Quantum optical emulation of molecular vibronic spectroscopy using a trapped-ion device

Large-scale photonic network with squeezed vacuum states for molecular vibronic spectroscopy

Although molecular vibronic spectra generation is pivotal for chemical analysis, tackling such exponentially complex tasks on classical computers remains inefficient. Quantum simulation, though theoretically promising, faces technological challenges in experimentally extracting vibronic spectra for molecules with multiple modes. Here, we propose a nontrivial algorithm to generate the vibronic spectra using states with zero displacements (squeezed vacuum states) coupled to a linear optical network, offering ease of experimental implementation. We also fabricate an integrated quantum photonic microprocessor chip as a versatile simulation platform containing 16 modes of single-mode squeezed vacuum states and a fully programmable interferometer network. Molecular vibronic spectra of formic acid and thymine under the Condon approximation are simulated using the quantum microprocessor chip with high reconstructed fidelity ( > 92%). Furthermore, vibronic spectra of naphthalene, phenanthrene, and benzene under the non-Condon approximation are also experimentally simulated. Such demonstrations could pave the way for solving complicated quantum chemistry problems involving vibronic spectra and computational tasks beyond the reach of classical computers.

Simulating Vibronic Spectra by Direct Application of Doktorov Formulas on a Superconducting Quantum Simulator

In this work, a direct quantum implementation of the Doktorov formulas for calculating the vibronic spectrum of molecules under the harmonic approximation is presented. It is applied to the three-atom molecules H2O, SO2, ClO2, HS2, and ZnOH. The method solves the classically hard problem of estimating the Franck-Condon (FC) factors by using the Duschinsky matrices as the only input via the Doktorov quantum circuit. This has the advantage of avoiding basis changes, artificial squeezing parameters, and symmetry dependencies. In other words, it is a general method for three-atom molecules that can easily be generalized to bigger molecules. The results are compared with other quantum algorithms and classical anharmonic algorithms. Furthermore, the circuit requirements are studied in order to estimate its applicability on real superconducting quantum hardware.

Seeking a quantum advantage with trapped-ion quantum simulations of condensed-phase chemical dynamics

Simulating the quantum dynamics of molecules in the condensed phase represents a longstanding challenge in chemistry. Trapped-ion quantum systems may serve as a platform for the analog-quantum simulation of chemical dynamics that is beyond the reach of current classical-digital simulation. To identify a 'quantum advantage' for these simulations, performance analysis of both analog-quantum simulation on noisy hardware and classical-digital algorithms is needed. In this Review, we make a comparison between a noisy analog trapped-ion simulator and a few choice classical-digital methods on simulating the dynamics of a model molecular Hamiltonian with linear vibronic coupling. We describe several simple Hamiltonians that are commonly used to model molecular systems, which can be simulated with existing or emerging trapped-ion hardware. These Hamiltonians may serve as stepping stones towards the use of trapped-ion simulators for systems beyond the reach of classical-digital methods. Finally, we identify dynamical regimes in which classical-digital simulations seem to have the weakest performance with respect to analog-quantum simulations. These regimes may provide the lowest hanging fruit to make the most of potential quantum advantages.

Experimental realization of entangled coherent states in two-dimensional harmonic oscillators of a trapped ion

Entangled coherent states play pivotal roles in various fields such as quantum computation, quantum communication, and quantum sensing. We experimentally demonstrate the generation of entangled coherent states with the two-dimensional motion of a trapped ion system. Using Raman transitions with appropriate detunings, we simultaneously drive the red and blue sidebands of the two transverse axes of a single trapped ion and observe multi-periodic entanglement and disentanglement of its spin and two-dimensional motion. Then, by measuring the spin state, we herald entangled coherent states of the transverse motions of the trapped ion and observe the corresponding modulation in the parity of the phonon distribution of one of the harmonic oscillators. Lastly, we trap two ions in a linear chain and realize Mølmer-Sørensen gate using two-dimensional motion.

Mapping Molecular Hamiltonians into Hamiltonians of Modular cQED Processors

We introduce a general method based on the operators of the Dyson-Masleev transformation to map the Hamiltonian of an arbitrary model system into the Hamiltonian of a circuit Quantum Electrodynamics (cQED) processor. Furthermore, we introduce a modular approach to programming a cQED processor with components corresponding to the mapping Hamiltonian. The method is illustrated as applied to quantum dynamics simulations of the Fenna-Matthews-Olson (FMO) complex and the spin-boson model of charge transfer. Beyond applications to molecular Hamiltonians, the mapping provides a general approach to implement any unitary operator in terms of a sequence of unitary transformations corresponding to powers of creation and annihilation operators of a single bosonic mode in a cQED processor.

