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Nuclear quantum phenomena beyond the Born–Oppenheimer approximation are known to play an important role in a growing number of chemical and biological processes. While there exists no unique consensus on a rigorous and efficient implementation of coupled electron–nuclear quantum dynamics, it is recognized that these problems scale exponentially with system size on classical processors and, therefore, may benefit from quantum computing implementations. Here, we introduce a methodology for the efficient quantum treatment of the electron–nuclear problem on near-term quantum computers, based upon the Nuclear–Electronic Orbital (NEO) approach. We generalize the electronic two-qubit tapering scheme to include nuclei by exploiting symmetries inherent in the NEO framework, thereby reducing the Hamiltonian dimension, number of qubits, gates, and measurements needed for calculations. We also develop parameter transfer and initialization techniques, which improve convergence behavior relative to conventional initialization. These techniques are applied to H2 and malonaldehyde for which results agree with NEO full configuration interaction and NEO complete active space configuration interaction benchmarks for ground state energy to within 10−6 hartree and entanglement entropy to within 10−4. These implementations therefore significantly reduce resource requirements for full quantum simulations of molecules on near-term quantum devices while maintaining high accuracy. [ABSTRACT FROM AUTHOR]

Quantum simulation of chemical Hamiltonians enables the efficient calculation of chemical properties. Mapping is one of the essential steps in simulating fermionic systems on quantum computers. In this work, a unified framework of transformations mapping fermionic systems to qubit systems is presented and many existing transformations—such as Jordan–Wigner, Bravyi–Kitaev, and parity transformations—are included in this framework. Based on this framework, the Multilayer Segmented Parity (MSP) transformation is proposed. The MSP transformation is a general mapping with an adjustable parameter vector, which can be viewed as a generalization of the above-mentioned mappings. Furthermore, the MSP transformation can adjust flexibly when dealing with different systems. Applying these mappings to the electronic structure Hamiltonians of various molecules, the MSP transformation is found to perform better on a number of Pauli operators and gates needed in the circuit of Hamiltonian simulation. The MSP transformation will reduce the qubit gate requirement for Hamiltonian simulation on noisy intermediate-scale quantum devices, and it will provide a much wider choice of mappings for researchers. [ABSTRACT FROM AUTHOR]

We present a 2D-Raman-terahertz (THz) setup with multichannel (single-shot) THz detection, utilizing two crossed echelons, in order to reduce the acquisition time of typical 2D-Raman-THz experiments from days to a few hours. This speed-up is obtained in combination with a high repetition rate (100 kHz) Yb-based femtosecond laser system and a correspondingly fast array detector. The wavelength of the Yb-laser (1030 nm) is advantageous, since it assures almost perfect phase matching in GaP for THz generation and detection and since the dispersion in the transmissive echelons is minimal. 2D-Raman-THz test measurements on liquid bromoform (CHBr3) are reported. An enhancement of a factor ∼5.8 in signal-to-noise ratio is obtained for single-shot detection when compared to conventional step-scanning measurements in the THz time domain, corresponding to a speed-up of acquisition time of ∼34. [ABSTRACT FROM AUTHOR]

Nonlinear two-dimensional terahertz (2D-THz) spectroscopy at frequencies of the emitted THz signal different from the driving frequencies allows for exploring the regime of (off-)resonant even-order nonlinearities in condensed matter. To demonstrate the potential of this method, we study two phenomena in the nonlinear THz response of bulk GaAs: (i) The nonlinear THz response to a pair of femtosecond near-infrared pulses unravels novel fourth- and sixth-order contributions involving interband shift currents, Raman-like excitations of transverse-optical phonon and intervalence-band coherences. (ii) Transient interband tunneling of electrons driven by ultrashort mid-infrared pulses can be effectively controlled by a low-frequency THz field with amplitudes below 50 kV/cm. The THz field controls the electron–hole separation modifying decoherence and the irreversibility of carrier generation. [ABSTRACT FROM AUTHOR]

Nonlinear terahertz (THz) spectroscopy relies on the interaction of matter with few-cycle THz pulses of electric field amplitudes up to megavolts/centimeter (MV/cm). In condensed-phase molecular systems, both resonant interactions with elementary excitations at low frequencies such as intra- and intermolecular vibrations and nonresonant field-driven processes are relevant. Two-dimensional THz (2D-THz) spectroscopy is a key method for following nonequilibrium processes and dynamics of excitations to decipher the underlying interactions and molecular couplings. This article addresses the state of the art in 2D-THz spectroscopy by discussing the main concepts and illustrating them with recent results. The latter include the response of vibrational excitations in molecular crystals up to the nonperturbative regime of light–matter interaction and field-driven ionization processes and electron transport in liquid water. [ABSTRACT FROM AUTHOR]

