Talks

Apoorva Patel: Understanding Quantum Advantage in Machine Learning

Machine learning models are used for pattern recognition analysis of big data, without direct human intervention. The task of supervised learning is to classify new data after learning patterns from training data, while that of unsupervised learning is to find the probability distribution that would best describe the available data, and then use it to make predictions. The former uses feature maps, while the latter uses Boltzmann distributions, both with a large number of tunable parameters. Quantum extensions of these models replace classical probability distributions with the quantum density matrix. An advantage can be obtained only when features of quantum density matrices that are missing in classical probability distributions are exploited. Such situations depend on the input data as well as the targeted observables. Illustrative examples bring out the constraints limiting possible quantum advantage. The problem-dependent extent of quantum advantage has implications for both data analysis and sensing applications.

Debajyoti Bera: Generalized Quantum Branching Programs

Branching programs are generalizations of decision trees which are used heavily in machine learning. In the realm of classical computing, branching programs have been used to model both the time and space requirement of a computation. I will introduce the quantum branching program model which hopes to tightly characterize both the time-complexity and space-complexity of problems. I will also discuss a few initial results on the space-complexity and time-space trade-off of combinatorial problems. The results are based on a joint work with SAPV Tharrmashastha.

Navin Kashyap: Characterizations of Bias-Preserving Quantum Gates

The kind of errors encountered in quantum computing systems depend strongly on the specific physical realization of the qubits used in the system. Certain bosonic systems (Kerr-cat qubits) and systems based on Rydberg atoms are more susceptible to phase-flip errors than bit-flip errors. If this bias in errors can be maintained throughout the computation process, then one can design fault-tolerant mechanisms that target the dominant form of error. This leads naturally to the study of bias-preserving quantum computation, which has seen a lot of recent research activity. In this talk, I will present some recent results obtained in my research group and elsewhere on characterizing bias-preserving quantum gates.

Krishnakumar Sabapathy: Overview of Fujitsu Quantum and FRIPL

This talk will provide an overview of the Fujitsu Quantum Strategy. I will provide a brief background of the quantum effort touching upon aspects of the hardware as well as software, that can be viewed in totality as the quantum platform. I will also share some recent works from Fujitsu Research in topics relevant to the workshop. Finally, I will end by sharing some information on the quantum effort in Fujitsu Research India, and some opportunities for future engagements with us.

Chandrashekar CM: Quantum walk – an algorithm for simulating quantum systems

Quantum walk, an embodiment of quantum mechanics resembling classical random walk serves as a foundation for numerous quantum algorithms and protocols for quantum simulations. I will briefly review the operational and algorithmic approach for digital quantum simulation using different forms of quantum walk as algorithm and present the example for simulating Dirac equations [1], many-body systems dynamics, complex quantum networks and open quantum systems [2]. I will also present the progress made in experimentally realizing and controlling quantum walks [3].
[1] Nature Communications 11, 3720 (2020)
[2] New J. Phys. 22, 123027 (2020) ; New Journal of Physics 23, 113013 (2021)
[3] EPJ Quantum Technology 10, 43 (2023); Physical Review A 110 (3), 032615 (2024)

Naipunnya Raj: Adversarial Learning of the Quantum Autoencoder Latent Space for Quantum Data Generation

The emerging field of Quantum Generative models attempts to formalize the principles of Generative AI in the quantum domain. Inspired from the classical Generative Adversarial Networks (GANs), the formalism of Quantum Generative Adversarial Learning was developed to learn the statistics of a quantum process, and also to learn the generation of quantum states conditioned on some labelled information. We show that the quantum adversarial learning formalism can be used to learn the quantum latent space representation of a trained Quantum Autoencoder (QAE) allowing direct access to the latent space of the trained QAE and thus conferring it with the capability of quantum data generation which it inherently lacks. We demonstrate this utility through a motivating example of generation of entangled states within a range of entanglement entropy. Looking from a different perspective, the use of a trained QAE in this framework reduces the resource count required to train a Quantum GAN. We explore this perspective by deploying this framework to generate parameterized molecular ground states. We show that both these quantum models can enhance each others utility for fully-quantum generative applications.

