arXiv subjects

Akash Kundu

Publications and source records attributed to Akash Kundu.

32 records · Page 2Linked to original sources

arXiv2024

A quantum information theoretic analysis of reinforcement learning-assisted quantum architecture search

In the field of quantum computing, variational quantum algorithms (VQAs) represent a pivotal category of quantum solutions across a broad spectrum of applications. These algorithms demonstrate significant potential for realising quantum computational advantage. A fundamental aspect of VQAs involves formulating expressive and efficient quantum circuits (namely ansatz), and automating the search of such ansatz is known as quantum architecture search (QAS). Recently, reinforcement learning (RL) techniques is utilized to automate the search for ansatzes, known as RL-QAS. This study investigates RL-QAS for crafting ansatz tailored to the variational quantum state diagonalisation problem. Our investigation includes a comprehensive analysis of various dimensions, such as the entanglement thresholds of the resultant states, the impact of initial conditions on the performance of RL-agent, the phase transition behaviour of correlation in concurrence bounds, and the discrete contributions of qubits in deducing eigenvalues through conditional entropy metrics. We leverage these insights to devise an entanglement-guided admissible ansatz in QAS to diagonalise random quantum states using optimal resources. Furthermore, the methodologies presented herein offer a generalised framework for constructing reward functions within RL-QAS applicable to variational quantum algorithms.

quant-ph↗

arXiv2024

YAQQ: Yet Another Quantum Quantizer -- Design Space Exploration of Quantum Gate Sets using Novelty Search

In the standard circuit model of quantum computation, the number and quality of the quantum gates composing the circuit influence the runtime and fidelity of the computation. The fidelity of the decomposition of quantum algorithms, represented as unitary matrices, to bounded depth quantum circuits depends strongly on the set of gates available for the decomposition routine. To investigate this dependence, we explore the design space of discrete quantum gate sets and present a software tool for comparative analysis of quantum processing units and control protocols based on their native gates. The evaluation is conditioned on a set of unitary transformations representing target use cases on the quantum processors. The cost function considers three key factors: (i) the statistical distribution of the decomposed circuits' depth, (ii) the statistical distribution of process fidelities for the approximate decomposition, and (iii) the relative novelty of a gate set compared to other gate sets in terms of the aforementioned properties. The developed software, YAQQ (Yet Another Quantum Quantizer), enables the discovery of an optimized set of quantum gates through this tunable joint cost function. To identify these gate sets, we use the novelty search algorithm, circuit decomposition techniques, and stochastic optimization to implement YAQQ within the Qiskit quantum simulator environment. YAQQ exploits reachability tradeoffs conceptually derived from quantum algorithmic information theory. Our results demonstrate the pragmatic application of identifying gate sets that are advantageous to popularly used quantum gate sets in representing quantum algorithms. Consequently, we demonstrate pragmatic use cases of YAQQ in comparing transversal logical gate sets in quantum error correction codes, designing optimal quantum instruction sets, and compiling to specific quantum processors.

quant-ph↗

arXiv2024

Curriculum reinforcement learning for quantum architecture search under hardware errors

The key challenge in the noisy intermediate-scale quantum era is finding useful circuits compatible with current device limitations. Variational quantum algorithms (VQAs) offer a potential solution by fixing the circuit architecture and optimizing individual gate parameters in an external loop. However, parameter optimization can become intractable, and the overall performance of the algorithm depends heavily on the initially chosen circuit architecture. Several quantum architecture search (QAS) algorithms have been developed to design useful circuit architectures automatically. In the case of parameter optimization alone, noise effects have been observed to dramatically influence the performance of the optimizer and final outcomes, which is a key line of study. However, the effects of noise on the architecture search, which could be just as critical, are poorly understood. This work addresses this gap by introducing a curriculum-based reinforcement learning QAS (CRLQAS) algorithm designed to tackle challenges in realistic VQA deployment. The algorithm incorporates (i) a 3D architecture encoding and restrictions on environment dynamics to explore the search space of possible circuits efficiently, (ii) an episode halting scheme to steer the agent to find shorter circuits, and (iii) a novel variant of simultaneous perturbation stochastic approximation as an optimizer for faster convergence. To facilitate studies, we developed an optimized simulator for our algorithm, significantly improving computational efficiency in simulating noisy quantum circuits by employing the Pauli-transfer matrix formalism in the Pauli-Liouville basis. Numerical experiments focusing on quantum chemistry tasks demonstrate that CRLQAS outperforms existing QAS algorithms across several metrics in both noiseless and noisy environments.

quant-ph↗

arXiv2024

Enhancing variational quantum state diagonalization using reinforcement learning techniques

