Related papers: Optimal exact quantum algorithm for the promised e…
In this paper, we present a new exact algorithm for counting perfect matchings, which relies on neither inclusion-exclusion principle nor tree-decompositions. For any bipartite graph of $2n$ nodes and $\Delta n$ edges such that $\Delta \geq…
In this paper, we present efficient quantum algorithms that are exponentially faster than classical algorithms for solving the quantum optimal control problem. This problem involves finding the control variable that maximizes a physical…
Quantum adiabatic optimization seeks to solve combinatorial problems using quantum dynamics, requiring the Hamiltonian of the system to align with the problem of interest. However, these Hamiltonians are often incompatible with the native…
Testing graph completeness is a critical problem in computer science and network theory. Leveraging quantum computation, we present an efficient algorithm using the Szegedy quantum walk and quantum phase estimation (QPE). Our algorithm,…
This paper establishes the exact comparison complexity of finding an element repeated $n$ times in a $2n$-element array containing $n+1$ distinct values, under the equality-comparison model with $O(1)$ extra space. We present a simple…
The hidden shift problem is a natural place to look for new separations between classical and quantum models of computation. One advantage of this problem is its flexibility, since it can be defined for a whole range of functions and a…
Providing an optimal path to a quantum annealing algorithm is key to finding good approximate solutions to computationally hard optimization problems. Reinforcement is one of the strategies that can be used to circumvent the exponentially…
We mainly study exceptional configuration for coined quantum walk search. For searching on a two-dimensional grid by AKR algorithm, we find some new classes of exceptional configurations that cannot be found by the AKR algorithm effectively…
There has been a surge of progress in recent years in developing algorithms for testing and learning quantum states that achieve optimal copy complexity. Unfortunately, they require the use of entangled measurements across many copies of…
The so-called welded tree problem provides an example of a black-box problem that can be solved exponentially faster by a quantum walk than by any classical algorithm. Given the name of a special ENTRANCE vertex, a quantum walk can find…
This paper proposes a highly efficient quantum algorithm for portfolio optimisation targeted at near-term noisy intermediate-scale quantum computers. Recent work by Hodson et al. (2019) explored potential application of hybrid…
Designing proper time-dependent control fields for slowly varying the system to the ground state that encodes the problem solution is crucial for adiabatic quantum computation. However, inevitable perturbations in real applications demand…
One specific subset of quantum algorithms is Grovers Ordered Search Problem (OSP), the quantum counterpart of the classical binary search algorithm, which utilizes oracle functions to produce a specified value within an ordered database.…
Finding a good approximation of the top eigenvector of a given $d\times d$ matrix $A$ is a basic and important computational problem, with many applications. We give two different quantum algorithms that, given query access to the entries…
The quantum walk dynamics obey the laws of quantum mechanics with an extra locality constraint, which demands that the evolution operator is local in the sense that the walker must visit the neighboring locations before endeavoring to…
Quantum computation has attracted much attention since it was shown by Shor and Grover the possibility to implement quantum algorithms able to realize, respectively, factoring and searching in a faster way than any other known classical…
Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…
This work considers a generalization of Grover's search problem, viz., to find any one element in a set of acceptable choices which constitute a fraction f of the total number of choices in an unsorted data base. An infinite family of…
The question of which resources drive the advantages in quantum algorithms has long been a fundamental challenge. While entanglement and coherence are critical to many quantum algorithms, our results indicate that they do not fully explain…
Adiabatic quantum computing~(AQC) is based on the adiabatic principle, where a quantum system remains in an instantaneous eigenstate of the driving Hamiltonian. The final state of the Hamiltonian encodes solution to the problem of interest.…