### Parallel Simulation of Quantum Coherent dynamics by Parameterized Time-dependent Hamiltonians (PSiQCoPATH)

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Mark Rudner, Massachusetts Institute of Technology
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PSiQCoPATH is the result of the authors’ work in the parallel computing course at MIT (6.338J) taught by Professor Alan Edelman. Our goal was to design a scalable parallel algorithm for calculating the exact evolution of finite dimensional quantum systems with time-dependent Hamiltonians to arbitrary precision. Examples of such systems are the qubits of a quantum computer, and finite sized spin-lattices. Simulations with time-dependent Hamiltonians can help to investigate important issues related to the adiabatic model of quantum computation. Additionally, the code can be used to simulate NMR pulse sequences in the absence of relaxation/decoherence.

For small systems, PSiQCoPATH computes the full time evolution matrix over a given time interval using a matrix-multiply version of the parallel prefix (scan) algorithm. For larger systems where the memory requirements of the individual time-step evolution matrices approach or exceed the available system memory, a data-parallel algorithm is used to calculate the time evolution of a particular quantum state. This mode of operation yields less information about the dynamics of the system, but in return can be applied to larger systems.

**Abstract Author(s): **Mark Rudner and Eric Fellheimer