Related papers: On the practicality of quantum sieving algorithms …
Lattice-based cryptography is a foundation for post-quantum security, with the Learning with Errors (LWE) problem as a core component in key exchange, encryption, and homomorphic computation. Structured variants like Ring-LWE (RLWE) and…
Quantum algorithms are conventionally formulated for implementation on a single system of qubits amenable to projective measurements. However, in expectation value quantum computation, such as nuclear magnetic resonance realizations, the…
Many signature applications-such as root certificates, secure software updates, and authentication protocols-involve long-lived public keys that are transferred or installed once and then used for many verifications. This key longevity…
Quantum algorithms have demonstrated promising speed-ups over classical algorithms in the context of computational learning theory - despite the presence of noise. In this work, we give an overview of recent quantum speed-ups, revisit the…
Grover's algorithm constitutes the optimal quantum solution to the search problem and provides a quadratic speed-up over all possible classical search algorithms. Quantum interference between computational paths has been posited as a key…
An essential component of many sophisticated metaheuristics for solving combinatorial optimization problems is some variation of a local search routine that iteratively searches for a better solution within a chosen set of immediate…
The integer factorization problem (IFP) underpins the security of RSA, yet becomes efficiently solvable on a quantum computer through Shor's algorithm. Regev's recent high-dimensional variant reduces the circuit size through lattice-based…
The availability of working quantum computers has led to several proposals and claims of quantum advantage. In 2023, this has included claims that quantum computers can successfully factor large integers, by optimizing the search for nearby…
Developing hardware-efficient implementations of quantum algorithms is crucial in the NISQ era to achieve practical quantum advantage. Here, we construct a generic quantum solver for NP problems based on Grover's search algorithm,…
We consider the problem of finding the optimal coefficient vector that maximizes the computation rate at a relay in the compute-and-forward scheme. Based on the idea of sphere decoding, we propose a highly efficient algorithm that finds the…
Searching a database is a central task in computer science and is paradigmatic of transport and optimization problems in physics. For an unstructured search, Grover's algorithm predicts a quadratic speedup, with the search time…
Extensive quantum error correction is necessary in order to scale quantum hardware to the regime of practical applications. As a result, a significant amount of decoding hardware is necessary to process the colossal amount of data required…
We study quantum algorithms for spatial search on finite dimensional grids. Patel et al. and Falk have proposed algorithms based on a quantum walk without a coin, with different operators applied at even and odd steps. Until now, such…
We consider the quantum time complexity of the all pairs shortest paths (APSP) problem and some of its variants. The trivial classical algorithm for APSP and most all pairs path problems runs in $O(n^3)$ time, while the trivial algorithm in…
Quantum computers have the potential to break classical cryptographic systems by efficiently solving problems such as the elliptic curve discrete logarithm problem using Shor's algorithm. While resource estimates for factoring-based…
Satisfiability (SAT) is a central problem in computer science, and advances in SAT-solving algorithms have a far-reaching impact across many fields. Recent works have proposed quantum SAT solvers based on Grover's algorithm, a quantum…
Post-quantum cryptography currently rests on a small number of hardness assumptions, posing significant risks should any one of them be compromised. This vulnerability motivates the search for new and cryptographically versatile assumptions…
In this work, we study the solution of shortest vector problems (SVPs) arising in terms of learning with error problems (LWEs). LWEs are linear systems of equations over a modular ring, where a perturbation vector is added to the right-hand…
Vector perturbation (VP) precoding is an effective nonlinear precoding technique in the downlink (DL) with modulo channels, providing an approximation of dirty paper coding (DPC) which is capacity-achieving. Especially, when combined with…
Bl\"omer and Seifert showed that $\mathsf{SIVP}_2$ is NP-hard to approximate by giving a reduction from $\mathsf{CVP}_2$ to $\mathsf{SIVP}_2$ for constant approximation factors as long as the $\mathsf{CVP}$ instance has a certain property.…