arXiv subjects

Anirban Chowdhury

Publications and source records attributed to Anirban Chowdhury.

15 recordsLinked to original sources

arXiv2026

Simulating dynamics of RLC circuits with a quantum differential-algebraic equations solver

We introduce a quantum algorithm for simulating the dynamics of electrical circuits consisting of resistors, inductors and capacitors (aka RLC circuits) along with power sources. Given oracle access to the connectivity of the circuit and values of the electrical elements, our algorithm prepares a quantum state that encodes voltages and current values either at a specified time or the history of their evolution over a time-interval. For an RLC circuit with $N$ components, our algorithm runs in time $\textsf{polylog}(N)$ under mild assumptions on the connectivity of the circuit and values of its components. This provides an exponential speed-up over classical algorithms that take $\textsf{poly}(N)$ time in the worst-case. Our algorithm can be used to estimate energy across a set of components or dissipated power in $\textsf{polylog}(N)$ time, a problem that we prove is BQP-hard and therefore unlikely to be efficiently solved by classical algorithms. The main challenge in simulating the dynamics of RLC circuits is that they are governed by differential-algebraic equations (DAEs), a coupled system of differential equations with hidden algebraic constraints. Consequentially, existing quantum algorithms for ordinary differential equations cannot be directly utilized. We therefore develop a quantum DAE solver for simulating the time-evolution of linear DAEs. For RLC circuits, we employ modified nodal analysis to create a system of DAEs compatible with our quantum algorithm. We establish BQP-hardness by demonstrating that any network of classical harmonic oscillators, for which an energy-estimation problem is known to be BQP-hard, is a special case of an LC circuit. Our work gives theoretical evidence of quantum advantage in simulating RLC circuits and we expect that our quantum DAE solver will find broader use in the simulation of dynamical systems.

quant-ph↗

arXiv2025

Wavefunction Flows: Efficient Quantum Simulation of Continuous Flow Models

Flow models are a cornerstone of modern machine learning. They are generative models that progressively transform probability distributions according to learned dynamics. Specifically, they learn a continuous-time Markov process that efficiently maps samples from a simple source distribution into samples from a complex target distribution. We show that these models are naturally related to the Schrödinger equation, for an unusual Hamiltonian on continuous variables. Moreover, we prove that the dynamics generated by this Hamiltonian can be efficiently simulated on a quantum computer. Together, these results give a quantum algorithm for preparing coherent encodings (a.k.a., qsamples) for a vast family of probability distributions--namely, those expressible by flow models--by reducing the task to an existing classical learning problem, plus Hamiltonian simulation. For statistical problems defined by flow models, such as mean estimation and property testing, this enables the use of quantum algorithms tailored to qsamples, which may offer advantages over classical algorithms based only on samples from a flow model. More broadly, these results reveal a close connection between state-of-the-art machine learning models, such as flow matching and diffusion models, and one of the main expected capabilities of quantum computers: simulating quantum dynamics.

quant-ph↗

arXiv2025

Quantum Krylov Algorithm for Szegö Quadrature

We present a quantum algorithm to evaluate matrix elements of functions of unitary operators. The method is based on calculating quadrature nodes and weights using data collected from a quantum processor. Given a unitary $U$ and quantum states $|ψ_0\rangle$, $|ψ_1\rangle$, the resulting quadrature rules form a functional that can then be used to classically approximate $\langleψ_1|f(U)|ψ_0\rangle$ for any function $f$. In particular, the algorithm calculates Szegö quadrature rules, which, when $f$ is a Laurent polynomial, have the optimal relation between degree of $f$ and number of distinct quantum circuits required. The unitary operator $U$ could approximate a time evolution, opening the door to applications like estimating properties of Hamiltonian spectra and Gibbs states, but more generally could be any operator implementable via a quantum circuit. We expect this algorithm to be useful as a subroutine in other quantum algorithms, much like quantum signal processing or the quantum eigenvalue transformation of unitaries. Key advantages of our algorithm are that it does not require approximating $f$ directly, via a series expansion or in any other way, and once the output functional has been constructed using the quantum algorithm, it can be applied to any $f$ classically after the fact.