Prabha Mandayam: Smallest quantum error correcting codes for amplitude-damping noise

We describe the smallest quantum error correcting (QEC) code to correct for amplitude-damping (AD) noise, namely, a 3-qubit code that corrects up to first order in the damping strength. We generalize this construction to create a family of codes that correct AD noise up to any fixed order. We underpin the fundamental connection between the structure of our codes and the noise structure via a relaxed form of the Knill-Laflamme conditions, that are different from existing formulations of approximate QEC conditions. Although the recovery procedure for this code is non-deterministic, our codes are optimal with respect to overheads and outperform existing codes to tackle AD noise in terms of entanglement fidelity. This alternate formulation of approximate QEC in fact leads us to a new class of quantum codes tailored to AD noise and also gives rise to a noise-adapted quantum Hamming bound for AD noise. Based on: arXiv:2410.00155

Riki Toshio: Practical quantum advantage on partially fault-tolerant quantum computer

Achieving quantum speedups in practical tasks remains challenging for current noisy intermediate-scale quantum (NISQ) devices. These devices always encounter significant obstacles such as inevitable physical errors and the limited scalability of current near-term algorithms. Meanwhile, assuming a typical architecture for fault-tolerant quantum computing (FTQC), realistic applications inevitably require a vast number of qubits, typically exceeding 10^6.
In this work, to bridge the gap between the NISQ and FTQC eras, we propose an alternative approach to achieve practical quantum advantages on early-FTQC devices [1], based on the so-called Space-Time efficient Analog Rotation quantum computing (STAR) architecture [2]. Our framework is based on partially fault-tolerant logical operations to minimize spatial overhead and avoids the costly distillation techniques typically required for executing non-Clifford gates. To this end, we develop a space-time efficient state preparation protocol to generate an ancillary non-Clifford state consumed for implementing an analog rotation gate with a notably high fidelity. Finally, we demonstrate that our framework allows us to perform the QPE for 8×8-site Hubbard model with fewer than 6.8×10^4 qubits and an execution time shorter than recent classical estimation with tensor network techniques (DMRG and PEPS).

Ruchira Bhat: Faster training of variational Quantum Boltzmann Machine using collective optimization.

In this talk, I will introduce two finite-temperature collective optimization algorithms known as Meta variational quantum thermalizer (Meta-VQT) and Neural Network (NN) Meta-VQT , developed for preparing the quantum Gibbs state of parametrized Hamiltonians. Using examples, we demonstrate that once the model is trained, it serves in the efficient preparation of Gibbs states for parameters that are not in the trained set, and in all quantum phases as well as quantum critical regimes of complex many-body Hamiltonians that exhibit a finite temperature quantum phase transition. Further, it finds application in one of the extensively studied quantum machine learning models , the variational Quantum Boltzmann Machine (QBM). The Meta and NN Meta-VQT algorithms when used in QBM training avoids the nested loop required otherwise, thus reducing the quantum resources and the runtime of the training process.

Rutuja Kshirsagar: Exponential Improvement on Asian Option Pricing Through Quantum Preconditioning Methods

This talk focuses on a novel quantum algorithm to solve differential equations used in the pricing of Asian options, with a particular focus on the Black-Scholes model. Unlike standard vanilla options, where the payoff is determined at a single point in time, Asian options are a type of average option where the final payoff depends on the average price of the underlying asset over a specified time period. These options tend to be less volatile, making them an attractive choice for more stable investment strategies, particularly within the commodities derivatives market. We demonstrate an exponential improvement over the scaling factor for classical methods.

Shantanav Chakraborty: Implementing any Linear Combination of Unitaries on Intermediate-term Quantum Computers

