Ivan Kassal

Continuous-variable-discrete-variable (CV-DV) quantum simulators offer a natural route to simulating bosonic dynamics relevant to many branches of physics and chemistry. However, programmable simulation of arbitrary dynamics is an outstanding challenge. In particular, simulating anharmonic dynamics, which is ubiquitous across the physical sciences, is challenging due to the highly harmonic nature of oscillators used in CV-DV simulators. Here, we experimentally demonstrate programmable CV-DV quantum simulation of anharmonic dynamics in a range of double-well potentials, implemented in a trapped-ion system. We synthesise the time-evolution operators using a bosonic-quantum-signal-processing subroutine, which allows the potential to be tuned between experiments by controlling classical experimental parameters. We observe coherent dynamics in various double-well potentials, where a wavepacket tunnels through the potential barrier, and we suppress this effect by programmatically introducing asymmetry.

Conical intersections are ubiquitous in chemistry and physics, often governing processes such as light harvesting, vision, photocatalysis, and chemical reactivity. They act as funnels between electronic states of molecules, allowing rapid and efficient relaxation during chemical dynamics. In addition, when a reaction path encircles a conical intersection, the molecular wavefunction experiences a geometric phase, which can affect the outcome of the reaction through quantum-mechanical interference. Past experiments have measured indirect signatures of geometric phases in scattering patterns and spectroscopic observables, but there has been no direct observation of the underlying wavepacket interference. Here, we experimentally observe geometric-phase interference in the dynamics of a wavepacket travelling around an engineered conical intersection in a programmable trapped-ion quantum simulator. To achieve this, we develop a technique to reconstruct the two-dimensional wavepacket densities of a trapped ion. Experiments agree with the theoretical model, demonstrating the ability of analog quantum simulators -- such as those realised using trapped ions -- to accurately describe nuclear quantum effects.

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 that is difficult to scale because the number of eigenstates 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. 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 SO$_2$.

Ultrafast chemical reactions are difficult to simulate because they involve entangled, many-body wavefunctions whose computational complexity grows rapidly with molecular size. In photochemistry, the breakdown of the Born-Oppenheimer approximation further complicates the problem by entangling nuclear and electronic degrees of freedom. Here, we show that analog quantum simulators can efficiently simulate molecular dynamics using commonly available bosonic modes to represent molecular vibrations. Our approach can be implemented in any device with a qudit controllably coupled to bosonic oscillators and with quantum hardware resources that scale linearly with molecular size, and offers significant resource savings compared to digital quantum simulation algorithms. Advantages of our approach include a time resolution orders of magnitude better than ultrafast spectroscopy, the ability to simulate large molecules with limited hardware using a Suzuki-Trotter expansion, and the ability to implement realistic system-bath interactions with only one additional interaction per mode. Our approach can be implemented with current technology; e.g., the conical intersection in pyrazine can be simulated using a single trapped ion. Therefore, we expect our method will enable classically intractable chemical dynamics simulations in the near term.