Graph states are a very important class of quantum states. They are in one-to-one correspondence with a graph, which makes it extremely interesting because we can use the rich field of graph theory to investigate the properties of these quantum states. Among other things, they are the main resource of an important paradigm in quantum computing called measurement-based quantum computing where a quantum algorithm is carried out only through adaptive single-qubit measurements on a resource graph state. They are also interesting in quantum communications as their graph structure can also denote a quantum network. At Quriosity, we interested in the best way to generate these graphs in practice, particularly with photonic platforms. We also explore their application to quantum computing and quantum communications.
Associated PIs: Paul Hilaire
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Quantum Error Correction (QEC) is a method to actively protect quantum information from non-negligible physical noise. Logical qubits are thus encoded onto a larger number of physical noisy qubits using a QEC code. By actively detecting and correcting errors, if the physical noise is sufficiently low, we can reduce the errors on the logical qubits to arbitrarily low values. Usually, the achievable performances and resource overhead depends a lot on the way we implement QEC. The way we implement quantum error correction onto a physical system is called a fault-tolerant ‘‘architecture’’. At Quriosity, we are interested in finding the best architecture to process quantum information for specific hardware platforms, in particular photonic platforms.
Associated PIs: Paul Hilaire
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One of the earliest applications where quantum computers are expected to outperform current supercomputers is the simulation of quantum systems. This would transform various scientific fields, including condensed matter physics and quantum chemistry. To this end, advanced quantum algorithms have been developed to tackle critical tasks, such as preparing complex quantum systems and computing their physical properties. At Quriosity, we establish fundamental efficiency guarantees for these algorithms along with proving quantum advantage over the best classical methods, an urgent priority in quantum computing, using tools ranging from operator algebras to quantum complexity theory.
Associated PIs: Cambyse Rouzé
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Quantum computation is usually seen in terms of quantum gates transforming quantum states. The idea of high-order quantum computation is to shift the focus to how the gates themselves can be transformed and arranged with one another, for instance when queried as subroutines of a larger algorithm. Interesting cases of such transformations are for instance the quantum version of the ‘if’ clause (a notoriously thorny problem), or the quantum switch, a processing architecture in which two quantum gates are called in a superposition of orders. In Quriosity, we study how higher-order quantum computation can be described at the mathematical and formal levels.
Associated PIs: Augustin Vanrietvelde
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