Related papers: A simpler proof of zero-knowledge against quantum …
A new approach to the classical limit of Grover's algorithm is discussed by assuming a very rapid dephasing of a system between consecutive Grover's unitary operations, which drives pure quantum states to decohered mixed states. One can…
Logic entailment is essential to reasoning, but entailment checking has the worst-case complexity of an exponential of the variable size. With recent development, quantum computing when mature may allow an effective approach for various…
A quantum computer encodes information in quantum states and runs quantum algorithms to surpass the classical counterparts by exploiting quantum superposition and quantum correlation. Grover's quantum search algorithm is a typical quantum…
Grover's algorithm is a primary algorithm offered as evidence that quantum computers can provide an advantage over classical computers. It involves an "oracle" specified for a given application whose structure is not part of the formal…
Grover's search algorithm was a groundbreaking advancement in quantum algorithms, displaying a quadratic speed-up of querying for items. Since the creation of this algorithm it has been utilized in various ways, including in preparing…
We initiate the study of relativistic zero-knowledge quantum proof of knowledge systems with classical communication, formally defining a number of useful concepts and constructing appropriate knowledge extractors for all the existing…
On-demand authentication is critical for scalable quantum systems, yet current approaches require the signer to initiate communication, creating unnecessary overhead. We introduce a new method where the verifier can request authentication…
The search problem is to find a state satisfying certain properties out of a given set. Grover's algorithm drives a quantum computer from a prepared initial state to the target state and solves the problem quadratically faster than a…
This paper is a gentle but rigorous introduction to quantum computing intended for discrete mathematicians. Starting from a small set of assumptions on the behavior of quantum computing devices, we analyze their main characteristics,…
Quantum amplification is essential for various quantum technologies such as communication and weak-signal detection. However, its practical use is still limited due to inevitable device fragility that brings about distortion in the output…
We study the notion of zero-knowledge secure against quantum polynomial-time verifiers (referred to as quantum zero-knowledge) in the concurrent composition setting. Despite being extensively studied in the classical setting, concurrent…
Zero-knowledge proof system is an important protocol that can be used as a basic block for construction of other more complex cryptographic protocols. An intrinsic characteristic of a zero-knowledge systems is the assumption that is…
Grover's algorithm is a quantum search algorithm that proceeds by repeated applications of the Grover operator and the Oracle until the state evolves to one of the target states. In the standard version of the algorithm, the Grover operator…
We study some extensions of Grover's quantum searching algorithm. First, we generalize the Grover iteration in the light of a concept called amplitude amplification. Then, we show that the quadratic speedup obtained by the quantum searching…
Foundational results in theoretical computer science have established that everything provable, is provable in zero knowledge. However, this assertion fundamentally assumes a classical interpretation of computation and many interesting…
In this paper, we prove classical coin-flipping secure in the presence of quantum adversaries. The proof uses a recent result of Watrous [Wat09] that allows quantum rewinding for protocols of a certain form. We then discuss two…
Search-base algorithms have widespread applications in different scenarios. Grover's quantum search algorithms and its generalization, amplitude amplification, provide a quadratic speedup over classical search algorithms for unstructured…
We present a simple and general simulation technique that transforms any black-box quantum algorithm (a la Grover's database search algorithm) to a quantum communication protocol for a related problem, in a way that fully exploits the…
In standard Grover's algorithm for quantum searching, the probability of finding the marked item is not exactly 1. In this Letter we present a modified version of Grover's algorithm that searches a marked state with full successful rate.…
Hypothesis elimination is a special case of Bayesian updating, where each piece of new data rules out a set of prior hypotheses. We describe how to use Grover's algorithm to perform hypothesis elimination for a class of probability…