Simulating quantum collision models with Hamiltonian simulations using early fault-tolerant quantum computers

2025-04-30

AI Summary

Early fault-tolerant quantum computers face severe resource constraints, hindering efficient simulation of open quantum systems—particularly quantum collision models (QCMs) that unify Markovian and non-Markovian dynamics. Method: We propose a lightweight randomized quantum algorithm for QCM simulation, eliminating reliance on specialized oracles (e.g., block-encoding) and auxiliary qubit overhead. Our compact framework introduces a memory-retaining collision mechanism to capture non-Markovianity and enables end-to-end Lindblad master equation solving. It integrates randomized Hamiltonian simulation, partial trace elimination, XX-Heisenberg chain modeling, and amplitude-damping channel implementation, with optimized CNOT gate synthesis. Results: On a 10-qubit system, our method estimates transverse magnetization using only 12 physical qubits, achieving substantially reduced circuit depth and CNOT count compared to state-of-the-art approximate Hamiltonian simulation approaches—demonstrating superior resource efficiency for open-system dynamics simulation.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

We develop randomized quantum algorithms to simulate quantum collision models, also known as repeated interaction schemes, which provide a rich framework to model various open-system dynamics. The underlying technique involves composing time evolutions of the total (system, bath, and interaction) Hamiltonian and intermittent tracing out of the environment degrees of freedom. This results in a unified framework where any near-term Hamiltonian simulation algorithm can be incorporated to implement an arbitrary number of such collisions on early fault-tolerant quantum computers: we do not assume access to specialized oracles such as block encodings and minimize the number of ancilla qubits needed. In particular, using the correspondence between Lindbladian evolution and completely positive trace-preserving maps arising out of memoryless collisions, we provide an end-to-end quantum algorithm for simulating Lindbladian dynamics. For a system of $n$-qubits, we exhaustively compare the circuit depth needed to estimate the expectation value of an observable with respect to the reduced state of the system after time $t$ while employing different near-term Hamiltonian simulation techniques, requiring at most $n+2$ qubits in all. We compare the CNOT gate counts of the various approaches for estimating the Transverse Field Magnetization of a $10$-qubit XX-Heisenberg spin chain under amplitude damping. Finally, we also develop a framework to efficiently simulate an arbitrary number of memory-retaining collisions, i.e., where environments interact, leading to non-Markovian dynamics. Overall, our methods can leverage quantum collision models for both Markovian and non-Markovian dynamics on early fault-tolerant quantum computers, shedding light on the advantages and limitations of simulating open systems dynamics using this framework.

Problem

• Simulating quantum collision models with early fault-tolerant quantum computers
• Developing randomized algorithms for open-system dynamics simulation
• Comparing circuit depths for Hamiltonian simulation techniques

Innovation

• Randomized quantum algorithms simulate collision models
• Unified framework incorporates near-term Hamiltonian simulations
• Efficiently simulates Markovian and non-Markovian dynamics