arXiv subjects

Dhrumil Patel

Publications and source records attributed to Dhrumil Patel.

27 records · Page 2Linked to original sources

arXiv2024

Variational Quantum Algorithms for Semidefinite Programming

A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum algorithms for approximately solving SDPs. For one class of SDPs, we provide a rigorous analysis of their convergence to approximate locally optimal solutions, under the assumption that they are weakly constrained (i.e., $N\gg M$, where $N$ is the dimension of the input matrices and $M$ is the number of constraints). We also provide algorithms for a more general class of SDPs that requires fewer assumptions. Finally, we numerically simulate our quantum algorithms for applications such as MaxCut, and the results of these simulations provide evidence that convergence still occurs in noisy settings.

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arXiv2024

Broadcasting of non-locality

Bell nonlocality and steering are archetypal characteristics of quantum mechanics that mark a significant departure from conventional classical notions. They basically refer to the presence of quantum correlations between separated systems which violate a nonlocal inequality, the violation otherwise not possible if we restrict ourselves only to classical correlations. In view of the importance of such unique correlations one may be interested to generate more states exhibiting nonlocality starting from a few, a protocol which is termed as broadcasting. However, in the present submission, we show using universal Buzek-Hillary(BH) quantum cloning machine that, if one restricts to broadcasting through local quantum cloning, then such nonlocality cannot be broadcasted. Our study is done in the purview of the Bell-CHSH inequality and the CJWR (E.G.Cavalcanti,S.J. Jones,H.M Wiseman and M.D. Reid, Phys.Rev.A 80,032112(2009)) steering inequality. It is observed that when number of measurement settings is greater than 6, some of the output states are steerable after the application of local optimal B-H cloners. We find that, under some restrictions, if the Werner and Bell diagonal states are subjected to such procedures, then the resultant state is rendered unsteerable. We extend this study to three qubit systems and find that genuine tripartite nonlocality cannot be broadcasted using universal BH local quantum cloners, when we consider the Svetlichny's inequality. For two qubit systems, we have considered $10^5$ simulated general local unitaries over Werner and Bell-diagonal states and find that for none of these states broadcasting on nonlocality and 3-steerability is possible.

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arXiv2024

Quantum Neural Estimation of Entropies

Entropy measures quantify the amount of information and correlation present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are available, one must resort to the estimation of such entropy measures. Here we propose a variational quantum algorithm for estimating the von Neumann and Rényi entropies, as well as the measured relative entropy and measured Rényi relative entropy. Our approach first parameterizes a variational formula for the measure of interest by a quantum circuit and a classical neural network, and then optimizes the resulting objective over parameter space. Numerical simulations of our quantum algorithm are provided, using a noiseless quantum simulator. The algorithm provides accurate estimates of the various entropy measures for the examples tested, which renders it as a promising approach for usage in downstream tasks.

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arXiv2023

QSlack: A slack-variable approach for variational quantum semi-definite programming

Solving optimization problems is a key task for which quantum computers could possibly provide a speedup over the best known classical algorithms. Particular classes of optimization problems including semi-definite programming (SDP) and linear programming (LP) have wide applicability in many domains of computer science, engineering, mathematics, and physics. Here we focus on semi-definite and linear programs for which the dimensions of the variables involved are exponentially large, so that standard classical SDP and LP solvers are not helpful for such large-scale problems. We propose the QSlack and CSlack methods for estimating their optimal values, respectively, which work by 1) introducing slack variables to transform inequality constraints to equality constraints, 2) transforming a constrained optimization to an unconstrained one via the penalty method, and 3) replacing the optimizations over all possible non-negative variables by optimizations over parameterized quantum states and parameterized probability distributions. Under the assumption that the SDP and LP inputs are efficiently measurable observables, it follows that all terms in the resulting objective functions are efficiently estimable by either a quantum computer in the SDP case or a quantum or probabilistic computer in the LP case. Furthermore, by making use of SDP and LP duality theory, we prove that these methods provide a theoretical guarantee that, if one could find global optima of the objective functions, then the resulting values sandwich the true optimal values from both above and below. Finally, we showcase the QSlack and CSlack methods on a variety of example optimization problems and discuss details of our implementation, as well as the resulting performance. We find that our implementations of both the primal and dual for these problems approach the ground truth, typically achieving errors of order $10^{-2}$.

