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Apoorva D. Patel

Publications and source records attributed to Apoorva D. Patel.

14 recordsLinked to original sources

Image classification via a quantum-inspired strategy involving a mixture of experts

Pattern recognition problems arise in a variety of physical image processing situations, and convolutional neural networks are a popular scheme for the required feature extraction and classification tasks. The classical networks use diffusion-based smearing and block-wise pooling to downsample the image data and capture important structural features. In this work, we propose and demonstrate a more efficient quantum-inspired strategy involving a mixture of experts. It is a hybrid classical-quantum framework. The quantum part consists of amplitude encoding of the images, convolution using local unitary operations, multiple experts processing the same image with different parameters, and feature extraction using quantum stabiliser codes. The classical part then jointly processes the features extracted by different experts using a standard fully connected neural network for image class prediction. Using MNIST and Fashion-MNIST datasets as benchmarks, we demonstrate that the joint expert analysis outperforms the individual expert one, as well as reduces the failure rate of image class prediction by around a factor of two. The overhead of our quantum-inspired strategy is only moderate on GPU workstations, which makes our proposal a practical alternative to existing classical schemes. We also point out how the quantum part of our framework can be executed on a quantum processor.

cs.LG

Quantum Correlations in Frustrated Three-Body Systems

Many physical systems are not understood from first principles due to the presence of multi-body quantum correlations. The effort taken to simulate such systems on classical computers increases exponentially with increase in the system size. We study simple, yet non-trivial, three-body frustrated systems that can help in understanding the underlying quantum correlations. First we investigate the ground state of helium-like atoms using the variational method and physically meaningful ansatze, revealing how quantum entanglement arises due to frustration in the system. Next we consider another frustrated three-body system, the hydrogen molecular ion, and analytically demonstrate the nature of its wavefunction arising from the quantum tunneling phenomenon. Finally, we extend these results to model yet another physically important system, the hydrogen bond.

quant-ph

Understanding nature's selection of genetic languages

All living organisms use two universal genetic languages in their molecular biology machinery, one containing four nucleotide bases in its alphabet, and the other containing twenty amino acids in its alphabet. They can be understood as the optimal encodings of genetic information for the tasks they carry out, i.e. replication/transcription for DNA/RNA and translation for polypeptide chains. These tasks select needed letters of the alphabet by complementary nucleotide base-pairing, from a collection of molecules in the cell. The computer science paradigm for this process is database search; various algorithms for it can be constructed and compared according to number of attempts (or queries) they need to make to find the correct nucleotide base-pairing. Grover's search algorithm based on oscillatory wave dynamics perfectly fits the number of queries needed to search the genetic alphabets, and it is more efficient than the best Boolean search algorithm (i.e. binary tree search) that needs a larger number of queries. This result strongly suggests that the universal genetic languages have been selected by evolution as the optimal alphabets for the tasks they carry out, and are not an accident of history. The outstanding challenge is to demonstrate how Grover's search algorithm would be executed in vivo by the living organisms.

q-bio.OT

Limitations of Quantum Advantage in Unsupervised Machine Learning

Machine learning models are used for pattern recognition analysis of big data, without direct human intervention. The task of unsupervised learning is to find the probability distribution that would best describe the available data, and then use it to make predictions for observables of interest. Classical models generally fit the data to Boltzmann distribution of Hamiltonians with a large number of tunable parameters. Quantum extensions of these models replace classical probability distributions with quantum density matrices. An advantage can be obtained only when features of density matrices that are absent in classical probability distributions are exploited. Such situations depend on the input data as well as the targeted observables. Explicit examples are discussed that bring out the constraints limiting possible quantum advantage. The problem-dependent extent of quantum advantage has implications for both data analysis and sensing applications.

quant-ph

EPR Paradox, Bell Inequalities and Peculiarities of Quantum Correlations

Quantum theory revolutionised physics by introducing a new fundamental constant and a new mathematical framework to describe the observed phenomena at the atomic scale. These new concepts run counter to our familiar notions of classical physics, and pose questions about how to understand quantum physics as a fundamental theory of nature. Peculiarities of quantum correlations underlie all these questions, and this article describes their formulation, tests and resolution within the standard framework of quantum theory.

