Related papers: Quantum Hidden Subgroup Algorithms: The Devil Is i…
The relative power of quantum algorithms, using an adaptive access to quantum devices, versus classical post-processing methods that rely only on an initial quantum data set, remains the subject of active debate. Here, we present evidence…
Quantum technologies hold the promise of not only faster algorithmic processing of data, via quantum computation, but also of more secure communications, in the form of quantum cryptography. In recent years, a number of protocols have…
We suggest the usage of algebraic subsets instead of subgroups in public-key cryptography. In particular, we present the subset version of two protocols introduced by Shpilrain and Ushakov with some examples in ascending HNN-extensions of…
The first quantum algorithm to offer an exponential speedup (in the query complexity setting) over classical algorithms was Simon's algorithm for identifying a hidden exclusive-or mask. Here we observe how part of Simon's algorithm can be…
Control of quantum operations is a crucial yet expensive construct for quantum computation. Efficient implementations of controlled operations often avoid applying control to certain subcircuits, which can significantly reduce the number of…
The article explores the creation of a cryptosystem using a halidon group ring of a dihedral group. Due to the non-abelian nature of the group, constructing the cryptosystem is more challenging compared to an abelian group. The logic used…
Quantum Fourier transformations are an essential component of many quantum algorithms, from prime factoring to quantum simulation. While the standard abelian QFT is well-studied, important variants corresponding to \emph{nonabelian} groups…
Under rather general assumptions about the properties of a noisy quantum channel, a first quantum protocol is proposed which allows to implement the secret bit commitment with the probability arbitrarily close to unity.
The quantum Fourier transform (QFT) is central to many quantum algorithms, yet its necessity is not always well understood. We re-examine its role in canonical query problems. The Deutsch-Jozsa algorithm requires neither a QFT nor a domain…
Entanglement constitutes a key characteristic feature of quantum matter. Its detection, however, still faces major challenges. In this letter, we formulate a framework for probing entanglement based on machine learning techniques. The…
A secure quantum identification system combining a classical identification procedure and quantum key distribution is proposed. Each identification sequence is always used just once and new sequences are ``refuelled'' from a shared provably…
The Harrow-Hassidim-Lloyd algorithm is intended for solving the system of linear equations on quantum devices. The exponential advantage of the algorithm comes with four caveats. We present a numerical study of the performance of the…
This report continues the discussion of unitary error bases and quantum codes begun in "Non-binary Unitary Error Bases and Quantum Codes". Nice error bases are characterized in terms of the existence of certain characters in a group. A…
Known protocols for secure delegation of quantum computations from a client to a server in an information theoretic setting require quantum communication. In this work, we investigate methods to reduce communication overhead. First, we…
The advent of quantum computers has justified the development of quantum machine learning algorithms , based on the adaptation of the principles of machine learning to the formalism of qubits. Among such quantum algorithms, anomaly…
Many physicists limit oneself to an instrumentalist description of quantum phenomena and ignore the problems of foundation and interpretation of quantum mechanics. This instrumentalist approach results to "specialization barbarism" and mass…
In many natural and engineered systems, unknown quantum channels act on a subsystem that cannot be directly controlled and measured, but is instead learned through a controllable subsystem that weakly interacts with it. We study quantum…
A new quantum cryptography protocol, based on all unselected states of a qubit as a sort of alphabet with continuous set of letters, is proposed. Its effectiveness is calculated and shown to be essentially higher than those of the other…
The challenge in building high-fidelity quantum gates lies in overcoming control errors and decoherence effects caused by the coupling between the quantum system and the external environment. Nonadiabatic holonomic quantum computation uses…
We present a polynomial time exact quantum algorithm for the hidden subgroup problem in $Z_{m^k}^n$. The algorithm uses the quantum Fourier transform modulo m and does not require factorization of m. For smooth m, i.e., when the prime…