quant-ph↗

arXiv2025

Quasiprobabilistic imaginary-time evolution on quantum computers

Imaginary-time evolution plays an important role in algorithms for computing ground-state and thermal equilibrium properties of quantum systems, but can be challenging to simulate on classical computers. Many quantum algorithms for imaginary-time evolution have resource requirements that are prohibitive for current quantum devices and face performance issues due to noise. Here, we propose a new algorithm for computing imaginary-time evolved expectation values on quantum computers, inspired by probabilistic error cancellation, an error-mitigation technique. Our algorithm works by decomposing a Trotterization of imaginary-time evolution into a probabilistic linear combination of operations, each of which is then implemented on a quantum computer. The measurement data is then classically post-processed to obtain the expectation value of the imaginary-time evolved state. Our algorithm requires no ancillary qubits and can be made noise-resilient without additional error mitigation. It is well-suited for estimating thermal expectation values by making use of the notion of a thermal pure quantum state. We demonstrate our algorithm by performing numerical simulations of thermal pure quantum state preparation for the 1D Heisenberg Hamiltonian on 8 qubits, and by using an IBM quantum computer to estimate the energy of the same Hamiltonian on 2 qubits. We observe promising results compared to the exact values, illustrating the potential of our algorithm for probing the physics of quantum many-body systems on current hardware.

quant-ph↗

arXiv2025

Quantum Approximate Counting with Additive Error: Hardness and Optimality

Quantum counting is the task of determining the dimension of the subspace of states that are accepted by a quantum verifier circuit. It is the quantum analog of counting the number of valid solutions to NP problems -- a problem well-studied in theoretical computer science with far-reaching implications in computational complexity. The complexity of solving the class #BQP of quantum counting problems, either exactly or within suitable approximations, is related to the hardness of computing many-body physics quantities arising in algebraic combinatorics. Here, we address the complexity of quantum approximate counting under additive error. First, we show that computing additive approximations to #BQP problems to within an error exponential in the number of witness qubits in the corresponding verifier circuit is as powerful as polynomial-time quantum computation. Next, we show that returning an estimate within error that is any smaller is #BQP-hard. Finally, we show that additive approximations to a restricted class of #BQP problems are equivalent in computational hardness to the class DQC1. Our work parallels results on additively approximating #P and GapP functions.

quant-ph↗

arXiv2025

Controlization Schemes Based on Orthogonal Arrays

Realizing controlled operations is fundamental to the design and execution of quantum algorithms. In quantum simulation and learning of quantum many-body systems, an important subroutine consists of implementing a controlled Hamiltonian time-evolution. Given only black-box access to the uncontrolled evolution $e^{-iHt}$, controlizing it, i.e., implementing $\mathrm{ctrl}(e^{-iHt}) = |0\rangle\langle 0|\otimes I + |1\rangle\langle 1 |\otimes e^{-iHt}$ is non-trivial. Controlization has been recently used in quantum algorithms for transforming unknown Hamiltonian dynamics [OKTM24] leveraging a scheme introduced in Refs. [NSM15, DNSM21]. The main idea behind the scheme is to intersperse the uncontrolled evolution with suitable operations such that the overall dynamics approximates the desired controlled evolution. Although efficient, this scheme uses operations randomly sampled from an exponentially large set. In the present work, we show that more efficient controlization schemes can be constructed with the help of orthogonal arrays for unknown 2-local Hamiltonians. We conduct a detailed analysis of their performance and demonstrate the resulting improvements through numerical experiments. This construction can also be generalized to $k$-local Hamiltonians. Moreover, our controlization schemes based on orthogonal arrays can take advantage of the interaction graph's structure and be made more efficient.

quant-ph↗

arXiv2024

On-chain Validation of Tracking Data Messages (TDM) Using Distributed Deep Learning on a Proof of Stake (PoS) Blockchain

Trustless tracking of Resident Space Objects (RSOs) is crucial for Space Situational Awareness (SSA), especially during adverse situations. The importance of transparent SSA cannot be overstated, as it is vital for ensuring space safety and security. In an era where RSO location information can be easily manipulated, the risk of RSOs being used as weapons is a growing concern. The Tracking Data Message (TDM) is a standardized format for broadcasting RSO observations. However, the varying quality of observations from diverse sensors poses challenges to SSA reliability. While many countries operate space assets, relatively few have SSA capabilities, making it crucial to ensure the accuracy and reliability of the data. Current practices assume complete trust in the transmitting party, leaving SSA capabilities vulnerable to adversarial actions such as spoofing TDMs. This work introduces a trustless mechanism for TDM validation and verification using deep learning over blockchain. By leveraging the trustless nature of blockchain, our approach eliminates the need for a central authority, establishing consensus-based truth. We propose a state-of-the-art, transformer-based orbit propagator that outperforms traditional methods like SGP4, enabling cross-validation of multiple observations for a single RSO. This deep learning-based transformer model can be distributed over a blockchain, allowing interested parties to host a node that contains a part of the distributed deep learning model. Our system comprises decentralised observers and validators within a Proof of Stake (PoS) blockchain. Observers contribute TDM data along with a stake to ensure honesty, while validators run the propagation and validation algorithms. The system rewards observers for contributing verified TDMs and penalizes those submitting unverifiable data.

