Periodic Reporting for period 1 - MOQS (MOlecular Quantum Simulations) Reporting period: 2020-11-01 to 2022-10-31 Summary of the context and overall objectives of the project Funded by the Marie Skłodowska-Curie Actions programme, the MOQS project aims to provide interdisciplinary and intersectoral training to 15 early-stage researchers in the emerging field of quantum computing of molecular structure and dynamics. The field sits at the crossroads of chemistry, solid-state and quantum optical physics, computer science and quantum information. It covers a large variety of possible industrial (e.g. catalysis-on-demand and drug design) as well as scientific (e.g. fully ab initio and complete quantum mechanical description of complex molecular reactions) applications. The consortium comprises eight academic partners, three non-academic beneficiaries and five organisations.MOQS has four main scientific Research Objectives, each one developed in a separate Work Package:• Development of optimal algorithms that exploit quantum resources to solve chemistry problems [WP1 - Quantum chemistry: From classical algorithms to quantum algorithms]• Development of solid state superconducting qubit and atomic systems based on Rydberg states in terms of scalability and interaction control with aim to deliver quantum advantage [WP2 - Pushing the limits of quantum hardware]• Development of computational methods that best exploit the unique capabilities of physical platforms, including noisy, lossy, limited resources of near-term quantum hardware [WP3 - Development of platform-optimized computational strategies]• Quantum simulations of electronic structure and energy transfer dynamics of relevance to chemistry [WP4 - Demonstration of quantum simulations of chemical structures and dynamics] Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far In this reporting period, we achieved significant progress towards the Objectives of MOQS in all the WorkPackages. For example, in ongoing work relevant to both WP1 and WP3 we progressed in the development and benchmarking – both numerically and on actual commercial quantum hardware from IBM -- of variational algorithms for quantum computers, as well as of other complementary computational techniques for time-dependent problems aimed at MOQS quantum computing hardware. In work published in Phys. Rev. relevant to the Objectives of WP1, we have started to tackle theoretically the finite size and frustration effects arising in simulations of strongly interacting many-particle systems. In work directly achieving the Objectives and Tasks of WP2 and WP3, we focused on understanding the role of realistic experimental noise for quantum simulations and quantum computations and developing improved noise-robust strategies for qubit control and entanglement. For examples, in several works published in Quantum, Phys. Rev. and in the arXiv (under review for publication), the MOQS team has developed complementary quantum optimal control techniques to generate time-optimal pulses for realizing two-qubit and three-qubit quantum gates with Rydberg atoms (both alkali metal and earth atoms), as well as pulses for one-qubit and two-qubit gates that are robust to common sources of noise in that setup, such as Doppler shifts and laser intensity noise, lifetimes, polarisabilities and blockade strengths. This allows them to identify the optimal regime of Rydberg states that minimise these errors, for their protocols to operate. The MOQS team has further implemented primitives for scalable quantum computation in the superconducting setup, including high fidelity entangling gates using a qubit as a sensor, a new multiplexing method for reading out two qubits with a single pulse and a software package for analyzing experimental data from quantum computers. We have further performed preliminary studies of digital-analog quantum simulations using tailor made gate pulses for superconducting qubits and resonators. In work published in Phys. Rev. we have shown how to implement a general class of generalized quantum measurements without ancilla qubits by exploiting the higher dimensional Hilbert space of superconducting transmon qubits and presented an experimental demonstration on IBM quantum Hardware. Relevant to the Objectives of WP4, the MOQS team is now developing algorithmic improvements for quantum chemistry applications that cover the whole stack of a superconducting quantum computer. On the theory side, in work published in Phys. Rev. the MOQS team has leveraged informationally complete measurements based on POVMs as a novel tool to parallelize near-term quantum algorithms and thus drastically reduce measurement overheads. On the hardware side, we have developed techniques to use higher-excited states of transmon qubits for quantum information processing as well as methods that tailor quantum circuits to the limited connectivity imposed by the device. Combined, these efforts will bridge the gap towards practically useful chemistry applications on state-of-the-art superconducting transmon hardware. Furthermore, a collaboration between different MOQS partners (published on the arXiv and submitted for publication) has led to a complete analysis of exciton dynamics in the presence of strong dephasing relevant to molecular complexes that can be efficiently simulated on the Rydberg platform. The training goal of the project – recruiting 15 ESRs and training them to become leaders in their field – has so far been achieved with the minor set-back of the preliminary leave of one ESR who chose another career field. The monitoring of the individual training via the PCDPs and the surveys carried out after the training events ensure the overall progress and general satisfaction level of the fellows. Related communication and outreach measures have been implemented and to further improve their impact, an additional training is foreseen at the beginning of Reporting Period 2. Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far) For the first reporting period, the project progressed as expected and along the outlines listed above. This corresponds to innovation beyond the state-of-the-art described in the Grant Agreement. Further assessments of the impact will be done during the second reporting period.