Predicting molecular vibronic spectra using time-domain analog quantum simulation

Spectroscopy is one of the most accurate probes of the molecular world. However, predicting molecular spectra accurately is computationally difficult because of the presence of entanglement between electronic and nuclear degrees of freedom. Although quantum computers promise to reduce this computational cost, existing quantum approaches rely on combining signals from individual eigenstates, an approach whose cost grows exponentially with molecule size. Here, we introduce a method for scalable analog quantum simulation of molecular spectroscopy: by performing simulations in the time domain, the number of required measurements depends on the desired spectral range and resolution, not molecular size. Our approach can treat more complicated molecular models than previous ones, requires fewer approximations, and can be extended to open quantum systems with minimal overhead. We present a direct mapping of the underlying problem of time-domain simulation of molecular spectra to the degrees of freedom and control fields available in a trapped-ion quantum simulator. We experimentally demonstrate our algorithm on a trapped-ion device, exploiting both intrinsic electronic and motional degrees of freedom, showing excellent quantitative agreement for a single-mode vibronic photoelectron spectrum of SO2.

Programmable Quantum Simulations of Bosonic Systems with Trapped Ions

Trapped atomic ion crystals are a leading platform for quantum simulations of spin systems, with programmable and long-range spin-spin interactions mediated by excitations of phonons in the crystal. We describe a complementary approach for quantum simulations of bosonic systems using phonons in trapped-ion crystals, here mediated by excitations of the trapped-ion spins. The scheme enables a high degree of programability across a dense graph of bosonic couplings, utilizing long-lived collective phonon modes in a trapped-ion chain. As such, it is well suited for tackling hard problems such as boson sampling and simulations of long-range bosonic and spin-boson Hamiltonians.

Hybrid Quantum-Classical Boson Sampling Algorithm for Molecular Vibrationally Resolved Electronic Spectroscopy with Duschinsky Rotation and Anharmonicity

Using a photonic quantum computer for boson sampling has demonstrated a tremendous advantage over classical supercomputers. It is highly desirable to develop boson sampling algorithms for realistic scientific problems. In this work, we propose a hybrid quantum-classical sampling (HQCS) algorithm to calculate the optical spectrum for complex molecules considering Duschinsky rotation effects and anharmonicity. The classical sum-over-states method for this problem has a computational complexity that exponentially increases with system size. The HQCS algorithm creates an intermediate harmonic potential energy surface (PES) to bridge the initial and final PESs. The magnitude and sign of the overlap between the initial and the intermediate state are estimated by boson sampling and classical algorithms, respectively. The overlap between the intermediate and the final state is efficiently evaluated by classical algorithms. The feasibility of HQCS is demonstrated in calculations of the emission spectrum of a Morse model as well as the pyridine molecule.

Simulation of Condensed-Phase Spectroscopy with Near-Term Digital Quantum Computers

Spectroscopy is an indispensable tool for understanding the structures and dynamics of molecular systems. However, computational modeling of spectroscopy is challenging due to the exponential scaling of computational complexity with system sizes unless drastic approximations are made. Quantum computers could potentially overcome these classically intractable computational tasks, but the existing approaches using quantum computers to simulate spectroscopy can only handle isolated and static molecules. In this work, we develop a workflow that combines multi-scale modeling and a time-dependent variational quantum algorithm to compute the linear spectroscopy of systems interacting with their condensed-phase environment via the relevant time correlation function. We demonstrate the feasibility of our approach by numerically simulating the UV-vis absorption spectra of organic semiconductors. We show that our dynamical approach captures several spectral features that are otherwise overlooked by static methods. Our method can be directly used for other linear condensed-phase spectroscopy and could potentially be extended to nonlinear multi-dimensional spectroscopy.

Double-Electromagnetically-Induced-Transparency Ground-State Cooling of Stationary Two-Dimensional Ion Crystals

We theoretically and experimentally investigate double-electromagnetically-induced transparency (double-EIT) cooling of two-dimensional ion crystals confined in a Paul trap. The double-EIT ground-state cooling is observed for ^{171}Yb^{+} ions with a clock state, for which EIT cooling has not been realized like many other ions with a simple Λ scheme. A cooling rate of n[over ¯][over ˙]=34(±1.8)  ms^{-1} and a cooling limit of n[over ¯]=0.06(±0.059) are observed for a single ion. The measured cooling rate and limit are consistent with theoretical predictions. We apply double-EIT cooling to the transverse modes of two-dimensional (2D) crystals with up to 12 ions. In our 2D crystals, the micromotion and the transverse mode directions are perpendicular, which makes them decoupled. Therefore, the cooling on transverse modes is not disturbed by micromotion, which is confirmed in our experiment. For the center of mass mode of a 12-ion crystal, we observe a cooling rate and a cooling limit that are consistent with those of a single ion, including heating rates proportional to the number of ions. This method can be extended to other hyperfine qubits, and near ground-state cooling of stationary 2D crystals with large numbers of ions may advance the field of quantum information sciences.