cs.CR↗

arXiv2024

L-DIT: A dApp for Live Detectability, Identifiability and Trackability for ASOs on the Behavioral Dynamics Blockchain

As the number of Anthropogenic Space Objects (ASOs) grows, there is an urgent need to ensure space safety, security, and sustainability (S3) for long-term space use. Currently, no globally effective method can quantify the safety, security, and Sustainability of all ASOs in orbit. Existing methods such as the Space Sustainability Rating (SSR) rely on volunteering private information to provide sustainability ratings. However, the need for such sensitive data might prove to be a barrier to adoption for space entities. For effective comparison of ASOs, the rating mechanism should apply to all ASOs, even retroactively, so that the sustainability of a single ASO can be assessed holistically. Lastly, geopolitical boundaries and alignments play a crucial and limiting role in a volunteered rating system, limiting the space safety, security, and sustainability. This work presents a Live Detectability, Identifiability, and Trackability (L-DIT) score through a distributed app (dApp) built on top of the Behavioral Dynamics blockchain (BDB). The BDB chain is a space situational awareness (SSA) chain that provides verified and cross-checked ASO data from multiple sources. This unique combination of consensus-based information from BDB and permissionless access to data allows the DIT scoring method presented here to be applied to all ASOs. While the underlying BDB chain collects, filters, and validates SSA data from various open (and closed if available) sources, the L-DIT dApp consumes the data from the chain to provide L-DIT score that can contribute towards an operator's, manufacturer's, or owner's sustainability practices. Our dApp provides data for all ASOs, allowing their sustainability score to be compared against other ASOs, regardless of geopolitical alignments, providing business value to entities such as space insurance providers and enabling compliance validation and enforcement.

cs.CR↗

arXiv2024

Quantum complexity of the Kronecker coefficients

Whether or not the Kronecker coefficients of the symmetric group count some set of combinatorial objects is a longstanding open question. In this work we show that a given Kronecker coefficient is proportional to the rank of a projector that can be measured efficiently using a quantum computer. In other words a Kronecker coefficient counts the dimension of the vector space spanned by the accepting witnesses of a QMA verifier, where QMA is the quantum analogue of NP. This implies that approximating the Kronecker coefficients to within a given relative error is not harder than a certain natural class of quantum approximate counting problems that captures the complexity of estimating thermal properties of quantum many-body systems. A second consequence is that deciding positivity of Kronecker coefficients is contained in QMA, complementing a recent NP-hardness result of Ikenmeyer, Mulmuley and Walter. We obtain similar results for the related problem of approximating row sums of the character table of the symmetric group. Finally, we discuss an efficient quantum algorithm that approximates normalized Kronecker coefficients to inverse-polynomial additive error.

quant-ph↗

arXiv2024

Relaxations and Exact Solutions to Quantum Max Cut via the Algebraic Structure of Swap Operators

The Quantum Max Cut (QMC) problem has emerged as a test-problem for designing approximation algorithms for local Hamiltonian problems. In this paper we attack this problem using the algebraic structure of QMC, in particular the relationship between the quantum max cut Hamiltonian and the representation theory of the symmetric group. The first major contribution of this paper is an extension of non-commutative Sum of Squares (ncSoS) optimization techniques to give a new hierarchy of relaxations to Quantum Max Cut. The hierarchy we present is based on optimizations over polynomials in the qubit swap operators. This is in contrast to the "standard" quantum Lasserre Hierarchy, which is based on polynomials expressed in terms of the Pauli matrices. To prove correctness of this hierarchy, we exploit a finite presentation of the algebra generated by the qubit swap operators. This presentation allows for the use of computer algebraic techniques to manipulate and simplify polynomials written in terms of the swap operators, and may be of independent interest. Surprisingly, we find that level-2 of this new hierarchy is numerically exact (up to tolerance 10^(-7)) on all QMC instances with uniform edge weights on graphs with at most 8 vertices. The second major contribution of this paper is a polynomial-time algorithm that computes (in exact arithmetic) the maximum eigenvalue of the QMC Hamiltonian for certain graphs, including graphs that can be "decomposed" as a signed combination of cliques. A special case of the latter are complete bipartite graphs with uniform edge-weights, for which exact solutions are known from the work of Lieb and Mattis. Our methods, which use representation theory of the symmetric group, can be seen as a generalization of the Lieb-Mattis result.

