Kavli Affiliate: Birgitta Whaley
| First 5 Authors: Nikolay V. Tkachenko, Hang Ren, Wendy M. Billings, Rebecca Tomann, K. Birgitta Whaley
| Summary:
Near-term quantum devices require wavefunction ans"atze that are expressive
while also of shallow circuit depth in order to both accurately and efficiently
simulate molecular electronic structure. While unitary coupled cluster (e.g.,
UCCSD) has become a standard, the high gate count associated with the
implementation of this limits its feasibility on noisy intermediate-scale
quantum (NISQ) hardware. K-fold unitary cluster Jastrow (uCJ) ans"atze
mitigate this challenge by providing $O(kN^2)$ circuit scaling and favorable
linear depth circuit implementation. Previous work has focused on the real
orbital-rotation (Re-uCJ) variant of uCJ, which allows an exact (Trotter-free)
implementation. Here we extend and generalize the $k$-fold uCJ framework by
introducing two new variants, Im-uCJ and g-uCJ, which incorporate imaginary and
fully complex orbital rotation operators, respectively. Similar to Re-uCJ, both
of the new variants achieve quadratic gate-count scaling. Our results focus on
the simplest $k=1$ model, and show that the uCJ models frequently maintain
energy errors within chemical accuracy. Both g-uCJ and Im-uCJ are more
expressive in terms of capturing electron correlation and are also more
accurate than the earlier Re-uCJ ansatz. We further show that Im-uCJ and g-uCJ
circuits can also be implemented exactly, without any Trotter decomposition.
Numerical tests using $k=1$ on $H_2$, $H_3^+$, $Be_2$, $C_2H_4$, $C_2H_6$ and
$C_6H_6$ in various basis sets confirm the practical feasibility of these
shallow Jastrow-based ans"atze for applications on near-term quantum hardware.
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