相关论文: Simulating quantum computation by contracting tens…

Classical simulations of quantum circuits are vital for assessing potential quantum advantage and benchmarking devices, yet they require sophisticated methods to avoid the exponential growth of resources. Tensor network approaches, in…

In this paper we isolate the combinatorial property responsible (at least in part) for the computational speedups recently observed in some quantum walk algorithms. We find that continuous-time quantum walks can exploit the covering space…

It has recently been shown that starting with a classical query algorithm (decision tree) and a guessing algorithm that tries to predict the query answers, we can design a quantum algorithm with query complexity $O(\sqrt{GT})$ where $T$ is…

Cubicity of a graph $G$ is the smallest dimension $d$, for which $G$ is a unit disc graph in ${\mathbb{R}}^d$, under the $l^\infty$ metric, i.e. $G$ can be represented as an intersection graph of $d$-dimensional (axis-parallel) unit…

Dynamic programming on various graph decompositions is one of the most fundamental techniques used in parameterized complexity. Unfortunately, even if we consider concepts as simple as path or tree decompositions, such dynamic programming…

In some physical implementations of quantum computers, 2-qubit operations can be applied only on certain pairs of qubits. Compilation of a quantum circuit into one compliant to such qubit connectivity constraint results in an increase of…

Near-term quantum hardware can support two-qubit operations only on the qubits that can interact with each other. Therefore, to execute an arbitrary quantum circuit on the hardware, compilers have to first perform the task of qubit routing,…

We consider the classic problem of Network Reliability. A network is given together with a source vertex, one or more target vertices, and probabilities assigned to each of the edges. Each edge appears in the network with its associated…

Treewidth is an important and well-known graph parameter that measures the complexity of a graph. The Kneser graph Kneser(n,k) is the graph with vertex set $\binom{[n]}{k}$, such that two vertices are adjacent if they are disjoint. We…

Motivated by the increasing need to understand the algorithmic foundations of distributed large-scale graph computations, we study a number of fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…

We consider quantum circuits composed of Clifford and T gates. In this context the T gate has a special status since it confers universal computation when added to the (classically simulable) Clifford gates. However it can be very expensive…

In this work, we present a quantum circuit for a binary classification prediction algorithm using a random forest model. The quantum prediction algorithm is presented in our previous works. We construct a circuit and implement it using…

Connectivity (or equivalently, unweighted maximum flow) is an important measure in graph theory and combinatorial optimization. Given a graph $G$ with vertices $s$ and $t$, the connectivity $\lambda(s,t)$ from $s$ to $t$ is defined to be…

We introduce an algorithm which estimates the number of circuits in a graph as a function of their length. This approach provides analytical results for the typical entropy of circuits in sparse random graphs. When applied to real-world…

Random quantum states have various applications in quantum information science. We discover a new ensemble of quantum states that serve as an $\epsilon$-approximate state $t$-design while possessing extremely low entanglement, magic, and…

We study space and time efficient quantum algorithms for two graph problems -- deciding whether an $n$-vertex graph is a forest, and whether it is bipartite. Via a reduction to the s-t connectivity problem, we describe quantum algorithms…

Quantum computers are expected to enable fast solving of large-scale combinatorial optimization problems. However, their limitations in fidelity and the number of qubits prevent them from handling real-world problems. Recently, a…

Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links.…

The quantum circuit model is the most commonly used model for implementing quantum computers and quantum neural networks whose essential tasks are to realize certain unitary operations. Here we propose an alternative approach; we use a…

Quantum computing is currently strongly limited by the impact of noise, in particular introduced by the application of two-qubit gates. For this reason, reducing the number of two-qubit gates is of paramount importance on noisy…