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The Bin Packing Problem (BPP) stands out as a paradigmatic combinatorial optimization problem in logistics. Quantum and hybrid quantum-classical algorithms are expected to show an advantage over their classical counterparts in obtaining…
This work investigates a discrete-time quantum walk on a one-dimensional lattice driven by three entangled coins, each initialized via a Hadamard operator. The walker moves only when all three coins yield identical outcomes (HHH or TTT),…
We present benchmarks of the parity transformation for the Quantum Approximate Optimization Algorithm (QAOA). We analyse the gate resources required to implement a single QAOA cycle for real-world scenarios. In particular, we consider…
Analog quantum optimization methods, such as quantum annealing, are promising and at least partially noise tolerant ways to solve hard optimization and sampling problems with quantum hardware. However, they have thus far failed to…
We discuss an efficient physical realization of topological quantum walks on a finite lattice. The $N$-point lattice is realized with $\log_2 N$ qubits, and the quantum circuit utilizes a number of quantum gates which is polynomial in the…
We investigate the performance and accuracy of digital quantum algorithms for the study of static and dynamic properties of the fermionic Hubbard model at half-filling with next-nearest neighbour hopping terms. We provide quantum circuits…
The question of whether quantum spatial search in two dimensions can be made optimal has long been an open problem. We report progress towards its resolution by showing that the oracle complexity for target location can be made optimal, by…
Quantum search has emerged as one of the most promising fields in quantum computing. State-of-the-art quantum search algorithms enable the search for specific elements in a distribution by monotonically increasing the density of these…
For quantum computation using photons, performing deterministic quantum gate operations is a challenge due to the probabilistic nature of the photon-photon interaction. Encoding qubits in multiple degrees-of-freedom of photons and…
Quantum walks represent paradigmatic quantum evolutions, enabling powerful applications in the context of topological physics and quantum computation. They have been implemented in diverse photonic architectures, but the realization of a…
We implement the discrete-time quantum walk model using the continuous-time evolution of the Hamiltonian that includes both the shift and the coin generators. Based on the Trotter-Suzuki first-order approximation, we consider an…
In the present paper, we study the continuous-time quantum walk on quotient graphs. On such graphs, there is a straightforward reduction of problem to a subspace that can be considerably smaller than the original one. Along the lines of…
Linear optical quantum computation (LOQC) offers a promising platform for scalable quantum information processing, but its scalability is fundamentally constrained by the probabilistic nature of non-local entangling gates. Qudit circuit…
In this tutorial, which contains some original results, we bridge the fields of quantum computing algorithms, conservation laws, and many-body quantum systems by examining three algorithms for searching an unordered database of size $N$…
A noteworthy discovery is that the minimal evolution time is smaller for parity-time ($\mathcal{PT}$) symmetric systems compared to Hermitian setups. Moreover, there is a significant acceleration of two-qubit quantum entanglement…
Lackadaisical quantum walk(LQW) has been an efficient technique in searching a target state from a database which is distributed on a two-dimensional lattice. We numerically study the quantum search algorithm based on the lackadaisical…
The quantum-walk-based spatial search problem aims to find a marked vertex using a quantum walk on a graph with marked vertices. We describe a framework for determining the computational complexity of spatial search by continuous-time…
This work focuses on the quantum mixing time, which is crucial for efficient quantum sampling and algorithm performance. We extend Richter's previous analysis of continuous time quantum walks on the periodic lattice $\mathbb{Z}_{n_1}\times…
We make and generalize the observation that summing of probability amplitudes of a discrete-time quantum walk over partitions of the walking graph consistent with the step operator results in a unitary evolution on the reduced graph which…
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…