Nonadiabatic quantum transition-state theory in the golden-rule limit. I. Theory and application to model systems

We propose a new quantum transition-state theory for calculating Fermi's golden-rule rates in complex multidimensional systems. This method is able to account for the nuclear quantum effects of delocalization, zero-point energy and tunnelling in an electron-transfer reaction. It is related to instanton theory but can be computed by path-integral sampling and is thus applicable to treat molecular reactions in solution. A constraint functional based on energy conservation is introduced which ensures that the dominant paths contributing to the reaction rate are sampled. We prove that the theory gives exact results for a system of crossed linear potentials and also the correct classical limit for any system. In numerical tests, the new method is also seen to be accurate for anharmonic systems, and even gives good predictions for rates in the Marcus inverted regime.Comment: 18 pages and 6 figure

Benchmarking Digital-Analog Quantum Computation

Digital-Analog Quantum Computation (DAQC) has recently been proposed as an alternative to the standard paradigm of digital quantum computation. DAQC creates entanglement through a continuous or analog evolution of the whole device, rather than by applying two-qubit gates. This manuscript describes an in-depth analysis of DAQC by extending its implementation to arbitrary connectivities and by performing the first systematic study of its scaling properties. We specify the analysis for three examples of quantum algorithms, showing that except for a few specific cases, DAQC is in fact disadvantageous with respect to the digital case.Comment: 16+5 pages, 11 figure

Co-Design quantum simulation of nanoscale NMR

Quantum computers have the potential to efficiently simulate the dynamics of nanoscale NMR systems. In this work, we demonstrate that a noisy intermediate-scale quantum computer can be used to simulate and predict nanoscale NMR resonances. In order to minimize the required gate fidelities, we propose a superconducting application-specific Co-Design quantum processor that reduces the number of SWAP gates by over 90% for chips with more than 20 qubits. The processor consists of transmon qubits capacitively coupled via tunable couplers to a central co-planar waveguide resonator with a quantum circuit refrigerator (QCR) for fast resonator reset. The QCR implements the nonunitary quantum operations required to simulate nuclear hyperpolarization scenarios.The authors would like to thank Caspar Ockeloen-Korppi, Alessandro Landra, and Johannes Heinsoo for their help in de- veloping the idea of the star-architecture chip, Jani Tuorila for his support in developing the gate theory, Amin Hosseinkhani and Tianhan Liu for reviewing the manuscript, and Hen- rikki Mäkynen and Hoang-Mai Nguyen for graphic design. J.C. additionally acknowledges the Ramón y Cajal program (RYC2018-025197-I). We further acknowledge support from Atos with the Quantum Learning Machine (QLM). Finally, the authors acknowledge financial support to BMBF through the Q-Exa Project No. FZK: 13N16062

Nonadiabatic quantum transition-state theory in the golden-rule limit: II. Overcoming the pitfalls of the saddle-pointand semiclassical approximations

We describe a path-integral molecular dynamics implementation of our recently developed golden-rule quantum transition-state theory(GR-QTST). The method is applied to compute the reaction rate in various models of electron transfer and benchmarked against the exactresults. We demonstrate that for systems exhibiting two or more transition states, rates computed using Wolynes theory [P. G. Wolynes, J. Chem. Phys. 87, 6559 (1987)] can be overestimated by orders of magnitude, whereas the GR-QTST predictions are numerically accu-rate. This is the case both at low temperature, where nuclear tunneling makes a considerable contribution, and also in the classical limit,where only GR-QTST rigorously tends to the correct result. Analysis shows that the saddle-point approximation employed by Wolynestheory is not valid in this case, which results in the predictions of unphysical reaction pathways, while the energy constraint employedby GR-QTST resolves this problem. The GR-QTST method is also seen to give accurate results for a strongly anharmonic system bysampling configurations around the instanton pathway without making the semiclassical approximation. These promising results indicatethat the GR-QTST method could be an efficient and accurate approach for simulating electron-transfer reactions in complex molecularsystems.ISSN:0021-9606ISSN:1089-769

Semiclassical analysis of the quantum instanton approximation

We explore the relation between the quantum and semiclassical instanton approximations for the reaction rate constant. From the quantum instanton expression, we analyze the contributions to the rate constant in terms of minimum-action paths and find that two such paths dominate the expression. For symmetric barriers, these two paths join together to describe the semiclassical instanton periodic orbit. However, for asymmetric barriers, one of the two paths takes an unphysically low energy and dominates the expression, leading to order-of-magnitude errors in the rate predictions. Nevertheless, semiclassical instanton theory remains accurate. We conclude that semiclassical instanton theory can be obtained directly from the semiclassical limit of the quantum instanton for symmetric systems. We suggest a modification of the quantum instanton approach which avoids sampling the spurious path and thus has a stronger connection to semiclassical instanton theory, giving numerically accurate predictions even for very asymmetric systems in the low temperature limit