Understanding Constraint-Aware Quantum Algorithms

I’m excited to share the results of a great #quantumcomputing collaboration between Global Technology Applied Research at JPMorgan Chase & Co. and Infleqtion! In this work, we propose and benchmark Q-CHOP, a new #quantum adiabatic algorithm applicable to a broad range of constrained #optimization problems. Our algorithm leverages the observation that for many problems, while the best solution is difficult to find, the worst feasible (constraint-satisfying) solution is known. The basic idea is to to enforce a Hamiltonian constraint at all times, thereby restricting evolution to the subspace of feasible states, and slowly "rotate" an objective Hamiltonian to trace an adiabatic path from the worst feasible state to the best feasible state. Through extensive benchmarks, we show that our algorithm consistently outperforms the state-of-the-art adiabatic approach on a wide range of problems, including a real-world financial use case, namely bond #exchangetradedfunds (#etf) basket optimization. See our arXiv paper for more details: https://lnkd.in/epuBs98V Authors: Michael A Perlin, Ruslan Shaydulin, Benjamin Hall, Pierre Minssen, Changhao Li, Kabir Dubey, Rich Rines, Eric Anschuetz, Marco Pistoia, and Pranav Gokhale

Our latest paper is published: "Constrained Portfolio Optimization via Quantum Approximate Optimization Algorithm (QAOA) with XY-Mixers and Trotterized Initialization: A Hybrid Approach for Direct Indexing." We looked into how quantum computing can help solve the "Combinatorial Cliff" problem that asset managers face when trying to pick specific groups of assets (cardinality constraints) without using costly convex optimization methods. The approach: Business: We focused on the practical problem of selecting exactly K assets out of N to minimize risk and maximize return, a critical task for customizable Separately Managed Accounts (SMAs). Novelty: Instead of using standard soft penalties that distort the optimization landscape, we implemented a constraint-preserving ansatz using XY-mixers and Dicke state initialization to ensure valid portfolios are explored. We also introduced a Trotterized parameter initialization to mitigate the "Barren Plateau" problem often found in quantum training. Key Results: In a walk-forward backtest on US equities, our QAOA formulation achieved a Sharpe Ratio of 1.81, effectively outperforming classical heuristics like Simulated Annealing (1.31) and Hierarchical Risk Parity (0.98). While the turnover is higher, the theoretical optimality suggests a strong pathway for institutional relevance. A sincere thank you to my co-authors: Theodore Bouloumis, PhD for his rigorous quality analysis and driving the narrative of the research, and Frederic Goguikian for providing the critical business-side expertise that grounded our study in financial reality. Here the article: https://lnkd.in/d46ErUMH #quantumcomputing #fintech #qaoa #portfoliooptimization #algorithmictrading

Joint work with Dhrumil Patel and Patrick Coles now published in Quantum - the open journal for quantum science: https://lnkd.in/g7vUGDjn Popular Summary: Many real-world problems in science and industry can be expressed as optimization problems, which involve finding the best solution while meeting specific constraints. Among these, a special class of optimization problems called semidefinite programming holds significance. They are widely used to model or approximate problems arising in various fields such as operations research, combinatorial optimization, control theory, and quantum information theory. For solving these programs, quantum algorithms have been proven to provide a quadratic speedup over classical algorithms. However, these quantum algorithms are not well-suited for current quantum devices, which are noisy and limited in their capabilities. In this work, we propose three quantum algorithms designed to run on these noisy devices. Our algorithms are hybrid quantum-classical algorithms that have a classical computer available for optimization, only calling a quantum computer for tasks that are not efficiently solvable by it. We rigorously analyze the performance of one of our algorithms, quantifying how rapidly it converges to the optimal value. Finally, to demonstrate their practicality, we numerically simulate our quantum algorithms for problems like MaxCut, a prominent graph theoretic problem. Our simulations showcase their effectiveness even in the presence of noise.

Parity Quantum Optimization: Encoding Constraints “Constraints to optimization problems are crucial for many problems that are encountered in science, technology, and industry, ranging from scheduling problems to quantum chemistry. Quantum computing as a new paradigm of computing, which aims, among other things, at enhancing optimization algorithms by making use of quantum phenomena, may improve upon existing algorithms to solve these kinds of problems. However, quantum computers are limited in coherence, control, and connectivity which makes encoding of optimization problems one of the current grand challenges in the field. Constraints are an additional complication to the encoding challenge and they are typically encoded via large energy penalties given as quadratic terms leading to fully connected interactions. “ “To encode constraints we introduce a combination of exchange interactions and spin-flip terms in combination with the parity encoding. The parity trans-formation encodes optimization problems in a lattice gauge model with local 3-body and 4-body interac-tions on a square lattice. We introduce exchange terms that only act on qubits that are part of the constraints and spin-flip terms that act on the rest of the qubits. Using a compiler , qubits can be arranged on the square lattice with flexibility.”   By Maike Drieb-Schön , Kilian Ender , Younes Javanmard, and Wolfgang Lechner   ParityQC Universität Innsbruck Link https://lnkd.in/dJZknhiN