A novel approach for quantum financial simulation and quantum state preparation
arXiv:2308.01844 · doi:10.1007/s42484-024-00160-5
Abstract
Quantum state preparation is vital in quantum computing and information processing. The ability to accurately and reliably prepare specific quantum states is essential for various applications. One of the promising applications of quantum computers is quantum simulation. This requires preparing a quantum state representing the system we are trying to simulate. This research introduces a novel simulation algorithm, the multi-Split-Steps Quantum Walk (multi-SSQW), designed to learn and load complicated probability distributions using parameterized quantum circuits (PQC) with a variational solver on classical simulators. The multi-SSQW algorithm is a modified version of the split-steps quantum walk, enhanced to incorporate a multi-agent decision-making process, rendering it suitable for modeling financial markets. The study provides theoretical descriptions and empirical investigations of the multi-SSQW algorithm to demonstrate its promising capabilities in probability distribution simulation and financial market modeling. Harnessing the advantages of quantum computation, the multi-SSQW models complex financial distributions and scenarios with high accuracy, providing valuable insights and mechanisms for financial analysis and decision-making. The multi-SSQW's key benefits include its modeling flexibility, stable convergence, and instantaneous computation. These advantages underscore its rapid modeling and prediction potential in dynamic financial markets.
13 pages, 13 figures. arXiv admin note: text overlap with arXiv:2302.12500
References in corpus (29)
- Quantum algorithm for solving linear systems of equations
- Supervised learning with quantum enhanced feature spaces
- Quantum Amplitude Amplification and Estimation
- Quantum principal component analysis
- Quantum algorithms: an overview
- Universal computation by quantum walk
- Quantum walks: a comprehensive review
- Exponential algorithmic speedup by quantum walk
- Spatial search by quantum walk
- Quantum Generative Adversarial Networks for Learning and Loading Random Distributions
- Quantum Computing for Finance: State of the Art and Future Prospects
- Quantum computational finance: Monte Carlo pricing of financial derivatives
- Creating superpositions that correspond to efficiently integrable probability distributions
- Option Pricing using Quantum Computers
- A divide-and-conquer algorithm for quantum state preparation
- Quantum State Preparation with Optimal Circuit Depth: Implementations and Applications
- Preparing random states and benchmarking with many-body quantum chaos
- Black-box quantum state preparation without arithmetic
- A Threshold for Quantum Advantage in Derivative Pricing
- A Survey of Quantum Computing for Finance
- Learning hard quantum distributions with variational autoencoders
- Simple factorization of unitary transformations
- Quantum-accelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical finance
- Dirac Quantum Cellular Automaton from Split-step Quantum Walk
- Towards Quantum Advantage in Financial Market Risk using Quantum Gradient Algorithms
- Optimal (controlled) quantum state preparation and improved unitary synthesis by quantum circuits with any number of ancillary qubits
- Loading Probability Distributions in a Quantum circuit
- Unitary equivalence classes of split-step quantum walks
- Estimation of one-dimensional discrete-time quantum walk parameters by using machine learning algorithms