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Plausible claims for quantum advantage have been made using sampling problems such as random circuit sampling in superconducting qubit devices, and Gaussian boson sampling in quantum optics experiments. Now, the major next step is to channel the potential quantum advantage to solve practical applications rather than proof-of-principle experiments. It has recently been proposed that a Gaussian boson sampler can efficiently generate molecular vibronic spectra, which are an important tool for analysing chemical components and studying molecular structures. The best-known classical algorithm for calculating the molecular spectra scales super-exponentially in the system size. Therefore, an efficient quantum algorithm could represent a computational advantage. However, here we propose an efficient quantum-inspired classical algorithm for molecular vibronic spectra with harmonic potentials. Using our method, the zero-temperature molecular vibronic spectra problems that correspond to Gaussian boson sampling can be exactly solved. Consequently, we demonstrate that those problems are not candidates for quantum advantage. We then provide a more general molecular vibronic spectra problem, which is also chemically well motivated, for which our method does not work and so might be able to take advantage of a boson sampler. 

Abstract Advancements in quantum system lifetimes and control have enabled the creation of increasingly complex quantum states, such as those on multiple bosonic cavity modes. When characterizing these states, traditional tomography scales exponentially with the number of modes in both computational and experimental measurement requirement, which becomes prohibitive as the system size increases. Here, we implement a state reconstruction method whose sampling requirement instead scales polynomially with system size, and thus mode number, for states that can be represented within such a polynomial subspace. We demonstrate this improved scaling with Wigner tomography of multimode entangled W states of up to 4 modes on a 3D circuit quantum electrodynamics (cQED) system. This approach performs similarly in efficiency to existing matrix inversion methods for 2 modes, and demonstrates a noticeable improvement for 3 and 4 modes, with even greater theoretical gains at higher mode numbers. 

Quantum transducers convert quantum signals through hybrid interfaces of physical platforms in quantum networks. Modeled as quantum communication channels, performance of unidirectional quantum transducers can be measured by the quantum channel capacity. However, characterizing performance of quantum transducers used as bidirectional communication channels remains an open question. Here, we propose rate regions to characterize the performance of quantum transducers in the bidirectional scenario. Using this tool, we find that quantum transducers optimized for simultaneous bidirectional transduction can outperform strategies based on the standard protocol of time-shared unidirectional quantum transduction. Integrated over the frequency domain, we demonstrate that rate region can also characterize quantum transducers with finite bandwidth.