quant-ph↗

arXiv2023

On the complexity of quantum partition functions

The partition function and free energy of a quantum many-body system determine its physical properties in thermal equilibrium. Here we study the computational complexity of approximating these quantities for $n$-qubit local Hamiltonians. First, we report a classical algorithm with $\mathrm{poly}(n)$ runtime which approximates the free energy of a given $2$-local Hamiltonian provided that it satisfies a certain denseness condition. Our algorithm combines the variational characterization of the free energy and convex relaxation methods. It contributes to a body of work on efficient approximation algorithms for dense instances of optimization problems which are hard in the general case, and can be viewed as simultaneously extending existing algorithms for (a) the ground energy of dense $2$-local Hamiltonians, and (b) the free energy of dense classical Ising models. Secondly, we establish polynomial-time equivalence between the problem of approximating the free energy of local Hamiltonians and three other natural quantum approximate counting problems, including the problem of approximating the number of witness states accepted by a QMA verifier. These results suggest that simulation of quantum many-body systems in thermal equilibrium may precisely capture the complexity of a broad family of computational problems that has yet to be defined or characterized in terms of known complexity classes. Finally, we summarize state-of-the-art classical and quantum algorithms for approximating the free energy and show how to improve their runtime and memory footprint.

quant-ph↗

arXiv2022

Space-efficient Quantization Method for Reversible Markov Chains

In a seminal paper, Szegedy showed how to construct a quantum walk $W(P)$ for any reversible Markov chain $P$ such that its eigenvector with eigenphase $0$ is a quantum sample of the limiting distribution of the random walk and its eigenphase gap is quadratically larger than the spectral gap of $P$. The standard construction of Szegedy's quantum walk requires an ancilla register of Hilbert-space dimension equal to the size of the state space of the Markov chain. We show that it is possible to avoid this doubling of state space for certain Markov chains that employ a symmetric proposal probability and a subsequent accept/reject probability to sample from the Gibbs distribution. For such Markov chains, we give a quantization method which requires an ancilla register of dimension equal to only the number of different energy values, which is often significantly smaller than the size of the state space. To accomplish this, we develop a technique for block encoding Hadamard products of matrices which may be of wider interest.

quant-ph↗

arXiv2021

Clinical Brain-Computer Interface Challenge 2020 (CBCIC at WCCI2020): Overview, methods and results

In the field of brain-computer interface (BCI) research, the availability of high-quality open-access datasets is essential to benchmark the performance of emerging algorithms. The existing open-access datasets from past competitions mostly deal with healthy individuals' data, while the major application area of BCI is in the clinical domain. Thus the newly proposed algorithms to enhance the performance of BCI technology are very often tested against the healthy subjects' datasets only, which doesn't guarantee their success on patients' datasets which are more challenging due to the presence of more nonstationarity and altered neurodynamics. In order to partially mitigate this scarcity, Clinical BCI Challenge aimed to provide an open-access rich dataset of stroke patients recorded similar to a neurorehabilitation paradigm. Another key feature of this challenge is that unlike many competitions in the past, it was designed for algorithms in both with-in subject and cross-subject categories as a major thrust area of current BCI technology is to realize calibration-free BCI designs. In this paper, we have discussed the winning algorithms and their performances across both competition categories which may help develop advanced algorithms for reliable BCIs for real-world practical applications.

cs.HC↗

arXiv2018

RFID based Automated Car Theft Detection and Arresting system

In this paper, we are presenting a new approach to car theft detection and arresting system using RFID technology. The main purpose of this paper is to establish the concept and the architecture of the whole system. The system which we are able to develop still now is basically a demonstration model or a prototype of the system. The key thing in this system is the passive RFID tags which will be hidden inside the car and act as a unique identification number for the car. The information of all such tags will be maintained by a centralized server. In case of any car being theft, a report should be logged into the server by an authorized user and a network of RFID scanners installed in different check post, traffic signal or toll plazas in the city will search for the reported tag. Once it is found necessary security system would be activated for arresting the car.

eess.SP↗

arXiv2016

New perspectives on the fluorite-pyrochlore phase transition in La2Zr2O7 and the importance of local oxygen-related disordered states

The fluorite to pyrochlore phase transition in La2Zr2O7 has been studied in the literature for decades in the context of thermal barrier coatings and reinforcement materials. However, the nature of the phase transition in this system is still not well understood. In this article we have investigated the phase transition in La2Zr2O7, calcined at different temperatures, using powder x-ray diffraction and Raman measurements. Rietveld analyses of the x-ray data suggest a fluorite to pyrochlore phase transition in the system occurring between 1000-1450oC. Nonetheless, Raman spectra, recorded with different excitation wavelengths (λ_ex) reveal that the dynamics of phase transition is different in the near-surface region and in the bulk inside. While the near-surface region carried the signatures of a pure pyrochlore phase, the temperature dependent Raman measurements with λ_ex=785 nm suggest that locally formed oxygen related disordered states are present in the bulk of the system.

cond-mat.mtrl-sci↗