Resource-efficient encoding algorithm for variational bosonic quantum simulations

Abstract

Quantum algorithms are promising candidates for the enhancement of computational efficiency for a variety of computational tasks, allowing for the numerical study of physical systems intractable to classical computers. In the Noisy Intermediate Scale Quantum (NISQ) era of quantum computing, however, quantum resources are limited and thus quantum algorithms utilizing such resources efficiently are highly coveted. We present a resource-efficient quantum algorithm for bosonic quantum simulations using the Variational Quantum Eigensolver algorithm with the Unitary Coupled Cluster ansatz. Our algorithm proves to significantly increase accuracy with a simultaneous large reduction of required quantum resources, exhibiting increased performance for all relevant parameters compared to current approaches. It provides a shorter route to achieve a quantum advantage in bosonic quantum simulations along with a flexible method to tailor the utilized quantum resources of a quantum computer. While being specifically feasible for NISQ devices, the advantages of our algorithm are independent of hardware parameters, maintaining its superiority for future fault-tolerant quantum devices. The study of vibrational properties of molecular systems is crucial in a variety of contexts, such as spectroscopy, fluorescence, chemical reaction dynamics and transport properties. Thus, our algorithm provides a resourceefficient flexible approach to study such applications in the context of quantum computational chemistry on quantum computers.

Coarse-grained intermolecular interactions on quantum processors

“…Although more costly than ansätze designed to make efficient use of the quantum hardware [33], quantum advantage may be achieved for ab initio VQE by using chemistry-inspired ansätze such as unitary coupled cluster (UCC) [66]. Analogous ansätze for bosonic systems can be constructed [36,37,67], namely, the unitary-vibrationalcoupled-cluster (UVCC) ansatz (following the naming convention of McArdle et al [36]). This is a unitary extension to the vibrational coupled cluster (VCC) used in classical computations [68,69] and, unlike the VCC ansatz, the UVCC ansatz obeys the variational principle and may deal better with strong static correlations [36].…”

“…4 due to the nontrivial decomposition of bosonic operators into Pauli operators that can be implemented natively on quantum devices, thus we do not consider its application in this work. The analysis of commutation relations presented in Appendix C as well as various encoding methods [67] will be important in understanding the experimental cost of the Trotterization required for such an ansatz.…”