Related papers: Apparent Universal Behavior in Second Moments of R…
A discrete-time quantum walk on a graph is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. Hitting times for discrete quantum walks on graphs give an average time before the walk…
We prove that random 1D Clifford brickwork circuits form (in expectation) good approximate quantum error correction codes in logarithmic depth. Our proof makes use of the statistical mechanics techniques for random circuits developed by…
For a random set $\mathcal{S} \subset U(d)$ of quantum gates we provide bounds on the probability that $\mathcal{S}$ forms a $\delta$-approximate $t$-design. In particular we have found that for $\mathcal{S}$ drawn from an exact $t$-design…
Full connectivity of qubits is necessary for most quantum algorithms, which is difficult to directly implement on Noisy Intermediate-Scale Quantum processors. However, inserting swap gate to enable the two-qubit gates between uncoupled…
There are various gate sets that can be used to describe a quantum computation. A particularly popular gate set in the literature on quantum computing consists of arbitrary single-qubit gates and 2-qubit CNOT gates. A CNOT gate is however…
As the effort to scale up existing quantum hardware proceeds, it becomes necessary to schedule quantum gates in a way that minimizes the number of operations. There are three constraints that have to be satisfied: the order or dependency of…
We investigate the theoretical limits of the effect of the quantum interaction distance on the speed of exact quantum addition circuits. For this study, we exploit graph embedding for quantum circuit analysis. We study a logical mapping of…
We investigate the counterparts of random walk in universal quantum computing and their implementation using standard quantum circuits. Quantum walk have been recently well investigated for traversing graphs with certain oracles. We focus…
Quantum error detection (QED) offers a promising pathway to fault tolerance in near-term quantum devices by balancing error suppression with minimal resource overhead. However, its practical utility hinges on optimizing design…
Constructing ensembles of circuits which efficiently approximate the Haar measure over various groups is a long-standing and fundamental problem in quantum information theory. Recently it was shown that one can obtain approximate designs…
It is reasonable to expect the theory of quantum codes to be simplified in the case of codes of minimum distance 2; thus, it makes sense to examine such codes in the hopes that techniques that prove effective there will generalize. With…
In the standard CONGEST model for distributed network computing, it is known that "global" tasks such as minimum spanning tree, diameter, and all-pairs shortest paths, consume large bandwidth, for their running-time is…
A minimal depth quantum circuit implementing 5-qubit quantum error correction in a manner optimized for a linear nearest neighbor architecture is described. The canonical decomposition is used to construct fast and simple gates that…
In modern applications of graphs algorithms, where the graphs of interest are large and dynamic, it is unrealistic to assume that an input representation contains the full information of a graph being studied. Hence, it is desirable to use…
The bandwidth of a graph G on n vertices is the minimum b such that the vertices of G can be labeled from 1 to n such that the labels of every pair of adjacent vertices differ by at most b. In this paper, we present a 2-approximation…
Unitary $k$-designs are probabilistic ensembles of unitary matrices whose first $k$ statistical moments match that of the full unitary group endowed with the Haar measure. In prior work, we showed that the automorphism group of classical…
Many applications of quantum simulation require to prepare and then characterize quantum states by performing an efficient partial tomography to estimate observables corresponding to $k$-body reduced density matrices ($k$-RDMs). For…
The problems of computing eccentricity, radius, and diameter are fundamental to graph theory. These parameters are intrinsically defined based on the distance metric of the graph. In this work, we propose quantum algorithms for the diameter…
The quantum circuit Born machine (QCBM) is a quantum physics inspired implicit generative model naturally suitable for learning binary images, with a potential advantage of modeling discrete distributions that are hard to simulate…
Variational quantum circuits (VQCs) are a leading approach to quantum machine learning on near-term devices, yet it remains unclear which circuit architecture yields the best accuracy-parameter trade-off on classical tabular data. We…