The 2D-Raman-THz response in all possible time-orderings (Raman-THz-THz, THz-Raman-THz, and THz-THz-Raman) of amorphous water ice is calculated in two ways: from atomistic molecular dynamics simulations and with the help of a Feynman diagram model, the latter of which power-expands the potential energy surface and the dipole and polarizability surfaces up to leading order. Comparing both results allows one to dissect the 2D-Raman-THz response into contributions from mechanical anharmonicity, as well as electrical dipole and polarizability anharmonicities. Mechanical anharmonicity dominates the 2D-Raman-THz response of the hydrogen-bond stretching and hydrogen-bond bending bands of water, and dipole anharmonicity dominates that of the librational band, while the contribution of polarizability anharmonicity is comparably weak. A distinct echo of the hydrogen-bond stretching band is observed for the THz-Raman-THz pulse sequence, again dominated by mechanical anharmonicity. A peculiar mechanism is discussed, which is based on the coupling between the many normal modes within the hydrogen-bond stretching band and which will inevitably generate such an echo for an amorphous structure. [ABSTRACT FROM AUTHOR]

2D-Raman-THz spectroscopy of liquid water, which has been presented recently [J. Savolainen et al., Proc. Natl. Acad. Sci. U. S. A. 110, 20402 (2013)], directly probes the intermolecular degrees of freedom of the hydrogen-bond network. However, being a relatively new technique, its information content is not fully explored to date. While the spectroscopic signal can be simulated based on molecular dynamics simulation in connection with a water force field, it is difficult to relate spectroscopic signatures to the underlying microscopic features of the force field. Here, a completely different approach is taken that starts from an as simple as possible model, i.e., a single vibrational mode with electrical and mechanical anharmonicity augmented with homogeneous and inhomogeneous broadening. An intuitive Feynman diagram picture is developed for all possible pulse sequences of hybrid 2D-Raman-THz spectroscopy. It is shown that the model can explain the experimental data essentially quantitatively with a very small set of parameters, and it is tentatively concluded that the experimental signal originates from the hydrogen-bond stretching vibration around 170 cm−1. Furthermore, the echo observed in the experimental data can be quantified by fitting the model. A dominant fraction of its linewidth is attributed to quasi-inhomogeneous broadening in the slow-modulation limit with a correlation time of 370 fs, reflecting the lifetime of the hydrogen-bond networks giving rise to the absorption band. [ABSTRACT FROM AUTHOR]

Considering an electronic two-level system coupled to vibrational degrees of freedom and driven by short and intense non-overlapping laser pulses, we introduce the concept of nonperturbative response functions. These response functions are expressed in terms of effective electronic transition dipole moments which depend on the strength of the field-matter coupling and on the pulse durations. It is shown that the nonlinear polarization representing four-wave-mixing signals can elegantly be expressed in terms of these nonperturbative response functions to all orders in the field-matter coupling. The nonperturbative response functions generalize the interpretative power of the familiar third-order response functions to four-wave-mixing experiments with intense laser pulses. [ABSTRACT FROM AUTHOR]

Recently, various spectroscopic techniques have been developed, which can measure the 2D response of the inter-molecular degrees of freedom of liquids in the THz regime. By employing hybrid Raman-THz pulse sequences, the inherent experimental problems of 2D-Raman spectroscopy are circumvented completely, culminating in the recent measurement of the 2D-Raman-THz responses of water and aqueous salt solutions. This review article focuses on the possibility to observe echoes in such experiments, which would directly reveal the inhomogeneity of the typically extremely blurred THz bands of liquids, and hence the heterogeneity of local structures that are transiently formed, in particular, in a hydrogen-bonding liquid such as water. The generation mechanisms of echoes in 2D-Raman-THz spectroscopy are explained, which differ from those in "conventional" 2D-IR spectroscopy in a subtle but important manner. Subsequently, the circumstances are discussed, under which echoes are expected, revealing a physical picture of the information content of an echo. That is, the echo decay reflects the lifetime of local structures in the liquid on a length scale that equals the delocalization length of the intermolecular modes. Finally, recent experimental results are reviewed from an echo perspective. [ABSTRACT FROM AUTHOR]

We present the first two-dimensional (2D) terahertz (THz) experiment with three phase-locked THz pulses and a fully phase-resolved detection of the nonlinearly emitted field by electrooptic sampling. In a prototype experiment we study the ultrafast dynamics of nonlinear two-phonon and two-photon interband coherences in the narrow-gap semiconductor InSb. Due to the extraordinarily large optical interband dipole of InSb the experiments were performed in the strongly nonperturbative regime of light-matter interaction allowing for impulsive off-resonant excitation of both two-phonon coherences and two-photon interband coherences, the ultrafast dynamics of which is experimentally observed as a function of the waiting time in the three-pulse 2D experiment. Our novel three-pulse 2D THz spectroscopy paves the way for the detailed investigation of nonlinear quantum coherences in solids and holds potential for an extension to other systems. [ABSTRACT FROM AUTHOR]