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arXiv2023

Wave Matrix Lindbladization II: General Lindbladians, Linear Combinations, and Polynomials

In this paper, we investigate the problem of simulating open system dynamics governed by the well-known Lindblad master equation. In our prequel paper, we introduced an input model in which Lindblad operators are encoded into pure quantum states, called program states, and we also introduced a method, called wave matrix Lindbladization, for simulating Lindbladian evolution by means of interacting the system of interest with these program states. Therein, we focused on a simple case in which the Lindbladian consists of only one Lindblad operator and a Hamiltonian. Here, we extend the method to simulating general Lindbladians and other cases in which a Lindblad operator is expressed as a linear combination or a polynomial of the operators encoded into the program states. We propose quantum algorithms for all these cases and also investigate their sample complexity, i.e., the number of program states needed to simulate a given Lindbladian evolution approximately. Finally, we demonstrate that our quantum algorithms provide an efficient route for simulating Lindbladian evolution relative to full tomography of encoded operators, by proving that the sample complexity for tomography is dependent on the dimension of the system, whereas the sample complexity of wave matrix Lindbladization is dimension independent.

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arXiv2023

Wave Matrix Lindbladization I: Quantum Programs for Simulating Markovian Dynamics

Density Matrix Exponentiation is a technique for simulating Hamiltonian dynamics when the Hamiltonian to be simulated is available as a quantum state. In this paper, we present a natural analogue to this technique, for simulating Markovian dynamics governed by the well known Lindblad master equation. For this purpose, we first propose an input model in which a Lindblad operator $L$ is encoded into a quantum state $ψ$. Then, given access to $n$ copies of the state $ψ$, the task is to simulate the corresponding Markovian dynamics for time $t$. We propose a quantum algorithm for this task, called Wave Matrix Lindbladization, and we also investigate its sample complexity. We show that our algorithm uses $n = O(t^2/\varepsilon)$ samples of $ψ$ to achieve the target dynamics, with an approximation error of $O(\varepsilon)$.

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arXiv2023

Multi-class Brain Tumor Segmentation using Graph Attention Network

Brain tumor segmentation from magnetic resonance imaging (MRI) plays an important role in diagnostic radiology. To overcome the practical issues in manual approaches, there is a huge demand for building automatic tumor segmentation algorithms. This work introduces an efficient brain tumor summation model by exploiting the advancement in MRI and graph neural networks (GNNs). The model represents the volumetric MRI as a region adjacency graph (RAG) and learns to identify the type of tumors through a graph attention network (GAT) -- a variant of GNNs. The ablation analysis conducted on two benchmark datasets proves that the proposed model can produce competitive results compared to the leading-edge solutions. It achieves mean dice scores of 0.91, 0.86, 0.79, and mean Hausdorff distances in the 95th percentile (HD95) of 5.91, 6.08, and 9.52 mm, respectively, for whole tumor, core tumor, and enhancing tumor segmentation on BraTS2021 validation dataset. On average, these performances are >6\% and >50%, compared to a GNN-based baseline model, respectively, on dice score and HD95 evaluation metrics.

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arXiv2019

Broadcasting of quantum correlations in qubit-qudit systems

Quantum mechanical properties like entanglement, discord and coherence act as fundamental resources in various quantum information processing tasks. Consequently, generating more resources from a few, typically termed as broadcasting is a task of utmost significance. One such strategy of broadcasting is through the application of cloning machines. In this article, broadcasting of quantum resources beyond $2 \otimes 2$ systems is investigated. In particular, in $2\otimes3$ dimension, a class of states not useful for broadcasting of entanglement is characterized for a choice of optimal universal Heisenberg cloning machine. The broadcasting ranges for maximally entangled mixed states (MEMS) and two parameter class of states (TPCS) are obtained to exemplify our protocol. A significant derivative of the protocol is the generation of entangled states with positive partial transpose in $3 \otimes 3$ dimension and states which are absolutely separable in $2 \otimes 2$ dimension. Moving beyond entanglement, in $2 \otimes d$ dimension, the impossibility to optimally broadcast quantum correlations beyond entanglement (QCsbE) (discord) and quantum coherence ($l_{1}$-norm) is established. However, some significant illustrations are provided to highlight that non-optimal broadcasting of QCsbE and coherence are still possible.

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arXiv2018

Impossibility of Cloning of Quantum Coherence

It is well known that it is impossible to clone an arbitrary quantum state. However, this inability does not lead directly to no-cloning of quantum coherence. Here, we show that it is impossible to clone the coherence of an arbitrary quantum state which is a stronger statement than the 'no-cloning of quantum state'. In particular, with ancillary system as machine state, we show that it is impossible to clone the coherence of states whose coherence is greater than the coherence of the known states on which the transformations are defined. Also, we characterize the class of states for which coherence cloning will be possible for a given choice of machine. Furthermore, we find the maximum range of states whose coherence can be cloned perfectly. The impossibility proof also holds when we do not include machine states.

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