Quantum information processing (QIP) has developed in great strides over the recent years following the binary footsteps of its classical counterpart. Yet the underlying quantum hardware is not binary, but rather based on inherently multi-level quantum systems. As a result, much of today’s quantum hardware is artificially constrained to two-level information processing. Recent results by members of the consortium have shown that current trapped-ion quantum hardware supports universal computation using a high-dimensional (qudit) encoding. This allows us to fully utilize the available quantum hardware and thereby greatly increase the computational power of existing devices. Such an approach allows not only vastly increased computational complexity for a given register size but enables significantly more efficient quantum technologies, as suggested and demonstrated by members of the consortium.
Yet, despite these promising results and theoretical advantages, the qudit approach to quantum computation remains far less developed and understood than the conventional qubit QIP framework. In particular, methods for measurement-based quantum computing (MBQC) [Br09] and cluster states remain largely unexplored in the qudit setting. In MBQC, computations are performed through single-qubit measurements on a previously prepared resource quantum state, rather than through a sequence of local and entangling operations applied to a fixed set of qubits, as in the circuit model. This approach has become a core component of QIP, not only because not needing to perform costly entangling operations can be experimentally favourable. More importantly, the underlying mathematical structures of graphs and stabilizers have proven to be extremely powerful and enable among other things information-theoretically secure “blind” quantum computation, efficiently verifiable quantum-advantage experiments, and form the basis of quantum error correction (QEC). In order for qudit QIP to remain competitive with its binary counterpart, it is thus of utmost importance that these advanced capabilities are enabled in systems that use multi-state logic.
The aim of this project is to address this challenge and elevate the MBQC framework and stabilizer formalism to quantum computers working with multi-state logic (qudits). In alignment with the goals and focal area of the call, the results of the proposed research will be central in enhancing the competitiveness of emerging qudit quantum hardware and our ability to capitalize on this fundamentally more efficient QIP paradigm to seamlessly enhance the performance of quantum computing devices. The MBQC framework is also the key ingredient in secure quantum computing, achieving the highest standard of security: informationally-secure blind quantum computing, which we aim to generalize to qudits.
Through the intimate connection between the stabilizer formalism and QEC, the results of this project will also inform future work towards fault-tolerant quantum computing with qudits. Finally, we aim to develop qudit-based and qudit-enhanced algorithms for problems in computing and sensing, showing how qudits fundamentally outperform their binary counterparts. Key results will be demonstrated experimentally on a multi-qudit quantum computer.
The project consortium has long pioneered the development of qudit quantum technology, covering aspects of quantum communication and entanglement theory, to experimental qudit systems in photonics and trapped ions, through to qudit sensing, computing, and simulation applications as well as efficient verification of large-scale quantum systems. With the recent demonstration of a universal qudit quantum processor realizing quantum simulations vastly more efficiently than conventional qubit devices, the fundamental advantages of qudit computing for certain applications have become undeniable. While these results were achieved in the circuit model, they suggest that similar advantages with an even greater number of possibilities are to be expected within a suitable generalized MBQC and stabilizer framework. Notably, these results, while demonstrated in a trapped-ion platform, are agnostic to the used hardware and can thus be implemented by a range of QIP technologies. These results establish a competitive and all-encompassing toolbox for qudit MBQC and scalable verification tools, which would further cement Austria’s leading role in the rapidly developing field of qudit QIP.
