte Carlo Integration: The Full Advantage in Minimal Circuit Depth
• Towards Quantum Advantage in Financial Market Risk using Quantum Gradient Algorithms
• Reduction of Qubits in Quantum Algorithm for Monte Carlo Simulation by Pseudo-random Number Generator
• Quantum computed moments correction to variational estimates
• Predicting toxicity by quantum machine learning
• A variational quantum algorithm for the Feynman-Kac formula
• Electromagnetic Nanonetworks Beyond 6G: From Wearable and Implantable Networks to On-chip and Quantum Communication
• Quantum integration of elementary particle processes
• Towards Quantum Computational Mechanics
• A performance characterization of quantum generative models
• Linear-depth quantum circuits for loading Fourier approximations of arbitrary functions
• Hybrid quantum-classical optimization for financial index tracking
• The Problem with Grover-Rudolph State Preparation for Quantum Monte-Carlo
• Quantum algorithms for grid-based variational time evolution
• Modified Grover operator for amplitude estimation
• Sampling, rates, and reaction currents through reverse stochastic quantization on quantum computers
• Quantum AI simulator using a hybrid CPU-FPGA approach
• The effect of quantum noise on algorithmic perfect quantum state transfer on NISQ processors
• Efficient Hamiltonian Simulation for Solving Option Price Dynamics
• Quantum algorithm for credit valuation adjustments
• Quantum Monte Carlo for Economics: Stress Testing and Macroeconomic Deep Learning
• Derivative Pricing using Quantum Signal Processing
• Quantum Monte Carlo simulations for financial risk analytics: scenario generation for equity, rate, and credit risk factors
• Efficient option pricing with unary-based photonic computing chip and generative adversarial learning
• Interconnect Fabrics for Multi-Core Quantum Processors: A Context Analysis
• Implementing quantum dimensionality reduction for non-Markovian stochastic simulation
• Quantum-Enhanced Simulation-Based Optimization
• Deterministic one-way logic gates on a cloud quantum computer
• Deterministic and Entanglement-Efficient Preparation of Amplitude-Encoded Quantum Registers
• Simulating a ring-like Hubbard system with a quantum computer
• Noisy quantum amplitude estimation without noise estimation
• Accelerated quantum circuit Monte-Carlo simulation for heavy quark thermalization
• Efficient Quantum Circuits for Accurate State Preparation of Smooth, Differentiable Functions
• Quantum Amplitude Estimation in the Presence of Noise
• Circuit Partitioning for Multi-Core Quantum Architectures with Deep Reinforcement Learning
• Classical and quantum machine learning applications in spintronics
• Quantum Quantitative Trading: High-Frequency Statistical Arbitrage Algorithm
• Quantum data encoding as a distinct abstraction layer in the design of quantum circuits
• Towards practical Quantum Credit Risk Analysis
• Foundational Patterns for Efficient Quantum Computing
• Quantum Encoding and Analysis on Continuous Time Stochastic Process with Financial Applications
• Noise-Aware Quantum Amplitude Estimation
• Quantum Power Flows: From Theory to Practice
• Quantum Architecture Search for Quantum Monte Carlo Integration via Conditional Parameterized Circuits with Application to Finance
• Energy risk analysis with Dynamic Amplitude Estimation and Piecewise Approximate Quantum Compiling
• Application-Oriented Benchmarking of Quantum Generative Learning Using QUARK
• Quantum Computation for Pricing the Collateralized Debt Obligations
• Provable superior accuracy in machine learned quantum models
• Quantum Computing for Data Centric Engineering and Science
• Material matters in superconducting qubits
• Pricing multi-asset derivatives by finite difference method on a quantum computer
• The State Preparation of Multivariate Normal Distributions using Tree Tensor Network
• Quantum Subroutine for Variance Estimation: Algorithmic Design and Applications
• Performance of quantum annealing for 2-SAT problems with multiple satisfying assignments
• Conditions for a quadratic quantum speedup in nonlinear transforms with applications to energy contract pricing
• Contextual Quantum Neural Networks for Stock Price Prediction
• Bayesian Quantum Amplitude Estimation
• Adaptive measurement strategy for noisy quantum amplitude estimation with variational quantum circuits
• An Amplitude-Based Implementation of the Unit Step Function on a Quantum Computer
• Efficient Gaussian State Preparation in Quantum Circuits
• Evaluating Quantum Amplitude Estimation for Pricing Multi-Asset Basket Options
• A Quantum Algorithm for the Sensitivity Analysis of Business Risks
• Quantum State Preparation for Probability Distributions with Reflection Symmetry Using Matrix Product States
• Quantum generative modeling for financial time series with temporal correlations
• Entanglement Properties of Quantum Superpositions of Smooth, Differentiable Functions
• Quantum algorithm for copula-based risk aggregation using orthogonal series density estimation
• Classical post-processing approach for quantum amplitude estimation
• Quantum Bohmian Inspired Potential to Model Non-Gaussian Events and the Application in Financial Markets
• Dividing quantum circuits for time evolution of stochastic processes by orthogonal series density estimation
• Quantum Annealing Algorithm for Expected Shortfall based Dynamic Asset Allocation
• Diagonal-Budgeted Trotterization for Efficient Quantum Hamiltonian Simulation
• QAFE${}^2$: Quantum accelerated multiscale finite element analysis
• Quantum Implementation of Risk Analysis-relevant Copulas
• Quantum Speedup of Monte Carlo Integration with respect to the Number of Dimensions and its Application to Finance
• Quantum Encoding of Structured Data with Matrix Product States
• Risk Fluctuation Characteristics of Internet Finance: Combining Industry Characteristics with Ecological Value