Portfolio Optimization via Quantum Zeno Dynamics on a Quantum Processor

Abstract

Portfolio optimization is an important problem in mathematical finance, and a promising target for quantum optimization algorithms. The use cases solved daily in financial institutions are subject to many constraints that arise from business objectives and regulatory requirements, which make these problems challenging to solve on quantum computers. We introduce a technique that uses quantum Zeno dynamics to solve optimization problems with multiple arbitrary constraints, including inequalities. We show that the dynamics of the quantum optimization can be efficiently restricted to the in-constraint subspace via repeated projective measurements, requiring only a small number of auxiliary qubits and no post-selection. Our technique has broad applicability, which we demonstrate by incorporating it into the quantum approximate optimization algorithm (QAOA) and variational quantum circuits for optimization. We analytically show that achieving a constant minimum success probability in QAOA requires a number of measurements that is independent of the problem size for a specific choice of mixer operator. We evaluate our method numerically on the problem of portfolio optimization with multiple realistic constraints, and observe better solution quality and higher in-constraint probability than the state-of-the-art technique of enforcing constraints by introducing a penalty into the objective. We demonstrate the proposed method on the Quantinuum H1-2 trapped-ion quantum processor, observing performance improvements from circuits with two-qubit gate depths of up to 148.

Quantum-enhanced greedy combinatorial optimization solver

“…Note that this is only possible for some classes of constraints, as a general satisfiability problem is NP-complete. We investigate a proof of concept of the modified algorithm on a constrained binary portfolio optimization problem in the Supplementary Materials, comparing it to the state of the art (49).…”

Quantum Annealing vs. QAOA: 127 Qubit Higher-Order Ising Problems on NISQ Computers

“…There have been experimental QAOA implementations which used up to 27 qubits [18] and 23 qubits [19]. There have also been QAOA experiments which had circuit depth up to 159 [20] and 148 [21].…”

Quantum Zeno and Anti‐Zeno Effects in the Dynamics of Non‐Degenerate Hyper‐Raman Processes Coupled to Two Linear Waveguides

“…[49] Interesting applications of QZE and QAZE are also found in opposing decoherence by restricting the dynamics of the system in a decoherence-free subspace, [50] quantum interrogation measurement, [38] counterfactual secure quantum communication, [43,51] isolating quantum dot from its surrounding electron reservoir, [52] protecting the entanglement between two interacting atoms. [54] Even more practical problems, like portfolio optimization problem is proposed to be addressed using QZE, [53] and attempts have been made to study QZE in the macroscopic system, like a large black hole [56] and nonlinear waveguides, [57] nonlinear optical couplers. [55] Present study is motivated by the great possibilities of application of the QZE and QAZE established through these works, and the fact that the physical system under consideration is extremely general and experimentally realizable.…”