Kavli Affiliate: Zeeshan Ahmed
| First 5 Authors: Kushagra Garg, Zeeshan Ahmed, Subhadip Mitra, Shantanav Chakraborty,
| Summary:
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.
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