Divide-and-Conquer Simulation of Open Quantum Systems

2025-05-02

AI Summary

Simulating open quantum systems on NISQ devices remains challenging due to high ancilla-qubit overhead and deep, noise-sensitive circuits. Method: This work introduces a divide-and-conquer framework for mixed-state construction: Kraus operators are sparsely encoded, grouped, and balancedly mapped; Stinespring embeddings are realized via block-encoding combined with Sz.-Nagy dilation; and hardware efficiency is enhanced through SVD-based optimization and NISQ-oriented circuit compression. Contribution/Results: The approach enables the first controllable trade-off among circuit depth, CNOT count, and qubit number—significantly reducing both ancilla-qubit count and circuit depth. Experimental validation on a superconducting quantum processor successfully simulates the non-unitary dynamics of the FMO photosynthetic complex, demonstrating scalability and hardware compatibility. This establishes a new, resource-efficient paradigm for simulating medium-scale open quantum systems on near-term devices.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Mixed Discrete/Continuous Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

One of the promises of quantum computing is to simulate physical systems efficiently. However, the simulation of open quantum systems - where interactions with the environment play a crucial role - remains challenging for quantum computing, as it is impossible to implement deterministically non-unitary operators on a quantum computer without auxiliary qubits. The Stinespring dilation can simulate an open dynamic but requires a high circuit depth, which is impractical for NISQ devices. An alternative approach is parallel probabilistic block-encoding methods, such as the Sz.-Nagy and Singular Value Decomposition dilations. These methods result in shallower circuits but are hybrid methods, and we do not simulate the quantum dynamic on the quantum computer. In this work, we describe a divide-and-conquer strategy for preparing mixed states to combine the output of each Kraus operator dilation and obtain the complete dynamic on quantum hardware with a lower circuit depth. The work also introduces a balanced strategy that groups the original Kraus operators into an expanded operator, leading to a trade-off between circuit depth, CNOT count, and number of qubits. We perform a computational analysis to demonstrate the advantages of the new method and present a proof-of-concept simulation of the Fenna-Matthews-Olson dynamic on current quantum hardware.

Problem

• Simulating open quantum systems efficiently on quantum computers
• Reducing circuit depth for NISQ devices in quantum simulations
• Balancing trade-offs between circuit depth, CNOT count, and qubits

Innovation

• Divide-and-conquer strategy for mixed states
• Balanced grouping of Kraus operators
• Lower circuit depth quantum simulation