Related papers: Rademacher Complexity Bounds for Parameterized Qua…
The quantum simulation kernel is an important subroutine appearing as a very long gate sequence in many quantum programs. In this paper, we propose Paulihedral, a block-wise compiler framework that can deeply optimize this subroutine by…
Quantum-centric supercomputing presents a compelling framework for large-scale hybrid quantum-classical tasks. Although quantum machine learning (QML) offers theoretical benefits in various applications, challenges such as large-size data…
Quantum circuit compilation comprises many computationally hard reasoning tasks that nonetheless lie inside #$\mathbf{P}$ and its decision counterpart in $\mathbf{PP}$. The classical simulation of general quantum circuits is a core example.…
Over-parameterization is commonly used to increase the expressivity of variational quantum circuits (VQCs), yet deeper and more highly parameterized circuits often exhibit poor trainability and limited generalization. In this work, we…
We introduce a Pauli-measurement-based algorithm to certify the Schmidt number of $n$-qubit pure states. Our protocol achieves an average-case sample complexity of $\caO(\mathrm{poly}(n)\chi^2)$, a substantial improvement over the $\caO(2^n…
We study the classical and parameterized complexity of computing the positive non-clashing teaching dimension of a set of concepts, that is, the smallest number of examples per concept required to successfully teach an intelligent learner…
We consider the problem of finding a 1-planar drawing for a general graph, where a 1-planar drawing is a drawing in which each edge participates in at most one crossing. Since this problem is known to be NP-hard we investigate the…
Linear quantum cellular automata were introduced recently as one of the models of quantum computing. A basic postulate of quantum mechanics imposes a strong constraint on any quantum machine: it has to be unitary, that is its time evolution…
Pauli-based computation (PBC) is a universal model for quantum computation with qubits where the input state is a magic (resource) state and the computation is driven by a sequence of adaptively chosen and compatible multiqubit Pauli…
We propose an efficient algorithm for partitioning Pauli strings into subgroups, which can be simultaneously measured in a single quantum circuit. Our partitioning algorithm drastically reduces the total number of measurements in a…
We study the sample complexity of nondeterministically testable graph parameters and improve existing bounds on it by several orders of magnitude. The technique used would be also of independent interest. We also discuss the special case of…
We consider some random series parametrised by complex binary strings. The simplest case is that of Rademacher series, independent of a time parameter. This is then extended to the case of Fourier series on the circle with Rademacher…
A variety of quantum algorithms employ Pauli operators as a convenient basis for studying the spectrum or evolution of Hamiltonians or measuring multi-body observables. One strategy to reduce circuit depth in such algorithms involves…
Barren Plateaus are a formidable challenge for hybrid quantum-classical algorithms that lead to flat plateaus in the loss function landscape making it difficult to take advantage of the expressive power of parameterized quantum circuits…
The generalization performance of kernel methods is largely determined by the kernel, but common kernels are stationary thus input-independent and output-independent, that limits their applications on complicated tasks. In this paper, we…
Parameterized quantum circuits (PQC, aka, variational quantum circuits) are among the proposals for a computational advantage over classical computation of near-term (not fault tolerant) digital quantum computers. PQCs have to be "trained"…
This paper presents several novel generalization bounds for the problem of learning kernels based on the analysis of the Rademacher complexity of the corresponding hypothesis sets. Our bound for learning kernels with a convex combination of…
We extend existing results for the Nielsen complexity of scalar primaries and spinning primaries in four dimensions by including supersymmetry. Specifically, we study the Nielsen complexity of circuits that transform a superconformal…
Measurement-based quantum computation (MBQC) is a framework for quantum information processing in which a computational task is carried out through one-qubit measurements on a highly entangled resource state. Due to the indeterminacy of the…
In this paper, we describe a parameterized quantum circuit that can be considered as convolutional and pooling layers for graph neural networks. The circuit incorporates the parameterized quantum Fourier circuit where the qubit connections…