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We present a quantum algorithm for computing the period lattice of infrastructures of fixed dimension. The algorithm applies to infrastructures that satisfy certain conditions. The latter are always fulfilled for infrastructures obtained…
The National Institute of Standards and Technology (NIST) has finalized the selection of post-quantum cryptographic (PQC) algorithms for use in the era of quantum computing. Despite their integration into TLS protocol for key establishment…
Block encoding is a key ingredient in the recently developed quantum singular value transformation (QSVT) framework, which provides a unifying description for many quantum algorithms. Initially introduced to simplify and optimize resource…
Solving eigenproblem of the Laplacian matrix of a fully connected weighted graph has wide applications in data science, machine learning, and image processing, etc. However, this is very challenging because it involves expensive matrix…
We introduce a novel quantum algorithm for the lattice Boltzmann method (LBM) based on the one-step simplified LBM. The structure of the algorithm allows for more flexibility in modelling different physics in contrast to earlier quantum…
Quantum lattice models with large local Hilbert spaces emerge across various fields in quantum many-body physics. Problems such as the interplay between fermions and phonons, the BCS-BEC crossover of interacting bosons, or decoherence in…
We consider a version of the nearest-codeword problem on finite fields $\mathbb{F}_q$ using the Manhattan distance, an analog of the Hamming metric for non-binary alphabets. Similarly to other lattice related problems, this problem is…
A new approach to efficient quantum computation with probabilistic gates is proposed and analyzed in both a local and non-local setting. It combines heralded gates previously studied for atom or atom-like qubits with logical encoding from…
In this paper, we propose new classes of trapdoor functions to solve the closest vector problem in lattices. Specifically, we construct lattices based on properties of polynomials for which the closest vector problem is hard to solve unless…
The traditional method for computation in either the surface code or in the Raussendorf model is the creation of holes or "defects" within the encoded lattice of qubits that are manipulated via topological braiding to enact logic gates.…
The strongly correlated systems we use to realise quantum error-correcting codes may give rise to high-weight, problematic errors. Encouragingly, we can expect local quantum error-correcting codes with no string-like logical operators $-$…
We describe quantum circuits with only $\widetilde{\cal O}(N)$ Toffoli complexity that block encode the spectra of quantum chemistry Hamiltonians in a basis of $N$ arbitrary (e.g., molecular) orbitals. With ${\cal O}(\lambda / \epsilon)$…
Block encoding of sparse matrices underpins powerful quantum algorithms such as quantum singular value transformation, Hamiltonian simulation, and quantum linear solvers, yet its efficient gate-level realization for general sparse matrices…
Quantum Fourier transform (QFT) is a widely used building block for quantum algorithms, whose scalable implementation is challenging in experiments. Here, we propose a protocol of quadratic quantum Fourier transform (QQFT), considering cold…
We introduce the use of Fourier analysis on lattices as an integral part of a lattice based construction. The tools we develop provide an elegant description of certain Gaussian distributions around lattice points. Our results include two…
Topological quantum error correction is a milestone in the scaling roadmap of quantum computers, which targets circuits with trillions of gates that would allow running quantum algorithms for real-world problems. The square-lattice surface…
This paper studies how post-quantum cryptographic (PQC) security assumptions can be represented and communicated through a structured, layered framework that is useful for technical interpretation but does not replace formal cryptographic…
High-fidelity and robust quantum manipulation is the key for scalable quantum computation. Therefore, due to the intrinsic operational robustness, quantum manipulation induced by geometric phases is one of the promising candidates. However,…
We propose a recursive lattice reduction framework for finding short non-zero vectors or dense sublattices of a lattice. The framework works by recursively searching for dense sublattices of dense sublattices (or their duals) with…
Protein folding is a central challenge in computational biology, with important applications in molecular biology, drug discovery and catalyst design. As a hard combinatorial optimisation problem, it has been studied as a potential target…