A Threshold for Quantum Advantage in Derivative Pricing

Abstract

We give an upper bound on the resources required for valuable quantum advantage in pricing derivatives. To do so, we give the first complete resource estimates for useful quantum derivative pricing, using autocallable and Target Accrual Redemption Forward (TARF) derivatives as benchmark use cases. We uncover blocking challenges in known approaches and introduce a new method for quantum derivative pricing - the re-parameterization method - that avoids them. This method combines pre-trained variational circuits with fault-tolerant quantum computing to dramatically reduce resource requirements. We find that the benchmark use cases we examine require 8k logical qubits and a T-depth of 54 million. We estimate that quantum advantage would require executing this program at the order of a second. While the resource requirements given here are out of reach of current systems, we hope they will provide a roadmap for further improvements in algorithms, implementations, and planned hardware architectures.

arXiv commentVersion to be published at Quantum

References in corpus (25)

• A variational eigenvalue solver on a quantum processor
• Quantum Amplitude Amplification and Estimation
• How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits
• Variational ansatz-based quantum simulation of imaginary time evolution
• Quantum Generative Adversarial Networks for Learning and Loading Random Distributions
• Quantum Natural Gradient
• Efficient Simulation of Quantum Systems by Quantum Computers
• Quantum algorithms for electronic structure calculations: particle/hole Hamiltonian and optimized wavefunction expansions
• Quantum Computing for Finance: State of the Art and Future Prospects
• Quantum-state preparation with universal gate decompositions
• Quantum speedup of Monte Carlo methods
• Quantum Risk Analysis
• Quantum computational finance: Monte Carlo pricing of financial derivatives
• Amplitude estimation without phase estimation
• Quantum circuits of T-depth one
• Option Pricing using Quantum Computers
• Iterative Quantum Amplitude Estimation
• Focus beyond quadratic speedups for error-corrected quantum advantage
• Efficient synthesis of universal Repeat-Until-Success circuits
• Quantum Approximate Counting, Simplified
• Non-adiabatic molecular quantum dynamics with quantum computers
• Efficient State Preparation for Quantum Amplitude Estimation
• Reversible Circuit Optimization via Leaving the Boolean Domain
• Amplitude estimation via maximum likelihood on noisy quantum computer
• The Problem with Grover-Rudolph State Preparation for Quantum Monte-Carlo

Cited by in corpus (40)

• Quantum computing for finance
• Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
• Optimizing resource efficiencies for scalable full-stack quantum computers
• Grid-based methods for chemistry simulations on a quantum computer
• Challenges of variational quantum optimization with measurement shot noise
• Quantum Monte Carlo Integration: The Full Advantage in Minimal Circuit Depth
• Quantum computing for chemistry and physics applications from a Monte Carlo perspective
• Quantum algorithms for approximate function loading
• Towards Quantum Advantage in Financial Market Risk using Quantum Gradient Algorithms
• A variational quantum algorithm for the Feynman-Kac formula
• Minimum quantum run-time characterization and calibration via restless measurements with dynamic repetition rates
• Predicting Good Quantum Circuit Compilation Options
• Quantum Fourier analysis for multivariate functions and applications to a class of Schrödinger-type partial differential equations
• Sampling, rates, and reaction currents through reverse stochastic quantization on quantum computers
• Efficient Hamiltonian Simulation for Solving Option Price Dynamics
• Quantum Monte Carlo for Economics: Stress Testing and Macroeconomic Deep Learning
• Derivative Pricing using Quantum Signal Processing
• Fault-tolerant Post-Selection for Low Overhead Magic State Preparation
• Quantum Monte Carlo simulations for financial risk analytics: scenario generation for equity, rate, and credit risk factors
• Quantum Quantile Mechanics: Solving Stochastic Differential Equations for Generating Time-Series
• Noisy quantum amplitude estimation without noise estimation
• Option pricing under stochastic volatility on a quantum computer
• A novel approach for quantum financial simulation and quantum state preparation
• On proving the robustness of algorithms for early fault-tolerant quantum computers
• Protocols for Trainable and Differentiable Quantum Generative Modelling
• Hybrid Quantum-Classical Autoencoders for End-to-End Radio Communication
• Quantum Architecture Search for Quantum Monte Carlo Integration via Conditional Parameterized Circuits with Application to Finance
• Quantum mean estimation for lattice field theory
• Quantum Computing for Data Centric Engineering and Science
• Robust Quantum Arithmetic Operations with Intermediate Qutrits in the NISQ-era
• An Amplitude-Based Implementation of the Unit Step Function on a Quantum Computer
• Heisenberg-limited adaptive gradient estimation for multiple observables
• Leakage in restless quantum gate calibration
• Quantum state preparation via piecewise QSVT
• Low Depth Phase Oracle Using a Parallel Piecewise Circuit
• Conditional Generative Models for Learning Stochastic Processes
• Dividing quantum circuits for time evolution of stochastic processes by orthogonal series density estimation
• Quantum algorithm for solving McKean-Vlasov stochastic differential equations
• On the bias in iterative quantum amplitude estimation
• Time series generation for option pricing on quantum computers using tensor network