Related papers: Apparent Universal Behavior in Second Moments of R…
On sparse graphs, Roditty and Williams [2013] proved that no $O(n^{2-\varepsilon})$-time algorithm achieves an approximation factor smaller than $\frac{3}{2}$ for the diameter problem unless SETH fails. In this article, we solve an open…
We design quantum circuits by using the standard cell approach borrowed from classical circuit design, which can speed-up the layout of circuits with a regular structure. Our standard cells are general and can be used for all types of…
We present a very general construction for quantum annealing protocols to solve Combinational Circuit Fault Diagnosis (CCFD) problems that restricts the evolution to the space of valid diagnoses. This is accomplished by using special local…
We consider the \emph{two-dimensional range maximum query (2D-RMQ)} problem: given an array $A$ of ordered values, to pre-process it so that we can find the position of the smallest element in the sub-matrix defined by a (user-specified)…
The quantum approximate optimization algorithm (QAOA) can require considerable processing time for developers to test and debug their codes on expensive quantum devices. One avenue to circumvent this difficulty is to use the error maps of…
Quantum error correction (QEC) is believed to be essential for the realization of large-scale quantum computers. However, due to the complexity of operating on the encoded `logical' qubits, understanding the physical principles for building…
A 2-packing set for an undirected graph $G=(V,E)$ is a subset $\mathcal{S} \subset V$ such that any two vertices $v_1,v_2 \in \mathcal{S}$ have no common neighbors. Finding a 2-packing set of maximum cardinality is a NP-hard problem. We…
We consider three variants of the problem of finding a maximum weight restricted $2$-matching in a subcubic graph $G$. (A $2$-matching is any subset of the edges such that each vertex is incident to at most two of its edges.) Depending on…
A decision diagram (DD) is a graph-like data structure for homomorphic compression of Boolean and pseudo-Boolean functions. Over the past decades, decision diagrams have been successfully applied to verification, linear algebra, stochastic…
As the number of qubits increases, quantum circuits become more complex and their state space grows rapidly. This makes functional verification challenging for conventional techniques. Ensuring correctness is especially critical for quantum…
Many quantum information protocols require the implementation of random unitaries. Because it takes exponential resources to produce Haar-random unitaries drawn from the full $n$-qubit group, one often resorts to $t$-designs. Unitary…
We show that in a complex d-dimensional vector space, one can find O(d) bases whose elements form a 2-design. Such vector sets generalize the notion of a maximal collection of mutually unbiased bases (MUBs). MUBs have manifold applications…
We introduce a new concept of a subgraph class called a superbubble for analyzing assembly graphs, and propose an efficient algorithm for detecting it. Most assembly algorithms utilize assembly graphs like the de Bruijn graph or the overlap…
Random transformations are typically good at "scrambling" information. Specifically, in the quantum setting, scrambling usually refers to the process of mapping most initial pure product states under a unitary transformation to states which…
Fault-tolerant quantum computing typically requires the transpilation of arbitrary quantum circuits into a finite, universal gate set, such as Clifford+T. As a baseline, Diagonal approximation can be used for synthesizing single-qubit Pauli…
Distributed inner product estimation (DIPE) is a fundamental task in quantum information, aiming to estimate the inner product between two unknown quantum states prepared on distributed quantum platforms. Existing rigorous sample complexity…
The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other…
Quasiparticle tunneling events are a source of decoherence and correlated errors in superconducting circuits. Understanding and ultimately mitigating these errors calls for real-time detection of quasiparticle tunneling events on individual…
Superconducting quantum circuit is a promising system for building quantum computer. With this system we demonstrate the universal quantum computations, including the preparing of initial states, the single-qubit operations, the two-qubit…
Motivated by network resilience and insurance premiums in the context of cyber security, we derive universal upper bounds for the first and second moments of the size of bond percolation clusters on finite regular graphs. Thinking of the…