arXiv subjects

Navid Ghadermarzy

Publications and source records attributed to Navid Ghadermarzy.

7 recordsLinked to original sources

arXiv2025

A Benchmarking Study of Quantum Algorithms for Combinatorial Optimization

We study the performance scaling of three quantum algorithms for combinatorial optimization: measurement-feedback coherent Ising machines (MFB-CIM), discrete adiabatic quantum computation (DAQC), and the Dürr-Hoyer algorithm for quantum minimum finding (DH-QMF) that is based on Grover's search. We use MaxCut problems as a reference for comparison, and time-to-solution (TTS) as a practical measure of performance for these optimization algorithms. For each algorithm, we analyze its performance in solving two types of MaxCut problems: weighted graph instances with randomly generated edge weights attaining 21 equidistant values from $-1$ to $1$; and randomly generated Sherrington-Kirkpatrick (SK) spin glass instances. We empirically find a significant performance advantage for the studied MFB-CIM in comparison to the other two algorithms. We empirically observe a sub-exponential scaling for the median TTS for the MFB-CIM, in comparison to the almost exponential scaling for DAQC and the proven $\widetilde{O}\left(\sqrt{2^n}\right)$ scaling for DH-QMF. We conclude that the MFB-CIM outperforms DAQC and DH-QMF in solving MaxCut problems.

quant-ph↗

arXiv2022

Nuwa: A Quantum Circuit Transpiler Based on a Finite-Horizon Heuristic for Placement and Routing

We introduce a novel transpiler for the placement and routing of quantum circuits on arbitrary target hardware architectures. We use finite-horizon, and optionally discounted, reward functions to heuristically find a suitable placement and routing policy. We employ a finite lookahead to refine the reward functions when breaking a tie between multiple policies. We benchmark our transpiler against multiple alternative solutions and on various test sets of quantum algorithms to demonstrate the benefits of our approach.

quant-ph↗

arXiv2019

Reinforcement Learning Using Quantum Boltzmann Machines

We investigate whether quantum annealers with select chip layouts can outperform classical computers in reinforcement learning tasks. We associate a transverse field Ising spin Hamiltonian with a layout of qubits similar to that of a deep Boltzmann machine (DBM) and use simulated quantum annealing (SQA) to numerically simulate quantum sampling from this system. We design a reinforcement learning algorithm in which the set of visible nodes representing the states and actions of an optimal policy are the first and last layers of the deep network. In absence of a transverse field, our simulations show that DBMs are trained more effectively than restricted Boltzmann machines (RBM) with the same number of nodes. We then develop a framework for training the network as a quantum Boltzmann machine (QBM) in the presence of a significant transverse field for reinforcement learning. This method also outperforms the reinforcement learning method that uses RBMs.

quant-ph↗

arXiv2018

Learning tensors from partial binary measurements

In this paper we generalize the 1-bit matrix completion problem to higher order tensors. We prove that when $r=O(1)$ a bounded rank-$r$, order-$d$ tensor $T$ in $\mathbb{R}^{N} \times \mathbb{R}^{N} \times \cdots \times \mathbb{R}^{N}$ can be estimated efficiently by only $m=O(Nd)$ binary measurements by regularizing its max-qnorm and M-norm as surrogates for its rank. We prove that similar to the matrix case, i.e., when $d=2$, the sample complexity of recovering a low-rank tensor from 1-bit measurements of a subset of its entries is the same as recovering it from unquantized measurements. Moreover, we show the advantage of using 1-bit tensor completion over matricization both theoretically and numerically. Specifically, we show how the 1-bit measurement model can be used for context-aware recommender systems.

math.ST↗

arXiv2017

Near-optimal sample complexity for convex tensor completion

We analyze low rank tensor completion (TC) using noisy measurements of a subset of the tensor. Assuming a rank-$r$, order-$d$, $N \times N \times \cdots \times N$ tensor where $r=O(1)$, the best sampling complexity that was achieved is $O(N^{\frac{d}{2}})$, which is obtained by solving a tensor nuclear-norm minimization problem. However, this bound is significantly larger than the number of free variables in a low rank tensor which is $O(dN)$. In this paper, we show that by using an atomic-norm whose atoms are rank-$1$ sign tensors, one can obtain a sample complexity of $O(dN)$. Moreover, we generalize the matrix max-norm definition to tensors, which results in a max-quasi-norm (max-qnorm) whose unit ball has small Rademacher complexity. We prove that solving a constrained least squares estimation using either the convex atomic-norm or the nonconvex max-qnorm results in optimal sample complexity for the problem of low-rank tensor completion. Furthermore, we show that these bounds are nearly minimax rate-optimal. We also provide promising numerical results for max-qnorm constrained tensor completion, showing improved recovery results compared to matricization and alternating least squares.

cs.LG↗

arXiv2017

Free energy-based reinforcement learning using a quantum processor

Recent theoretical and experimental results suggest the possibility of using current and near-future quantum hardware in challenging sampling tasks. In this paper, we introduce free energy-based reinforcement learning (FERL) as an application of quantum hardware. We propose a method for processing a quantum annealer's measured qubit spin configurations in approximating the free energy of a quantum Boltzmann machine (QBM). We then apply this method to perform reinforcement learning on the grid-world problem using the D-Wave 2000Q quantum annealer. The experimental results show that our technique is a promising method for harnessing the power of quantum sampling in reinforcement learning tasks.

cs.LG↗

arXiv2013

Non-Convex Compressed Sensing Using Partial Support Information

In this paper we address the recovery conditions of weighted $\ell_p$ minimization for signal reconstruction from compressed sensing measurements when partial support information is available. We show that weighted $\ell_p$ minimization with $0<p<1$ is stable and robust under weaker sufficient conditions compared to weighted $\ell_1$ minimization. Moreover, the sufficient recovery conditions of weighted $\ell_p$ are weaker than those of regular $\ell_p$ minimization if at least $50%$ of the support estimate is accurate. We also review some algorithms which exist to solve the non-convex $\ell_p$ problem and illustrate our results with numerical experiments.

cs.IT↗