Related papers: Quantum approaches to learning parity with noise
It has recently been shown that there are efficient algorithms for quantum computers to solve certain problems, such as prime factorization, which are intractable to date on classical computers. The chances for practical implementation,…
We study the problem of learning a mixture of two subspaces over $\mathbb{F}_2^n$. The goal is to recover the individual subspaces, given samples from a (weighted) mixture of samples drawn uniformly from the two subspaces $A_0$ and $A_1$.…
Learning problems involving quantum data are natural candidates for demonstrating an advantage in quantum machine learning. Recent results indicate that, for certain tasks and under noiseless conditions, coherent processing of quantum data…
We introduce several probabilistic quantum algorithms that overcome the normal unitary restrictions in quantum machine learning by leveraging the Linear Combination of Unitaries (LCU) method. Among our investigations are quantum native…
Quantum computing promises the possibility of studying the real-time dynamics of nonperturbative quantum field theories while avoiding the sign problem that obstructs conventional lattice approaches. Current and near-future quantum devices…
Quantum computers, that may become available one day, would impact many scientific fields, most notably cryptography since many asymmetric primitives are insecure against an adversary with quantum capabilities. Cryptographers are already…
In a work by Raz (J. ACM and FOCS 16), it was proved that any algorithm for parity learning on $n$ bits requires either $\Omega(n^2)$ bits of classical memory or an exponential number (in~$n$) of random samples. A line of recent works…
There is mounting evidence of emergent phenomena in the capabilities of deep learning methods as we scale up datasets, model sizes, and training times. While there are some accounts of how these resources modulate statistical capacity, far…
Recent technological developments have focused the interest of the quantum computing community on investigating how near-term devices could outperform classical computers for practical applications. A central question that remains open is…
We solve the analysis sparse coding problem considering a combination of convex and non-convex sparsity promoting penalties. The multi-penalty formulation results in an iterative algorithm involving proximal-averaging. We then unfold the…
We present a polynomial-time quantum algorithm for the Hidden Subgroup Problem over $\mathbb{D}_{2^n}$. The usual approach to the Hidden Subgroup Problem relies on harmonic analysis in the domain of the problem, and the best known algorithm…
Variational quantum algorithms have received substantial theoretical and empirical attention. As the underlying variational quantum circuit (VQC) can be represented by Fourier series that contain an exponentially large spectrum in the…
The polynomial hierarchy plays a central role in classical complexity theory. Here, we define a quantum generalization of the polynomial hierarchy, and initiate its study. We show that not only are there natural complete problems for the…
Large-scale variational quantum algorithms are widely recognized as a potential pathway to achieve practical quantum advantages. However, the presence of quantum noise might suppress and undermine these advantages, which blurs the…
In this work, we unveil an analogy between well-known lattice based learning with error problem and ill-posed inverse problems. We show that LWE problem is a structured inverse problem. Further, we propose a symmetric encryption scheme…
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…
Upon integrating Quantum Neural Network (QNN) as the local model, Quantum Federated Learning (QFL) has recently confronted notable challenges. Firstly, exploration is hindered over sharp minima, decreasing learning performance. Secondly,…
The optimization of Variational Quantum Eigensolver is severely challenged by finite-shot sampling noise, which distorts the cost landscape, creates false variational minima, and induces statistical bias called winner's curse. We…
Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…
Recent progress in quantum computing has enabled systems with tens of reliable logical qubits, built from thousands of noisy physical qubits. However, many impactful applications demand quantum computations with millions of logical qubits,…