The variational quantum algorithms are crucial for the application of NISQ computers. Such algorithms require short quantum circuits, which are more amenable to implementation on near-term hardware, and many such methods have been developed. One of particular interest is the so-called variational quantum state diagonalization method, which constitutes an important algorithmic subroutine and can be used directly to work with data encoded in quantum states. In particular, it can be applied to discern the features of quantum states, such as entanglement properties of a system, or in quantum machine learning algorithms. In this work, we tackle the problem of designing a very shallow quantum circuit, required in the quantum state diagonalization task, by utilizing reinforcement learning (RL). We use a novel encoding method for the RL-state, a dense reward function, and an $ε$-greedy policy to achieve this. We demonstrate that the circuits proposed by the reinforcement learning methods are shallower than the standard variational quantum state diagonalization algorithm and thus can be used in situations where hardware capabilities limit the depth of quantum circuits. The methods we propose in the paper can be readily adapted to address a wide range of variational quantum algorithms.

quant-ph↗

arXiv2023

A scalable quantum gate-based implementation for causal hypothesis testing

In this work, we study quantum computing algorithms for accelerating causal inference. Specifically, we consider the formalism of causal hypothesis testing presented in [\textit{Nat Commun} 10, 1472 (2019)]. We develop a quantum circuit implementation and use it to demonstrate that the error probability introduced in the previous work requires modification. The practical scenario, which follows a theoretical description, is constructed as a scalable quantum gate-based algorithm on IBM Qiskit. We present the circuit construction of the oracle embedding the causal hypothesis and assess the associated gate complexities. Additionally, our experiments on a simulator platform validate the predicted speedup. We discuss applications of this framework for causal inference use cases in bioinformatics and artificial general intelligence.

quant-ph↗

arXiv2023

Visualizing Quantum Circuit Probability -- estimating computational action for quantum program synthesis

This research applies concepts from algorithmic probability to Boolean and quantum combinatorial logic circuits. A tutorial-style introduction to states and various notions of the complexity of states are presented. Thereafter, the probability of states in the circuit model of computation is defined. Classical and quantum gate sets are compared to select some characteristic sets. The reachability and expressibility in a space-time-bounded setting for these gate sets are enumerated and visualized. These results are studied in terms of computational resources, universality and quantum behavior. The article suggests how applications like geometric quantum machine learning, novel quantum algorithm synthesis and quantum artificial general intelligence can benefit by studying circuit probabilities.

quant-ph↗

arXiv2023

Hamiltonian-Oriented Homotopy QAOA

The classical homotopy optimization approach has the potential to deal with highly nonlinear landscape, such as the energy landscape of QAOA problems. Following this motivation, we introduce Hamiltonian-Oriented Homotopy QAOA (HOHo-QAOA), that is a heuristic method for combinatorial optimization using QAOA, based on classical homotopy optimization. The method consists of a homotopy map that produces an optimization problem for each value of interpolating parameter. Therefore, HOHo-QAOA decomposes the optimization of QAOA into several loops, each using a mixture of the mixer and the objective Hamiltonian for cost function evaluation. Furthermore, we conclude that the HOHo-QAOA improves the search for low energy states in the nonlinear energy landscape and outperforms other variants of QAOA.

quant-ph↗

arXiv2022

Transparency and enhancement in fast and slow light in $q$-deformed optomechanical system

Nonclassical phenomena can be enhanced by introducing $q$-deformation in optomechanical systems. This motivates investigation of the optical response in a $q$-deformed linearly coupled optomechanical system. The system consists of two deformed cavities that are linearly coupled to the motion of mechanical mirrors, and the cavities are coupled to each other by transmission strength parameter. This study shows that compared to non-deformed cases, the deformed system exhibits more rapid phase transition at the positions of transparency windows, causing stronger and enhanced fast and slow light phenomena. Moreover, in the region $0<q<0.5$, the optomechanical system results in gain. Additionally, for a fixed deformation of cavities, by tuning the tunneling strength and optomechanical coupling, one can observe a delay and advancement in probe field in the order of milliseconds and even above milliseconds for fine-tuning of the coupling parameters. Finally, the bridge between mathematical and physical models is built by assuming the deformation to be a primitive root of unity, which indicates a class of anyon models. These results demonstrate that $q$-deformation provides a novel method for manipulating and significantly enhancing optical phenomena not only in arbitrarily deformed optomechanical systems but also in anyon models.

quant-ph↗

arXiv2022

Variational certification of quantum devices

One of the requirements imposed on the realistic quantum computers is to provide computation results which can be repeated and reproduced. In the situation when one needs to repeat the quantum computation procedure several times, it is crucial that the copies of the quantum devices are similar in the sense of the produced results. In this work, we describe a simple procedure based on variational quantum eigensolver which can be utilized to compare quantum devices. The procedure is developed by combining Choi-Jamiołkowski isomorphism with the variational hybrid quantum-classical procedure for matrix diagonalization. We compare the introduced procedure with the scheme based on the standard bounds for the similarity between quantum operations by analysing its action on random quantum channels. We also discuss the sensitivity of the described procedure to the noise, and we provide numerical results demonstrating its feasibility in realistic scenarios by running the procedure on IBM quantum computer.