Quantum computers attract much attention as they promise to outperform their classical counterparts in solving certain type of problems. One of them with practical applications in quantum chemistry is simulation of complex quantum systems. An essential ingredient of efficient quantum simulation algorithms are initial guesses of the exact wave functions with high enough fidelity. As was proposed in Aspuru-Guzik et al. [Science 309, 1704 (2005)], the exact ground states can in principle be prepared by the adiabatic state preparation method. Here, we apply this approach to preparation of the lowest lying multireference singlet electronic state of methylene and numerically investigate preparation of this state at different molecular geometries. We then propose modifications that lead to speeding up the preparation process. Finally, we decompose the minimal adiabatic state preparation employing the direct mapping in terms of two-qubit interactions. [ABSTRACT FROM AUTHOR]

We give details of the spectroscopic observation of the gyroscopic destabilisation in the ν23 vibrational state of dimethylsulfoxide (DMSO) announced by Cuisset, Pirali, and Sadovskií [Phys. Rev. Lett. 109, 094101 (2012)]. Following the first successful high-resolution spectroscopic study of the rotational structure of the 'perpendicular' band of DMSO at 324 cm-1 associated with the ν23 bending vibrational mode, the rare subsystem of ν23 rotational levels consisting of a series of fourfold quasidegenerate levels (4-clusters) was identified. Our complete analysis of the underlying rotational dynamics uncovered a bifurcation leading to the gyroscopic destabilisation of one of the two stable principal axes of inertia, a phenomenon known previously only in a few triatomic molecules. [ABSTRACT FROM AUTHOR]

Quantum simulation is an important application of future quantum computers with applications in quantum chemistry, condensed matter, and beyond. Quantum simulation of fermionic systems presents a specific challenge. The Jordan-Wigner transformation allows for representation of a fermionic operator by O(n) qubit operations. Here, we develop an alternative method of simulating fermions with qubits, first proposed by Bravyi and Kitaev [Ann. Phys. 298, 210 (2002); e-print arXiv:quant-ph/0003137v2], that reduces the simulation cost to O(log n) qubit operations for one fermionic operation. We apply this new Bravyi-Kitaev transformation to the task of simulating quantum chemical Hamiltonians, and give a detailed example for the simplest possible case of molecular hydrogen in a minimal basis. We show that the quantum circuit for simulating a single Trotter time step of the Bravyi-Kitaev derived Hamiltonian for H2 requires fewer gate applications than the equivalent circuit derived from the Jordan-Wigner transformation. Since the scaling of the Bravyi-Kitaev method is asymptotically better than the Jordan-Wigner method, this result for molecular hydrogen in a minimal basis demonstrates the superior efficiency of the Bravyi-Kitaev method for all quantum computations of electronic structure. [ABSTRACT FROM AUTHOR]

Quantum computers are appealing for their ability to solve some tasks much faster than their classical counterparts. It was shown in [Aspuru-Guzik et al., Science 309, 1704 (2005)] that they, if available, would be able to perform the full configuration interaction (FCI) energy calculations with a polynomial scaling. This is in contrast to conventional computers where FCI scales exponentially. We have developed a code for simulation of quantum computers and implemented our version of the quantum FCI algorithm. We provide a detailed description of this algorithm and the results of the assessment of its performance on the four lowest lying electronic states of CH2 molecule. This molecule was chosen as a benchmark, since its two lowest lying 1A1 states exhibit a multireference character at the equilibrium geometry. It has been shown that with a suitably chosen initial state of the quantum register, one is able to achieve the probability amplification regime of the iterative phase estimation algorithm even in this case. [ABSTRACT FROM AUTHOR]

When a time-dependent perturbation acts on a quantum system that is initially in the nondegenerate ground state |0> of an unperturbed Hamiltonian H0, the wave function acquires excited-state components |k> with coefficients ck(t) exp(-iEkt/h), where Ek denotes the energy of the unperturbed state |k>. It is well known that each coefficient ck(t) separates into an adiabatic term ak(t) that reflects the adjustment of the ground state to the perturbation - without actual transitions - and a nonadiabatic term bk(t) that yields the probability amplitude for a transition to the excited state. In this work, we prove that the energy at any time t also separates completely into adiabatic and nonadiabatic components, after accounting for the secular and normalization terms that appear in the solution of the time-dependent Schrödinger equation via Dirac's method of variation of constants. This result is derived explicitly through third order in the perturbation. We prove that the cross-terms between the adiabatic and nonadiabatic parts of ck(t) vanish, when the energy at time t is determined as an expectation value. The adiabatic term in the energy is identical to the total energy obtained from static perturbation theory, for a system exposed to the instantaneous perturbation λH′(t). The nonadiabatic term is a sum over excited states |k> of the transition probability multiplied by the transition energy. By evaluating the probabilities of transition to the excited eigenstates |k′(t)> of the instantaneous Hamiltonian H(t), we provide a physically transparent explanation of the result for E(t). To lowest order in the perturbation parameter λ, the probability of finding the system in state |k′(t)> is given by λ2 |bk(t)|2. At third order, the transition probability depends on a second-order transition coefficient, derived in this work. We indicate expected differences between the results for transition probabilities obtained from this work and from Fermi's golden rule. [ABSTRACT FROM AUTHOR]