Implementing any Linear Combination of Unitaries on Intermediate-term Quantum Computers Abstract: I will discuss some new techniques we developed for implementing any Linear combination of Unitaries (LCU) on intermediate-term quantum computers. While the standard LCU procedure requires several ancilla qubits and sophisticated multi-qubit controlled operations, our methods consume significantly fewer quantum resources. I will primarily focus on the first method, known as Single-ancilla LCU, which implements any LCU using only a single ancilla qubit, no multi-qubit controlled logic, and quantum circuits of shorter depth than the standard method. The key idea is to substitute complicated controlled operations (in the standard LCU approach) with importance sampling and make several independent runs of short-depth quantum circuits to estimate the expectation value of observables vis-à-vis any state prepared by LCU. We apply this to develop new algorithms for ground state property estimation, Hamiltonian simulation, and quantum linear systems that are more amenable to intermediate-term implementation. We characterize the end-to-end complexities of our algorithms, which, remarkably in some regimes, have shorter gate depths than even state-of-the-art methods despite requiring significantly fewer resources. Time permitting, I will also talk about two other approaches: Analog LCU, a simple, physically motivated, continuous-time analogue of LCU tailored to hybrid qubit-qumode systems, and Ancilla-free LCU, which, as the name suggests, allows for implementing LCU without any ancilla qubits when we are interested in the projection of a quantum state (prepared by the LCU procedure) in some subspace of interest. Both these methods also find applications in different areas. Overall, our results are quite generic and can be readily applied to other problems, even beyond those considered in our work. (1) S. Chakraborty, Quantum 8, 1496 (2024).

Shayan Srinivasa Garani: Magic State Distillation and Entanglement-Assisted Fault-Tolerant Computing

Magic-state distillation is a protocol to purify noisy quantum states using quantum stabilizer codes. In this talk, I will explain the theory behind magic state distillation and explain how the noise threshold scales as a function of the minimum distance and the number of physical qudits of the underlying quantum stabilizer code. Quantum ECCs for distilling qubit and qutrit Hadamard states with near-optimal thresholds over the depolarizing channel will be described. Towards the end, I will motivate the ideas behind entanglement-assisted fault-tolerant computation and how these results are useful for quantum information processing. This is a joint work with my PhD student Abhi Kumar Sharma.

Bhanu Pratap Das: Quantum Algorithms for Atomic and Molecular Properties

There have been important advances in the applications of quantum algorithms to a wide range of problems including some atomic and molecular properties in recent years. Many different variants of the variational quantum eigensolver (VQE) algorithm have been used to compute the ground and excited states of molecules. In this talk I shall present the results of our ground state energies and the strength of a subtle magnetic interaction between the nucleus and the electrons of lithium atom and lithium-like ions and also the permanent dipole moments of certain molecules. I shall briefly mention the recently proposed Hamiltonian simulation based quantum selected configuration interaction algorithm and present our preliminary results based on this algorithm. The results of our work on the fine-structure intervals for boron-like ions due to relativistic and many-body effects using quantum annealing will be reported. The high accuracy (99%) achieved in our computation will be discussed and its significance explained.

Soumyabrata Hazra: Sample Complexity of Black Box Work Extraction

Extracting work from a physical system is one of the cornerstones of quantum thermodynamics. The extractable work, as quantified by ergotropy, necessitates a complete description of the quantum system. This is significantly more challenging when the state of the underlying system is unknown, as quantum tomography is extremely inefficient. In this article, we analyze the number of samples of the unknown state required to extract work. With only a single copy of an unknown state, we prove that extracting any work is nearly impossible. In contrast, when multiple copies are available, we quantify the sample complexity required to estimate extractable work, establishing a scaling relationship that balances the desired accuracy with success probability. Our work develops a sample-efficient protocol to assess the utility of unknown states as quantum batteries and opens avenues for estimating thermodynamic quantities using near-term quantum computers.

Abhi Sharma: Fault-Tolerant Encoder using Entanglement

Error propagation from faulty multi-qubit gates poses a significant challenge to the performance of quantum circuits and obstructs the development of scalable fault-tolerant quantum computers. This issue is particularly critical in designing quantum encoders for encoding the quantum information using error-correcting codes. Such error propagation can corrupt quantum information during encoding and rendering subsequent computations unusable. This talk presents a novel approach in designing transversal encoders that localize the impact of faulty multi-qubit gates to specific blocks, confining error propagation within individual blocks. By leveraging pre-shared entanglement across these blocks, we enable entanglement between qubit blocks while preventing cross-block error propagation during encoding, paving the way for more robust quantum error correction.

