Related papers: Implementing Semiclassical Szegedy Walks in Classi…
Suppose some data have been encrypted, can you compute with the data without decrypting them? This problem has been studied as homomorphic encryption and blind computing. We consider this problem in the context of quantum information…
Coined Quantum Walks (QWs) are being used in many contexts with the goal of understanding quantum systems and building quantum algorithms for quantum computers. Alternative models such as Szegedy's and continuous-time QWs were proposed…
We present a detailed circuit implementation of Szegedy's quantization of the Metropolis-Hastings walk. This quantum walk is usually defined with respect to an oracle. We find that a direct implementation of this oracle requires costly…
The recent discovery of fully-homomorphic classical encryption schemes has had a dramatic effect on the direction of modern cryptography. Such schemes, however, implicitly rely on the assumptions that solving certain computation problems…
Szegedy developed a generic method for quantizing classical algorithms based on random walks [Proceedings of FOCS, 2004, pp. 32-41]. A major contribution of his work was the construction of a walk unitary for any reversible random walk.…
Quantum computers promise not only to outperform classical machines for certain important tasks, but also to preserve privacy of computation. For example, the blind quantum computing protocol enables secure delegated quantum computation,…
Legacy encryption systems depend on sharing a key (public or private) among the peers involved in exchanging an encrypted message. However, this approach poses privacy concerns. Especially with popular cloud services, the control over the…
Szegedy's quantum walk is an algorithm for quantizing a general Markov chain. It has plenty of applications such as many variants of optimizations. In order to check its properties in an error-free environment, it is important to have a…
Homomorphic Encryption (HE) allows secure and privacy-protected computation on encrypted data without the need to decrypt it. Since Shor's algorithm rendered prime factorisation and discrete logarithm-based ciphers insecure with quantum…
The rise of quantum computing/technology potentially introduces significant security challenges to cloud computing, necessitating quantum-resistant encryption strategies as well as protection schemes and methods for cloud infrastructures…
Transversality is a simple and effective method for implementing quantum computation fault-tolerantly. However, no quantum error-correcting code (QECC) can transversally implement a quantum universal gate set (Eastin and Knill, Phys. Rev.…
Quantum walks, both discrete and continuous, serve as fundamental tools in quantum information processing with diverse applications. This work introduces a hybrid quantum walk model that integrates the coin mechanism of discrete walks with…
We present a lattice-based scheme for homomorphic evaluation of quantum programs and proofs that remains secure against quantum adversaries. Classical homomorphic encryption is lifted to the quantum setting by replacing composite-order…
Inspired by the concept of fault tolerance quantum computation, this article proposes a framework dubbed Exact Homomorphic Encryption, EHE, enabling exact computations on encrypted data without the need for pre-decryption. The introduction…
Performing smart computations in a context of cloud computing and big data is highly appreciated today. Fully homomorphic encryption (FHE) is a smart category of encryption schemes that allows working with the data in its encrypted form. It…
Quantum walks are recognizably useful for the development of new quantum algorithms, as well as for the investigation of several physical phenomena in quantum systems. Actual implementations of quantum walks face technological difficulties…
Szegedy's quantum walk is a quantization of a classical random walk or Markov chain, where the walk occurs on the edges of the bipartite double cover of the original graph. To search, one can simply quantize a Markov chain with absorbing…
A fully homomorphic encryption system hides data from unauthorized parties, while still allowing them to perform computations on the encrypted data. Aside from the straightforward benefit of allowing users to delegate computations to a more…
Quantum walks on graphs have shown prioritized benefits and applications in wide areas. In some scenarios, however, it may be more natural and accurate to mandate high-order relationships for hypergraphs, due to the density of information…
The widespread adoption of cloud infrastructures has revolutionised data storage and access. However, it has also raised concerns regarding the privacy of sensitive data stored in the cloud. To address these concerns, encryption techniques…