Hybrid Quantum Computing with Conditional Beam Splitter Gate in Trapped Ion System

The hybrid approach to quantum computation simultaneously utilizes both discrete and continuous variables, which offers the advantage of higher density encoding and processing powers for the same physical resources. Trapped ions, with discrete internal states and motional modes that can be described by continuous variables in an infinite-dimensional Hilbert space, offer a natural platform for this approach. A nonlinear gate for universal quantum computing can be implemented with the conditional beam splitter Hamiltonian |e⟩⟨e|(a[over ^]^{†}b[over ^]+a[over ^]b[over ^]^{†}) that swaps the quantum states of two motional modes, depending on the ion's internal state. We realize such a gate and demonstrate its applications for quantum state overlap measurements, single-shot parity measurement, and generation of NOON states.

Connection between BosonSampling with quantum and classical input states

BosonSampling is a problem of sampling events according to the transition probabilities of indistinguishable photons in a linear optical network. Computational hardness of BosonSampling depends on photon-number statistics of the input light. BosonSampling with multi-photon Fock states at the input is believed to be classically intractable but there exists an efficient classical algorithm for classical input states. In this paper, we present a mathematical connection between BosonSampling with quantum and classical light inputs. Specifically, we show that the generating function of a transition probability for Fock-state BosonSampling (FBS) can be expressed as a transition probability of thermal-light inputs. The closed-form expression of a thermal-light transition probability allows all possible transition probabilities of FBS to be obtained by calculating a single matrix permanent. Moreover, the transition probability of FBS is shown to be expressed as an integral involving a Gaussian function multiplied by a Laguerre polynomial, resulting in a fast oscillating integrand. Our work sheds new light on computational hardness of FBS by identifying the mathematical connection between BosonSampling with quantum and classical light.

Quantum Chemistry in the Age of Quantum Computing

Practical challenges in simulating quantum systems on classical computers have been widely recognized in the quantum physics and quantum chemistry communities over the past century. Although many approximation methods have been introduced, the complexity of quantum mechanics remains hard to appease. The advent of quantum computation brings new pathways to navigate this challenging and complex landscape. By manipulating quantum states of matter and taking advantage of their unique features such as superposition and entanglement, quantum computers promise to efficiently deliver accurate results for many important problems in quantum chemistry, such as the electronic structure of molecules. In the past two decades, significant advances have been made in developing algorithms and physical hardware for quantum computing, heralding a revolution in simulation of quantum systems. This Review provides an overview of the algorithms and results that are relevant for quantum chemistry. The intended audience is both quantum chemists who seek to learn more about quantum computing and quantum computing researchers who would like to explore applications in quantum chemistry.

Quantum Algorithm for Calculating Molecular Vibronic Spectra

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.

Digital quantum simulation of molecular vibrations

Molecular vibrations underpin important phenomena such as spectral properties, energy transfer, and molecular bonding. However, obtaining a detailed understanding of the vibrational structure of even small molecules is computationally expensive. While several algorithms exist for efficiently solving the electronic structure problem on a quantum computer, there has been comparatively little attention devoted to solving the vibrational structure problem with quantum hardware. In this work, we discuss the use of quantum algorithms for investigating both the static and dynamic vibrational properties of molecules. We introduce a physically motivated unitary vibrational coupled cluster ansatz, which also makes our method accessible to noisy, near-term quantum hardware. We numerically test our proposals for the water and sulfur dioxide molecules.

Experimental quantum simulation of fermion-antifermion scattering via boson exchange in a trapped ion

Quantum field theories describe a variety of fundamental phenomena in physics. However, their study often involves cumbersome numerical simulations. Quantum simulators, on the other hand, may outperform classical computational capacities due to their potential scalability. Here we report an experimental realization of a quantum simulation of fermion-antifermion scattering mediated by bosonic modes, using a multilevel trapped ion, which is a simplified model of fermion scattering in both perturbative and non-perturbative quantum electrodynamics. The simulated model exhibits prototypical features in quantum field theory including particle pair creation and annihilation, as well as self-energy interactions. These are experimentally observed by manipulating four internal levels of a ¹⁷¹Yb⁺ trapped ion, where we encode the fermionic modes, and two motional degrees of freedom that simulate the bosonic modes. Our experiment establishes an avenue towards the efficient implementation of field modes, which may prove useful in studies of quantum field theories including non-perturbative regimes.