Abhay Shastry: Ensuring robustness in quantum kernel classification

Noise is an inherent feature of quantum computing, arising both from measurement and due to insufficient isolation of the device from the environment. Quantum kernel methods are seen as a leading candidate for supervised quantum machine learning but its robustness to noise has not been well studied. These methods involve a hybrid setup where the optimization problem is solved on a classical machine but the kernels are evaluated on a quantum machine. A quantum kernel classifier may thus return different predictions due to the underlying noise. Here we first derive bounds on the number of measurements required to make the classification robust (i.e. predicted label is the same with high probability). We then use the techniques of chance constraint programming to design Shot-frugal and Robust (Shofar) classifiers, which use quantum resources frugally and are robust to the noise by construction.

Adit Vishnu: Quantum Latent Variable Models

Density matrices in quantum mechanics generalize the notion of a classical probability distribution, prompting their exploration as machine learning models. We initiate a systematic study of Quantum Latent Variable Models (QLVM), which are defined by parameterized density matrices on a composite Hilbert space comprising visible and latent components. Existing literature on the Quantum Boltzmann machine (QBM), the most prominent QLVM, has multiple issues, such as competing likelihood objectives, difficulty in training models with hidden units, and an inability to train models larger than ten qubits. Currently, there are no known computable expressions for the gradient of the quantum likelihood in the presence of latent variables due to mathematical challenges posed by the non-commutativity of quantum operators. We address this problem using perturbation theory and derives a computable expression for the gradient in the presence of hidden units. Our main contributions are algorithms to train QLVMs using a Density Operator Expectation Maximization (DO-EM) approach that exploits the monotonicity of relative entropy (MRE).

Debjyoti Biswas: Efficient Syndrome detection for approximate quantum error correction – Road towards the optimal recovery

Noise in quantum hardware poses the biggest challenge to realizing robust and scalable quantum computing devices. While conventional quantum error correction (QEC) schemes are relatively resource-intensive, approximate QEC (AQEC) promises a comparable degree of protection from specific noise channels using fewer physical qubits [1]. However, unlike standard QEC, the AQEC framework faces hurdles in reliable syndrome measurements due to the overlapping syndrome subspaces leading to the violation of the distinguishability criterion of error subspaces. Our work [2] provides an algorithm for discriminating overlapping syndrome subspaces based on the GramSchmidt-like orthogonalisation routine. In the recovery, we map these orthogonal and disjoint subspaces to the code space followed by a recovery like the perfect recovery [1, 3], or the Petz map [4, 5]. We further prove that this evolved recovery utilising the Petz map, RP,E gives optimal protection on the information regarding the measure of entanglement fidelity. The Table I shows that the performance of the Petz map RP,E is similar to that of the Feltcher recovery [6]. We list the performances of our protocols in Table I for two different quantum codes – one is the Leung [4,1] code [1], and the other is a four qubit code which comes out from a numerical search in the Ref[7].
[1] D. W. Leung, M. A. Nielsen, I. L. Chuang, and Y. Yamamoto, Approximate quantum error correction can lead to better codes, Physical Review A 56, 2567 (1997).
[2] D. Biswas and P. Mandayam, Efficient syndrome detection for approximate quantum error correction – road towards the optimal recovery, Manuscript is under preparation (2025).
[3] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).
[4] H. K. Ng and P. Mandayam, Simple approach to approximate quantum error correction based on the transpose channel, Phys. Rev. A 81, 062342 (2010).
[5] H. Barnum and E. Knill, Reversing quantum dynamics with nearoptimal quantum and classical fidelity, Journal of Mathematical Physics 43, 2097 (2002).
[6] A. S. Fletcher, P. W. Shor, and M. Z. Win, Channel-adapted quantum error correction for the amplitude damping channel, IEEE Transactions on Information Theory 54, 5705 (2008).
[7] A. Jayashankar, A. M. Babu, H. K. Ng, and P. Mandayam, Finding good quantum codes using the cartan form, Phys. Rev. A 101, 042307 (2020).

Aswanth Thamadathil: Codeword Stabilized Codes from m-Uniform Graph States

An m-uniform quantum state on n qubits is an entangled state in which every m-qubit subsystem is maximally mixed. Starting with an m-uniform state realized as the graph state associated with an m-regular graph, and a classical [n, k, d ≥ m + 1] binary linear code with certain additional properties, we show that pure [[n, k, m + 1]]2 quantum error-correcting codes (QECCs) can be constructed within the codeword stabilized (CWS) code framework. As illustrations, we construct pure [[22r −1, 22r −2r−3, 3]]2 and [[(24r −1)2, (24r −1)2−32r−7, 5]]2 QECCs. We also give measurement-based protocols for encoding into code states and for recovery of logical qubits from code states.

