--- tags: VQE, Hamiltonian-level, NISQ, Noise, Numerical, Invited sort-date: 2024-06-18 description: Ultrafast dynamics and Ultrafast bandgap photonics XI Symposium | 18 June 2024 12:30–13:00 CEST | Hersonissos, Crete, Greece --- [[/index|Christopher K. Long]], Kieran Dalton, Yordan S. Yordanov, Charles G. Smith, Frederico Martins, Crispin H. W. Barnes, Normann Mertig, and David R. M. Arvidsson-Shukur **Date & time:** 18 June 2024 12:30–13:00 CEST **Location:** Hersonissos, Crete, Greece **Conference:** [Ultrafast dynamics and Ultrafast bandgap photonics XI Symposium](https://udm-ubp2024.eventsadmin.com/Home/Welcome) [@udm_ubp2024] I presented work from Refs. [@Dalton2024; @PhysRevA.109.042413; @Long2025]. Download slide deck: [[PowerPoints/Towards chemistry simulations on silicon quantum processors (Hersonissos).pptx|PPTX]], [[PDFs/Towards chemistry simulations on silicon quantum processors (Hersonissos).pdf|PDF]][^1] # Abstract From Ref. [@udm_ubp2024_abstracts]: > Noisy intermediate-scale quantum (NISQ) devices could yield early-stage advantages over classical computers before large-scale fault-tolerant quantum computers emerge. A particularly promising group of NISQ-tailored algorithms are the variational quantum algorithms (VQAs), developed, e.g., for chemistry-simulation purposes. VQAs utilise classical optimisers that guide the operation of shallowdepth quantum circuits. Such quantum-classical symbioses could lead to less-stringent requirements on the coherence times and error rates of the quantum processor. The recent theoretical advances in VQA development have been complimented *(sic)* by rapid improvements of several quantum-processors platforms. Owing to their small size and the potential for rapid industrial scaling, silicon quantum processors constitute a particularly promising platform. Moreover, silicon processors’ diverse tunability could endow VAQs *(sic)* with additional degrees of freedom that could improve algorithmic performance. In this talk, I will present numerical results suggesting that current VQAs for quantum computational chemistry are not viable in the presence of realistic noise levels [@Dalton2024]. There are three possible directions for improvement. First, one could rely on error mitigation [@Dalton2024]. Second, one could rely on new noise-robust VQAs [@PhysRevA.109.042413]. I will argue that neither error mitigation nor algorithmic improvements will be sufficient to perform useful chemical computations on NISQ hardware. However, there is a third option. One can relax the digital gate-based model of quantum computation to a model where the hardware is controlled at the level of the Hamiltonian (experimental pulses) native to the specific platform [@Meitei2021; @PhysRevApplied.19.064071; @Long2025].[^2] To explore the prospect of pulse-based VQAs, I will consider the time it takes to variationally prepare molecular ground states on silicon quantum processors. I account for experimental constraints and the effects of pulse filtering such that my model investigates realistic pulse shapes. Finally, I will present an analysis of the effect of noise on these pulse-based computations. I find that silicon quantum processors boast competitive state-preparation times for chemical ground states (Fig. 1 [@Long2025]) when compared with superconducting hardware [@Meitei2021; @PhysRevApplied.19.064071].[^2] Further, there is a dramatic reduction in the state-preparation time when going from a digital gate-based model to the silicon pulse-based model. Thus, pulse-based computation with silicon hardware could be a promising route towards chemical simulations on quantum processors. > > ![[Figures/Towards chemistry simulations on silicon quantum processors (Hersonissos).png]] > **Fig. 1. Estimates of the disassociation *(sic)* curves for H₂ (left), 𝑯𝒆𝑯⁺ (centre), and +𝑳𝒊𝑯 *(sic)* (right).**[^3] For each molecule and bond separation the numerically simulated silicon quantum processor is given a fixed amount of evolution time as a resource and prepares the best possible approximation to the ground state in this time. As more time is allowed, the quantum processor can obtain better approximations. The top three panels plot the disassociation *(sic)* curves (energy against bond separation), with the colour of the curve corresponding to the allowed evolution time indicated by the colour bar above each panel. The yellow curve corresponds to zero evolution time. The purple curve corresponds to enough time to reach the full configuration interaction (FCI) energy (dashed curve). In the bottom panels, the error from the FCI energy is plotted on a log scale with the evolution time now on the vertical axis. In the bottom panels, we observe a sharp transition: above an evolution time called the minimal evolution time (MET), the ground state can be prepared exactly. We indicate the MET as a function of bond distance by a black-and-white curve. Below the MET, the error is large, and the corresponding colour is yellow, as indicated by the bottom right colour bar. While above the MET, the error is small and fluctuates around the simulation accuracy, and the corresponding colour is blue. # Other versions - [[Towards chemistry simulations on silicon quantum processors (UCL)]] - [[Towards chemistry simulations on silicon quantum processors (HCL)]] [^1]: Corrections have been made to the presentation since the talk. As I have lost the uncorrected version I have only uploaded the corrected version. [^2]: Ref. [@PhysRevApplied.19.064071] is not open access, however, the preprint [@Asthana_2023] is. [^3]: I do not have a higher-resolution version of this iteration of the figure. See the slide deck ([[PowerPoints/Towards chemistry simulations on silicon quantum processors (Hersonissos).pptx|PPTX]], [[PDFs/Towards chemistry simulations on silicon quantum processors (Hersonissos).pdf|PDF]][^1]) or Ref. [@Long2025] for a higher-resolution and updated version of the figure.