Related papers: Quantum Time-Space Tradeoff for Finding Multiple C…
The current paper improves the number of queries of the previous quantum multi-collision finding algorithms presented by Hosoyamada et al. at Asiacrypt 2017. Let an $l$-collision be a tuple of $l$ distinct inputs that result in the same…
We give a new version of the adversary method for proving lower bounds on quantum query algorithms. The new method is based on analyzing the eigenspace structure of the problem at hand. We use it to prove a new and optimal strong direct…
We introduce a structured quantum search algorithm that leverages entanglement maps and a fixed-point method to minimize oracle query complexity in unsorted datasets. By partitioning qubits into rows based on their entanglement order, the…
The main promise of quantum computing is to efficiently solve certain problems that are prohibitively expensive for a classical computer. Most problems with a proven quantum advantage involve the repeated use of a black box, or oracle,…
Kallampally and Tewari showed in 2016 that there can be a trade-off between determinism and time in space-bounded computations. This they did by describing an unambiguous non-deterministic algorithm to solve Directed Graph Reachability that…
An algorithm for structured database searching is presented and used to solve the set partition problem. O(n) oracle calls are required in order to obtain a solution, but the probability that this solution is optimal decreases exponentially…
The spatial search problem consists in minimizing the number of steps required to find a given site in a network, under the restriction that only oracle queries or translations to neighboring sites are allowed. We propose a quantum…
Performance of cryptanalytic quantum search algorithms is mainly inferred from query complexity which hides overhead induced by an implementation. To shed light on quantitative complexity analysis removing hidden factors, we provide a…
In the era of Noisy Intermediate-Scale Quantum (NISQ) computers it is crucial to design quantum algorithms which do not require many qubits or deep circuits. Unfortunately, the most well-known quantum algorithms are too demanding to be run…
Motivated by applications in recommender systems, web search, social choice and crowdsourcing, we consider the problem of identifying the set of top $K$ items from noisy pairwise comparisons. In our setting, we are non-actively given $r$…
I improve the tight bound on quantum searching by Boyer et al. (quant-ph/9605034) to a matching bound, thus showing that for any probability of success Grovers quantum searching algorithm is optimal. E.g. for near certain success we have to…
Given two unsorted lists each of length N that have a single common entry, a quantum computer can find that matching element with a work factor of $O(N^{3/4}\log N)$ (measured in quantum memory accesses and accesses to each list). The…
We consider the problem of finding the minimum element in a list of length $N$ using a noisy comparator. The noise is modelled as follows: given two elements to compare, if the values of the elements differ by at least $\alpha$ by some…
Collision-resistant hashing, a fundamental primitive in modern cryptography, ensures that there is no efficient way to find distinct inputs that produce the same hash value. This property underpins the security of various cryptographic…
Quantum search is a quantum mechanical technique for searching N possibilities in only sqrt(N) steps. This has been proved to be the best possible algorithm for the exhuastive search problem in the sense the number of queries it requires…
By considering an unreliable oracle in a query-based model of quantum learning, we present a tradeoff relation between the oracle's reliability and the reusability of quantum state of the input data. The tradeoff relation manifests as the…
Executing quantum circuits on currently available quantum computers requires compiling them to a representation that conforms to all restrictions imposed by the targeted architecture. Due to the limited connectivity of the devices' physical…
We present a message-passing based parallel version of the Space Saving algorithm designed to solve the $k$--majority problem. The algorithm determines in parallel frequent items, i.e., those whose frequency is greater than a given…
This work focuses on reducing the physical cost of implementing quantum algorithms when using the state-of-the-art fault-tolerant quantum error correcting codes, in particular, those for which implementing the T gate consumes vastly more…
In our pursuit of quantum supremacy during the NISQ era, this research introduces a novel approach rooted in the Quantum Approximate Optimization Algorithm (QAOA) framework to address the Traveling Salesman Problem (TSP). By strategically…