physics.gen-ph

The Quantum Density Matrix and its many uses: From quantum structure to quantum chaos and noisy simulators

The quantum density matrix generalises the classical concept of probability distribution to quantum theory. It gives the complete description of a quantum state as well as the observable quantities that can be extracted from it. Its mathematical structure is described, with applications to understanding quantum correlations, illustrating quantum chaos and its unravelling, and developing software simulators for noisy quantum systems with efficient quantum state tomography.

quant-ph

A Software Simulator for Noisy Quantum Circuits

We have developed a software library that simulates noisy quantum logic circuits. We represent quantum states by their density matrices in the Pauli basis, and incorporate possible errors in initialisation, logic gates, memory and measurement using simple models. Our quantum simulator is implemented as a new backend on IBM's open-source Qiskit platform. In this document, we provide its description, and illustrate it with some simple examples.

quant-ph

Grover's Algorithm in Natural Settings

The execution of Grover's quantum search algorithm needs rather limited resources without much fine tuning. Consequently, the algorithm can be implemented in a variety of physical set-ups, which involve wave dynamics but may not need other quantum features. Several of these set-ups are described, pointing out that some of them occur quite naturally. In particular, it is entirely possible that the algorithm played a key role in the selection of the universal structure of genetic languages.

quant-ph

Efficient Energy Transport in Photosynthesis: Roles of Coherence and Entanglement

Recently it has been discovered---contrary to expectations of physicists as well as biologists---that the energy transport during photosynthesis, from the chlorophyll pigment that captures the photon to the reaction centre where glucose is synthesised from carbon dioxide and water, is highly coherent even at ambient temperature and in the cellular environment. This process and the key molecular ingredients that it depends on are described. By looking at the process from the computer science view-point, we can study what has been optimised and how. A spatial search algorithmic model based on robust features of wave dynamics is presented.

quant-ph

Towards Understanding the Origin of Genetic Languages

Molecular biology is a nanotechnology that works--it has worked for billions of years and in an amazing variety of circumstances. At its core is a system for acquiring, processing and communicating information that is universal, from viruses and bacteria to human beings. Advances in genetics and experience in designing computers have taken us to a stage where we can understand the optimisation principles at the root of this system, from the availability of basic building blocks to the execution of tasks. The languages of DNA and proteins are argued to be the optimal solutions to the information processing tasks they carry out. The analysis also suggests simpler predecessors to these languages, and provides fascinating clues about their origin. Obviously, a comprehensive unraveling of the puzzle of life would have a lot to say about what we may design or convert ourselves into.

q-bio.GN

Wave Algorithms: Optimal Database Search and Catalysis

Grover's database search algorithm, although discovered in the context of quantum computation, can be implemented using any physical system that allows superposition of states. A physical realization of this algorithm is described using coupled simple harmonic oscillators, which can be exactly solved in both classical and quantum domains. Classical wave algorithms are far more stable against decoherence compared to their quantum counterparts. In addition to providing convenient demonstration models, they may have a role in practical situations, such as catalysis.

quant-ph

Large-N QCD at strong transverse lattice gauge coupling

We had previously obtained an integral equation for mesons in transverse lattice QCD, in the limit of large number of colours and strong transverse lattice gauge coupling [1]. This equation is a generalisation of the 't Hooft equation [2], by inclusion of the spin degrees of freedom. We analyse this equation to extract spectral properties and light-front wavefunctions of mesons. We also extend the method to study baryon properties in the same limit.

hep-lat

A derivation of Regge trajectories in large-N transverse lattice QCD

Large-N QCD is analysed in light-front coordinates with a transverse lattice at strong coupling. The general formalism can be looked up on as a d+n expansion with a stack of d-dimensional hyperplanes uniformly spaced in n transverse dimensions. It can arise by application of the renormalisation group transformations only in the transverse directions. At leading order in strong coupling, the gauge field dynamics reduces to the constraint that only colour singlet states can jump between the hyperplanes. With d=2, n=2 and large-N, the leading order strong coupling results are simple renormalisations of those for the 't Hooft model. The meson spectrum lies on a set of parallel trajectories labeled by spin. This is the first derivation of the widely anticipated Regge trajectories in a regulated systematic expansion in QCD.

hep-lat