Az Eszterházy Károly Tanárképző Főiskola tudományos közleményei. Tanulmányok a matematikai tudományok köréből/Az Eszterházy Károly Főiskola tudományos közleményei. Tanulmányok a matematikai tudományok köréből/Annales mathematicae et informaticae
Vibronic spectra of molecules – an experiment with a quantum computer simulator
In addition to the exciting fundamental questions of quantum computing and implementation possibilities of quantum computers, it is important to look for application areas of quantum computing, to point out practical cases which justify the need for this technology. Besides the wellknown qubit-based quantum computers, there are also devices based on other foundations that can surpass the capabilities of classical computers. Among these, devices operating on the basis of boson sampling have a naturally occurring application: the approximate calculation of the vibrational spectrum of molecules. Two separate research groups, Huh et al. [14] and Wang et al. [22] created quantum simulators based on boson sampling, which were successfully used to calculate the transition probabilities between specific states of small molecules. Following the methodology found in these two articles, this paper presents how the calculations of transition probabilities can be performed on a classical computer using a quantum computer simulator which is based on Gaussian boson sampling.
In addition to the exciting fundamental questions of quantum computing and implementation possibilities of quantum computers, it is important to look for application areas of quantum computing, to point out practical cases which justify the need for this technology. Besides the wellknown qubit-based quantum computers, there are also devices based on other foundations that can surpass the capabilities of classical computers. Among these, devices operating on the basis of boson sampling have a naturally occurring application: the approximate calculation of the vibrational spectrum of molecules. Two separate research groups, Huh et al. [14] and Wang et al. [22] created quantum simulators based on boson sampling, which were successfully used to calculate the transition probabilities between specific states of small molecules. Following the methodology found in these two articles, this paper presents how the calculations of transition probabilities can be performed on a classical computer using a quantum computer simulator which is based on Gaussian boson sampling.
Abstract Simulating vibronic spectra is a central task in physical chemistry, offering insight into important properties of molecules. Recently, it has been experimentally demonstrated that photonic platforms based on Gaussian boson sampling (GBS) are capable of performing these simulations. However, whether an actual GBS approach is required depends on the molecule under investigation. To develop a better understanding on the requirements for simulating vibronic spectra, we explore connections between theoretical approximations in physical chemistry and their photonic counterparts. Mapping these approximations into photonics, we show that for certain molecules the GBS approach is unnecessary. We place special emphasis on the linear coupling approximation, which in photonics corresponds to sampling from multiple coherent states. By implementing this approach in experiments, we demonstrate improved similarities over previously reported GBS results for formic acid and identify the particular attributes that a molecule must exhibit for this, and other approximations, to be valid. These results highlight the importance in forming deeper connections between traditional methods and photonic approaches.
We present a quantum algorithm for calculating the vibronic spectrum of a molecule, a useful but classically hard problem in chemistry. We show several advantages over previous quantum approaches: vibrational anharmonicity is naturally included; after measurement, some state information is preserved for further analysis; and there are potential error-related benefits. Considering four triatomic molecules, we numerically study truncation errors in the harmonic approximation. Further, in order to highlight the fact that our quantum algorithm's primary advantage over classical algorithms is in simulating anharmonic spectra, we consider the anharmonic vibronic spectrum of sulfur dioxide. In the future, our approach could aid in the design of materials with specific light-harvesting and energy transfer properties, and the general strategy is applicable to other spectral calculations in chemistry and condensed matter physics.
Molecular vibroic spectroscopy, where the transitions involve non-trivial Bosonic correlation due to the Duschinsky Rotation, is strongly believed to be in a similar complexity class as Boson Sampling. At finite temperature, the problem is represented as a Boson Sampling experiment with correlated Gaussian input states. This molecular problem with temperature effect is intimately related to the various versions of Boson Sampling sharing the similar computational complexity. Here we provide a full description to this relation in the context of Gaussian Boson Sampling. We find a hierarchical structure, which illustrates the relationship among various Boson Sampling schemes. Specifically, we show that every instance of Gaussian Boson Sampling with an initial correlation can be simulated by an instance of Gaussian Boson Sampling without initial correlation, with only a polynomial overhead. Since every Gaussian state is associated with a thermal state, our result implies that every sampling problem in molecular vibronic transitions, at any temperature, can be simulated by Gaussian Boson Sampling associated with a product of vacuum modes. We refer such a generalized Gaussian Boson Sampling motivated by the molecular sampling problem as Vibronic Boson Sampling.
Molecular vibronic spectra can be used to derive the structural properties of molecules. Although there is no known efficient classical algorithm for calculating these spectra, it has recently been shown that an ideal quantum optics simulator can in principle be used to efficiently perform this calculation. In this work, we demonstrate that imperfect quantum simulators can also yield approximations of these spectra, and illustrate our findings using a proof of principle experimental simulation of the partial vibronic spectrum of tropolone. Specifically, we demonstrate a method for designing an experiment in the presence of imperfections, show that the error on the resulting estimations of vibronic spectra can be efficiently bounded, and show that such experiments can outperform a classicality criterion. Our findings provide a roadmap for future simulations of large molecules beyond the reach of current classical computers.
Boson sampling (BS) is a multimode linear optical problem that is expected to be intractable on classical computers. It was recently suggested that molecular vibronic spectroscopy (MVS) is computationally as complex as BS. In this review, we discuss the correspondence relation between BS and MVS and briefly introduce the experimental demonstrations of the molecular spectroscopic process using quantum devices. The similarity of the two theories results in another BS setup, which is called "vibronic BS". The hierarchical structure of vibronic BS, which includes the original BS and other Gaussian BS, is also explained.
The efficient simulation of quantum systems is a primary motivating factor for developing controllable quantum machines.For addressing systems with underlying bosonic structure, it is advantageous to utilize a naturally bosonic platform.Optical photons passing through linear networks may be configured to perform quantum simulation tasks, but the efficient preparation and detection of multiphoton quantum states of light in linear optical systems are challenging.Here, we experimentally implement a boson sampling protocol for simulating molecular vibronic spectra [J.Huh et al., Nat. Photonics 9, 615 (2015)] in a two-mode superconducting device.In addition to enacting the requisite set of Gaussian operations across both modes, we fulfill the scalability requirement by demonstrating, for the first time in any platform, a high-fidelity single-shot photon number resolving detection scheme capable of resolving up to 15 photons per mode.Furthermore, we exercise the capability of synthesizing non-Gaussian input states to simulate spectra of molecular ensembles in vibrational excited states.We show the reprogrammability of our implementation by extracting the spectra of photoelectron processes in H 2 O, O 3 , NO 2 , and SO 2 .The capabilities highlighted in this work establish the superconducting architecture as a promising platform for bosonic simulations, and by combining them with tools such as Kerr interactions and engineered dissipation, enable the simulation of a wider class of bosonic systems.