Simulating quantum collision models with Hamiltonian simulations using early fault-tolerant quantum computers
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918126924333056 |
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| author | Garg, Kushagra Ahmed, Zeeshan Mitra, Subhadip Chakraborty, Shantanav |
| author_facet | Garg, Kushagra Ahmed, Zeeshan Mitra, Subhadip Chakraborty, Shantanav |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21564 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simulating quantum collision models with Hamiltonian simulations using early fault-tolerant quantum computers Garg, Kushagra Ahmed, Zeeshan Mitra, Subhadip Chakraborty, Shantanav Quantum Physics Data Structures and Algorithms 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. |
| title | Simulating quantum collision models with Hamiltonian simulations using early fault-tolerant quantum computers |
| topic | Quantum Physics Data Structures and Algorithms |
| url | https://arxiv.org/abs/2504.21564 |