Speaker
Description
The preparation of a given quantum state on a quantum computing register is a typically demanding operation, requiring a number of elementary gates that scales exponentially with the size of the problem. In view of performing quantum simulations of manybody systems, this limitation might severely hinder the actual application of the noisy quantum processors that are currently available.
In our work [https://arxiv.org/abs/2405.03656] we focus on adiabatic processes to prepare quantum states. In addition to the Hamiltonian of the system to be simulated, the adiabatic preparation requires an auxiliary Hamiltonian $H_0$ that can be chosen with high arbitrariness.
Our aim is to provide a theoretically guided procedure to select the optimal auxiliary Hamiltonian, i.e. the one that allows to prepare
the highest-fidelity approximation of the target quantum state within a fixed depth of the quantum circuit.
In our work we theoretically derive a bound to the error in state preparation that shows an exponential scaling as a function of the adiabatic timescale $\tau$, which is proportional to the circuit depth,
and we provide an expression for its characteristic time, where the dependence from $H_0$ is made explicit. Therefore, the auxiliary Hamiltonian minimizing the characteristic time formula showcases an exponential suppression of the error if compared with a naively-chosen one.
We perform extensive numerical experiments to test our mathematical result on typical spin-models, such as the one- and two-dimensional Ising and Heisenberg models, confirming that the exponential bound is indeed realized and observing an exponential advantage for the optimized adiabatic processes against the unoptimized one. Our results provide a promising strategy to perform quantum simulations of manybody models via Trotter evolution on near term quantum processors.
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