quant-ph↗

arXiv2022

Quadratic and Higher-Order Unconstrained Binary Optimization of Railway Rescheduling for Quantum Computing

As consequences of disruptions in railway traffic affect passenger experience/satisfaction, appropriate rerouting and/or rescheduling is necessary. These problems are known to be NP-hard, given the numerous restrictions of traffic nature. With the recent advances in quantum technologies, quantum annealing has become an alternative method to solve such optimization problems. To use quantum annealing, the problem needs to be encoded in QUBO (quadratic unconstrained binary optimization) or HOBO (higher-order binary optimization) formulation that can be recast as a QUBO. This paper introduces QUBO and HOBO representations for rescheduling problems of railway traffic management; the latter is a new approach up to our knowledge. This new approach takes into account not only the single-track lines but also the double- and multi-track lines, as well as stations composed of tracks and switches. We consider the conditions of minimal headway between trains, minimal stay on stations, track occupation, and rolling stock circulation. Furthermore, a hybrid quantum-classical procedure is presented that includes rerouting. We demonstrate the proof of concept implementation on the D-Wave Quantum Processing Unit and D-Wave hybrid solver.

cs.ET↗

arXiv2022

Optimizing the Production of Test Vehicles using Hybrid Constrained Quantum Annealing

Optimization of pre-production vehicle configurations is one of the challenges in the automotive industry. Given a list of tests requiring cars with certain features, it is desirable to find the minimum number of cars that cover the tests and obey the configuration rules. In this paper, we model the problem in the framework of satisfiability and solve it by utilizing the newly introduced hybrid constrained quadratic model (CQM) solver provided by D-Wave. The problem definition is based on the "Optimizing the Production of Test Vehicles" use case given in the BMW Quantum Computing Challenge. We formulate a constrained quadratic model for the problem and use a greedy algorithm to configure the cars. We benchmark the results obtained from the CQM solver with the results from the classical solvers like CBC (Coin-or branch and cut) and Gurobi. We conclude that the performance of the CQM solver is comparable to classical solvers in optimizing the number of test vehicles. As an extension to the problem, we describe how the scheduling of the tests can be incorporated into the model.

quant-ph↗

arXiv2021

Error mitigation for variational quantum algorithms through mid-circuit measurements

Noisy Intermediate-Scale Quantum (NISQ) algorithms require novel paradigms of error mitigation. To obtain noise-robust quantum computers, each logical qubit is equipped with hundreds or thousands of physical qubits. However, it is not possible to use memory-consuming techniques for current quantum devices having at most hundreds or at best thousands of physical qubits on their own. For specific problems, valid quantum states have a unique structure as in the case of Fock states and W-states where the Hamming weight is fixed, and the evolution takes place in a smaller subspace of the full Hilbert space. With this pre-knowledge, some errors can be detected in the course of the evolution of the circuit, by filtering the states not obeying the pattern through post-selection. In this paper, we present mid-circuit post-selection schemes for frequently used encodings such as one-hot, binary, gray, and domain-wall encoding. For the particular subspace of one-hot states, we propose a method that works by compressing the full Hilbert space to a smaller subspace, allowing projecting to the desired subspace without using any ancilla qubits. We demonstrate the effectiveness of the approach for the Quantum Alternating Operator Ansatz algorithm. Our method is particularly suitable for the currently available hardware, where measuring and resetting is possible, but classical control conditional operators are not.

quant-ph↗

arXiv2020

Optical response of a dual membrane active-passive optomechanical cavity

We investigate a dual membrane active-passive cavity where each mechanical membrane individually quadratically coupled to passive and active cavities via two-phonon process. Due to the fact that in the quadratically coupled optomechanical system mean-field approximation fails, hence to analyze the system completely, we switch to a more generalized out of equilibrium approach, namely Keldysh Green's functional approach. We calculate transmission rate using predetermined full retarded Green's function, and then numerically examine the effect of the various parameters on the transmission coefficient and discuss the features and physics behind them in detail. On the basis of the optical responsivity we further extend our study of fast and slow light phenomenon. The results show that our proposed system can not only realize ultra-fast light/ultra-slow light under proper choice of cavity parameters, but realization of the conversion between fast and slow light and vice versa.

physics.optics↗

arXiv2020

Optical Response and Drift Matrix of Quadratic Optomechanical System

Nonlinear interactions in optomechanical systems play a crucial role in many emerging number of interesting studies and phenomena such as existence of optomechanical chaos introduced by F. Monifi et al. [Nature Photonics 10, 399405 (2016)] and optomechanical symmetry breaking proposed by Zhong-Peng Liu et al. [Phys. Rev. Lett.117, 110802 (2016)]. In this article we have theoretically examined quadratically coupled optomechanical system containing two atomic levels. We have first studied the solution of various modes of the system at steady state and later we have observed the variation of Transmission Intensity (T) with several parameters of the system. Further we have extended our analyzation to find Drift matrix of the quadratic optomechanical system and stability conditions by adiabetically eliminating atomic degree of freedom.

quant-ph↗