A Lagrange-Sylvester interpolation scheme decomposes arbitrary non-unitary operators into a linear combination of at most 2N unitaries with no truncation error, enabling cheaper simulation of open quantum systems.
Quantum Simulation via Stochastic Combination of Unitaries
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abstract
Quantum simulation algorithms often require numerous ancilla qubits and deep circuits, prohibitive for near-term hardware. We introduce a framework for simulating quantum channels using ensembles of low-depth circuits in place of many-qubit dilations. This naturally enables simulations of open systems, which we demonstrate by preparing damped many-qubit GHZ states on ibm_hanoi. The technique further inspires two Hamiltonian simulation algorithms with gate counts that are asymptotically independent of the spectral precision target, reducing resource requirements by several orders of magnitude for a benchmark system.
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Unitary Dilation Strategy Towards Efficient and Exact Simulation of Non-Unitary Quantum Evolutions
A Lagrange-Sylvester interpolation scheme decomposes arbitrary non-unitary operators into a linear combination of at most 2N unitaries with no truncation error, enabling cheaper simulation of open quantum systems.