Related papers: On the practicality of quantum sieving algorithms …
Recent work [BGS17,ABGS19] has shown SETH hardness of CVP in the $\ell_p$ norm for any $p$ that is not an even integer. This result was shown by giving a Karp reduction from $k$-SAT on $n$ variables to CVP on a lattice of rank $n$. In this…
For any symmetric key cryptosystem with $n$-bit secret key, the key can be recovered in $O(2^{n/2})$ exploiting Grover search algorithm, resulting in the effective key length to be half. In this direction, subsequent work has been done on…
Given a k-dimensional subspace M\subseteq \R^n and a full rank integer lattice L\subseteq \R^n, the \emph{subspace avoiding problem} SAP is to find a shortest vector in L\setminus M. Treating k as a parameter, we obtain new parameterized…
We apply our recent work on empirical estimates of quantum speedups to the practical task of community detection in complex networks. We design several quantum variants of a popular classical algorithm -- the Louvain algorithm for community…
Quantum algorithms can enhance machine learning in different aspects. Here, we study quantum-enhanced least-square support vector machine (LS-SVM). Firstly, a novel quantum algorithm that uses continuous variable to assist matrix inversion…
Quantum computing has the potential to revolutionize cryptography by breaking classical public-key cryptography schemes, such as RSA and Diffie-Hellman. However, breaking the widely used 2048-bit RSA using Shor's quantum factoring algorithm…
As quantum machines have scaled up in their number of qubits, significant research has turned towards increasing their fidelity with quantum error correction codes. Although promising results have been shown with the surface code, which…
$ \newcommand{\SVP}{\mathsf{SVP}} \newcommand{\NP}{\mathsf{NP}} \newcommand{\RTIME}{\mathsf{RTIME}} \newcommand{\RSUBEXP}{\mathsf{RSUBEXP}} \newcommand{\eps}{\epsilon} \newcommand{\poly}{\mathop{\mathrm{poly}}} $We show that unless $\NP…
We propose a quantum algorithm for closest pattern matching which allows us to search for as many distinct patterns as we wish in a given string (database), requiring a query function per symbol of the pattern alphabet. This represents a…
The Schwinger model (quantum electrodynamics in 1+1 dimensions) is a testbed for the study of quantum gauge field theories. We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and…
Training a Support Vector Machine (SVM) requires the solution of a quadratic programming problem (QP) whose computational complexity becomes prohibitively expensive for large scale datasets. Traditional optimization methods cannot be…
Due to recent development in quantum computing, the invention of a large quantum computer is no longer a distant future. Quantum computing severely threatens modern cryptography, as the hard mathematical problems beneath classic public-key…
We define two new problems called SIAP and CAP related to solving SIVP and CVP in a subset of lattices called Simultaneous Approximation (SA) lattices. We give dimension- and gap-preserving, deterministic polynomial-time and space…
In August 2015 the cryptographic world was shaken by a sudden and surprising announcement by the US National Security Agency NSA concerning plans to transition to post-quantum algorithms. Since this announcement post-quantum cryptography…
We study the problem of compression for the purpose of similarity identification, where similarity is measured by the mean square Euclidean distance between vectors. While the asymptotical fundamental limits of the problem - the minimal…
We present a quantum algorithmic routine that extends the realm of Grover-based heuristics for tackling combinatorial optimization problems with arbitrary efficiently computable objective and constraint functions. Building on previously…
We give a quantum algorithm for solving semidefinite programs (SDPs). It has worst-case running time $n^{\frac{1}{2}} m^{\frac{1}{2}} s^2 \text{poly}(\log(n), \log(m), R, r, 1/\delta)$, with $n$ and $s$ the dimension and row-sparsity of the…
Quantum algorithms theoretically outperform classical algorithms in solving problems of increasing size, but computational errors must be kept to a minimum to realize this potential. Despite the development of increasingly capable quantum…
In the lattice approach to Loop Quantum Gravity on a fixed graph computations tend to be involved and are rarely analytically manageable. But, when interested in the expectation values of coherent states on the lattice which are sharply…
Quantum computing threatens the security foundations of consumer electronics (CE). Preparing the diverse CE ecosystem, particularly resource-constrained devices, for the post-quantum era requires quantitative understanding of…