The simulation of quantum dynamics calls for quantum algorithms working in first quantized grid encodings. Here, we propose a variational quantum algorithm for performing quantum dynamics in first quantization. In addition to the usual reduction in circuit depth conferred by variational approaches, this algorithm also enjoys several advantages compared to previously proposed ones. For instance, variational approaches suffer from the need for a large number of measurements. However, the grid encoding of first quantized Hamiltonians only requires measuring in position and momentum bases, irrespective of the system size. Their combination with variational approaches is therefore particularly attractive. Moreover, heuristic variational forms can be employed to overcome the limitation of the hard decomposition of Trotterized first quantized Hamiltonians into quantum gates. We apply this quantum algorithm to the dynamics of several systems in one and two dimensions. Our simulations exhibit the previously observed numerical instabilities of variational time propagation approaches. We show how they can be significantly attenuated through subspace diagonalization at a cost of an additional O(MN2) 2-qubit gates where M is the number of dimensions and NM is the total number of grid points.

Quantum algorithms for grid-based variational time evolution / P. J Ollitrault, S. Jandura, A. Miessen, I. Burghardt, R. Martinazzo, F. Tacchino, I. Tavernelli. - In: QUANTUM. - ISSN 2521-327X. - 7:(2023 Oct 12), pp. 1139.1-1139.28. [10.22331/q-2023-10-12-1139]

Quantum algorithms for grid-based variational time evolution

R. Martinazzo;
2023

Abstract

The simulation of quantum dynamics calls for quantum algorithms working in first quantized grid encodings. Here, we propose a variational quantum algorithm for performing quantum dynamics in first quantization. In addition to the usual reduction in circuit depth conferred by variational approaches, this algorithm also enjoys several advantages compared to previously proposed ones. For instance, variational approaches suffer from the need for a large number of measurements. However, the grid encoding of first quantized Hamiltonians only requires measuring in position and momentum bases, irrespective of the system size. Their combination with variational approaches is therefore particularly attractive. Moreover, heuristic variational forms can be employed to overcome the limitation of the hard decomposition of Trotterized first quantized Hamiltonians into quantum gates. We apply this quantum algorithm to the dynamics of several systems in one and two dimensions. Our simulations exhibit the previously observed numerical instabilities of variational time propagation approaches. We show how they can be significantly attenuated through subspace diagonalization at a cost of an additional O(MN2) 2-qubit gates where M is the number of dimensions and NM is the total number of grid points.
Settore CHIM/02 - Chimica Fisica
12-ott-2023
22-set-2023
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/1023951
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