Harsh Gupta: Fault-tolerance of [[6,1,3]] non-CSS code family generated using measurements on graph states

We construct and analyze the fault tolerance of [[6, 1, 3]] non-CSS quantum error correcting code under the anisotropic and depolarizing noise models. This rate-optimized code achieves fault-tolerance using a single ancilla qubit for syndrome measurement under anisotropic noise conditions. This method was called fault-tolerance using bare ancilla by Brown et al. We give explicit construction of the code using measurements on non-planar graph states. We also argue that using our approach, we can construct a family of such fault-tolerant codes. This method fills a notable gap in constructing fault-tolerant non-CSS code families.

Mainak Bhattacharyya: Decoding Quantum LDPC Codes using Collaborative Check Node Removal

Fault-tolerance of quantum devices requires on-par contributions from error-correcting codes and suitable decoders. One of the most explored error-correcting codes is the family of Quantum Low-Density Parity Check (QLDPC) codes. Although faster than many of the reported decoders for QLDPC codes, iterative decoders fail due to the colossal degeneracy and short cycles intrinsic to these codes. We present a strategy to improve the performance of the iterative decoders based on a collaborative way to use the message passing of the iterative decoders and check node removal from the code's Tanner graph. We use the concept of bit separation and generalize it to qubit separation. This gives us a metric to analyze and improve the decoder's performance towards harmful configurations of QLDPC codes. We present a simple decoding architecture to overcome iterative decoding failures by increasing the separation of trapped qubits without incurring any significant overhead.

Sowrabh Sudevan: A measurement based alternative to the use of SWAP-gates for qubit routing.

Qubit routing refers to the task of finding some optimum implementation of a quantum circuit on quantum computing hardware with limited qubit connectivity. This usually involves the use of SWAP gates. However, SWAP gates are known to be particularly noisy on many hardware. We propose an alternative method using ideas from measurement based computing and consequently dynamical circuits for qubit routing that avoids the use of SWAP operations. We illustrate with the preparation of graph states on star-type connectivity.

Rahul Bhowmick: Improved Training of Variational Quantum Algorithms through Delegation to Quantum and Classical Resources

Quantum computers promise solution to classically intractable problems like prime-factorization, solving large-scale linear algebra and simulating complex quantum systems. While large-scale fault-tolerant quantum computers might still take decades, variational quantum algorithms (VQA) may provide a near-term route to quantum advantage, by combining a classical optimizer with a parametrized quantum circuit (PQC). Although VQAs have been proposed for a multitude of tasks like ground-state estimation, combinatorial optimization and unitary compilation, there remain major challenges in trainability, efficiency and large quantum overhead of these algorithms. Here, we address some of these challenges in Variational Quantum Eigensolver (VQE), by an informed ansatz design and two novel training schemes that combine g-sim and Parameter-shift rule (PSR). Our methods show better accuracy and success, and need fewer calls to the quantum hardware on an average than PSR (upto 60% in some cases). We also numerically demonstrate the capability of the chosen ansatz in mitigating barren plaetaus, paving the way for training larger quantum models.

Shobhit Bhatnagar: Overview of GKP Codes and an Improved Minimum Distance Bound

In this brief talk, we will provide a quick overview of a class of continuous variable quantum error correction codes known as GKP code. We will also mention an improved bound on minimum distance.

Manish Kesarwani: Database Index Advisors on Quantum Platforms

Index Advisor tools settle for sub-optimal index configurations based on greedy heuristics, owing to the computational hardness of index selection. We investigate how this limitation can be addressed by leveraging the computing power offered by quantum platforms. In this talk, we will present a hybrid Quantum-Classical Index Advisor that judiciously incorporates gate-based quantum computing within a classical index selection wrapper.

Programme Committee

Organising Committee

We acknowledge the financial support by Quantum Research Park (QuRP), a CoE funded by KITS, Government of Karnataka