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FAult Tolerant MOLecular Spin processor

Periodic Reporting for period 1 - FATMOLS (FAult Tolerant MOLecular Spin processor)

Reporting period: 2020-03-01 to 2021-05-31

Exploiting the laws of Quantum Physics to process information helps solving problems that are unassailable even to the best current supercomputers. In the future, quantum algorithms may help to find medical therapies, efficient energy sources and fertilizers, assist experts in economic or weather forecast predictions and contribute to developing more powerful artificial intelligence systems. A key challenge to bringing this about is finding a platform able to reach a sufficiently high computational power. Some estimates suggest that operating over many thousands, or even millions, of qubits might be necessary. This daunting prediction arises not only from the complexity of such problems, but also from the need to protect quantum operations from noise and the fact that quantum error correction is based on redundancy. Although there is hope that the available Noisy Intermediate-Size Quantum devices will be useful for some specific tasks, it is essential to consider alternatives with a potential for integrating many quantum resources and for correcting errors in an efficient manner.

FATMOLS introduces a new paradigm, the molecular spin quantum processor, made of artificial molecules designed and synthesized by Chemistry wired up by their coupling to superconducting circuits. Molecules represent the smallest object in Nature that is tuneable, i.e. their properties can be modified by changing their structure and composition, yet they remain microscopic and fully reproducible. FATMOLS integrates quantum functionalities at three different scales (nuclear spins, electronic spins and circuits), is inherently modular and therefore scalable, and is also very flexible. Its competitive advantages for reaching large scale quantum computation are: a) integrating nontrivial quantum functionalities (e.g. quantum correction) at the level of each molecule; b) reducing the complexity, e.g. the number of gates, required to implement specific algorithms; and c) increasing the number of information units controlled by each device.

FATMOLS overall objective is to provide a proof-of-concept of this new platform on at least two molecules with multiple and fully addressable levels, from which more complex architectures can be derived. The project applies a creative collaboration between disciplines and between top-level academic and industrial partners to create, test and interconnect the different components of this technology (molecules, superconducting nano-resonators and control electronics) and to design suitable algorithms and architectures for applications like quantum chemistry and quantum error correction.
The activities carried out in the first year encompass four areas that define intermediate steps towards the overall goal.

1. From molecular spin qubits to molecular spin processors: We have generated molecular structures hosting up to six qubits or, in general, qudits with dimensions ranging from d = 4 up to 64 and addressable spin states. Some of them fulfil the conditions to efficiently implement specifically designed quantum error correction algorithms and quantum simulations, or even to perform as universal quantum processors. In parallel, we have put forward several strategies to reduce or mitigate the effect of decoherence. These have led to best coherence times of about 20-30 microseconds for electronic spins and 60 microseconds for nuclear spins, which are sufficiently long to carry out the algorithms mentioned above.

2. Novel superconducting circuits and enabling technologies: A sufficiently strong coupling of molecular spin processors to microwave cavity photons is a crucial ingredient in wiring them up into a scalable architecture. Using novel designs of on-chip superconducting resonators we have shown that spin-photon couplings of up to 50 kHz can be reached for single molecules, which should be enough to attain the coherent coupling regime. In parallel, we have developed instrumentation to manipulate the states of molecular spin qudits using arbitrary shape microwave pulses. To support to these instrumental advances, a FPGA library with programmable tools to control multiple gates and read-out signals has been worked out.

3. Optimize the circuit-molecule interface: Model spin qubits have been successfully transferred onto metallic and superconducting substrates and the first experiments on the single molecule spin dynamics have been carried out. The results show that the molecule-superconductor interaction affects spin coherence, thus calling for carefully engineering their interface, e.g. by inserting suitably designed molecular ligands or spacing layers. We have demonstrated experimentally the ability of directly transferring molecular nanodeposits onto specific areas of superconducting circuits, with very high control over dose and location.

4. Molecular spin-photon coupling: Experiments performed on molecular spin qubits deposited onto nanoscopic transmission waveguide resonators evidence single spin to single photon interactions as large as 1 kHz, a record value in units of coupling per photon energy. Proof-of-concept experiments have exploited the strong coupling of superconducting resonators to molecular spin ensembles to coherently control and read-out the spin polarization. We have extended the theory of magnetic quantum electrodynamics to multilevel spin qudits and shown that the coupling of such systems to cavity photons allows performance of all basic operations.
The results achieved so far establish molecular spin qudits as a very promising platform for next generation quantum computation and simulation. Each magnetic molecule realizes a microscopic quantum processor, in which all gates are controlled by local operations. This approach simplifies the implementation of some algorithms. For instance, simulations of quantum systems with multiple degrees of freedom (e.g. spin-boson models) benefit from the mapping onto the multiple qudit states. Also promising is the possibility of embedding quantum error correction in each molecular unit, profiting from specific codes optimized to deal with the most relevant error sources. The advances in novel instrumentation and control protocols should enable first proof-of-concept implementations of such algorithms before the end of the project.

The project has also led to novel superconducting circuits, designed to optimally interface microwave cavity photons with molecular spins. Results already show record spin-photon couplings and promise much higher values before the project ends. This will lay down the technological basis for wiring up distant molecular spin processors, thus contributing to developing a platform with a considerable scalability potential. In the medium to long term, it will define an alternative roadmap to the next level of computational power (100-1000 qubits) that could already tackle quantum optimization and quantum simulation problems with direct impact on agriculture, health-care, energy, artificial intelligence, etc.

Besides, these technologies will likely reshape and widen the scope of magnetic resonance, a key instrumentation for physics, chemistry, materials science or structural biology, which also finds applications as an analytical tool in medicine or in the detection of contaminants. The combination of optimized circuits and soft nanolithography based on molecular vehicles will likely take this technique to the level of femtolitre size samples.
Molecular spin quantum processor.