[Paper Review] Prospects and challenges of quantum finance

Adam Bouland, Wim van Dam+3 more|arXiv (Cornell University)|Nov 12, 2020

Quantum Computing Algorithms and Architecture110 references46 citations

TL;DR

A survey of how quantum computing could impact finance, detailing potential speedups in Monte Carlo methods, portfolio optimization, and machine learning, along with hardware and algorithmic challenges and near-term strategies.

ABSTRACT

Quantum computers are expected to have substantial impact on the finance industry, as they will be able to solve certain problems considerably faster than the best known classical algorithms. In this article we describe such potential applications of quantum computing to finance, starting with the state-of-the-art and focusing in particular on recent works by the QC Ware team. We consider quantum speedups for Monte Carlo methods, portfolio optimization, and machine learning. For each application we describe the extent of quantum speedup possible and estimate the quantum resources required to achieve a practical speedup. The near-term relevance of these quantum finance algorithms varies widely across applications - some of them are heuristic algorithms designed to be amenable to near-term prototype quantum computers, while others are proven speedups which require larger-scale quantum computers to implement. We also describe powerful ways to bring these speedups closer to experimental feasibility - in particular describing lower depth algorithms for Monte Carlo methods and quantum machine learning, as well as quantum annealing heuristics for portfolio optimization. This article is targeted at financial professionals and no particular background in quantum computation is assumed.

Motivation & Objective

• Assess which finance problems may benefit from quantum computing and estimate when speedups become practically relevant.
• Describe quantum algorithms for Monte Carlo, portfolio optimization, and machine learning in finance.
• Evaluate hardware resource requirements and realistic timelines for near-term and fault-tolerant quantum devices.
• Propose architectures and techniques to reduce quantum resource needs and advance NISQ-era feasibility.

Proposed method

• Review state-of-the-art quantum algorithms applicable to finance (Monte Carlo, portfolio optimization, machine learning).
• Analyze resource requirements and practicality for near-term (NISQ) and fault-tolerant quantum computers.
• Discuss algorithmic redesigns to reduce circuit depth and qubit counts while preserving performance guarantees.
• Present QC Ware-specific approaches to lower-depth Monte Carlo, quantum machine learning, and portfolio optimization heuristics.

Experimental results

Research questions

• RQ1 Which financial tasks can achieve quantum speedups, and under what hardware assumptions?
• RQ2 How can quantum Monte Carlo, portfolio optimization, and machine learning be adapted to reduce hardware requirements for practical use?
• RQ3 What are the near-term (NISQ) prospects versus long-term fault-tolerant prospects for quantum finance?
• RQ4 What redesigns or heuristics can bring proven-speedup algorithms into experimentally feasible regimes?

Key findings

• Quantum Monte Carlo offers quadratic speedups in sampling complexity, but practical deployment requires very low error rates and deep circuits for full-scale implementations.
• Near-term Monte Carlo improvements focus on reducing circuit depth and leveraging parallelism to approach partial speedups feasible on NISQ devices.
• Portfolio optimization can use quantum linear system solvers for convex cases, but current depth and qubit requirements limit near-term applicability; combinatorial (integer) cases rely on heuristics and quantum annealing.
• Quantum machine learning shows polynomial speedups in theory, but practical use requires efficient data loading (QRAM concerns) and data-loading techniques; QC Ware presents data loaders to enable NISQ-era work.
• Hybrid approaches and depth-reduction strategies can bring some quantum advantages closer to feasibility, though full asymptotic speedups typically require fault-tolerant quantum computing.