Mathematical and Physical Sciences

Alok Shukla is an Assistant Professor in the Mathematical and Physical Sciences division of the School of Arts and Sciences at Ahmedabad University. He received a Bachelor of Engineering degree in Electrical and Electronics Engineering from Birla Institute of Technology, Ranchi, and a MA and PhD in Mathematics from the University of Oklahoma, USA. He was selected for several scholarship awards by the Department of Mathematics at Oklahoma during his PhD, including the John Clark Brixey Graduate Scholarship award in 2015, and the Richard V. Andree Memorial Scholarship awards for academic excellence in 2016 and 2017. After receiving his PhD in 2018, Professor Shukla joined the Department of Mathematics at the University of Manitoba, Canada, as a Postdoctoral Fellow.

Prior to pursuing his doctoral studies in Mathematics, Professor Shukla worked for HAL (Hindustan Aeronautical Limited) for several years, first on the Avionics system of MiG-27 fighter aircraft, and later in the final assembly section of ALH (Advanced Light Helicopter), Dhruv. He learned the basics of Aeronautical Engineering in a special one-semester programme at IIT, Madras in 2004. He has also worked as a software engineer for IBM and TCS, for about a year in each organisation. In addition to research in Mathematics, he enjoys teaching the subject to students. Professor Shukla has organised several maths-popularisation and community outreach events to spread the ‘Joy of Mathematics’ among young students.

Professor Shukla has research interests in number theory, combinatorics, and quantum computing.

In number theory, he is primarily interested in classical and adelic modular forms, automorphic forms and representations. He has worked on a representation-theoretic approach to the Klingen lift in degree two, and generalize the classical construction of the Klingen-Eisenstein series to arbitrary levels for both paramodular and Siegel congruence subgroups. He is also interested in the areas of classical number theory influenced by the work of Ramanujan, such as Partitions, and q-series identities. 

Professor Shukla has a keen research interest in quantum computing and its applications. He is interested in applications of quantum computing for the solution of nonlinear ordinary and partial differential equations. He has used a Walsh-Hadamard basis functions-based approach to discover a hybrid classical-quantum algorithm for solving nonlinear ordinary differential equations. He has also applied a similar approach to obtain a hybrid classical-quantum algorithm for digital image processing applications. 

Professor Shukla has made significant contributions to the challenge of efficient state preparation in quantum computing, developing a highly efficient algorithm for preparing uniform superposition quantum states, even when the number of states in superposition is not a power of two (ref: A.Shukla, P. Vedula, Quantum Information Processing, 23, 38 (2024). DOI: 10.1007/s11128-024-04258-4). 

This algorithm achieves an exponential reduction in gate complexity and circuit depth compared to previous deterministic algorithms, without the need for ancilla qubits. As the creation of uniform superposition states is fundamental to many key quantum algorithms, including Grover's search, amplitude amplification, and the quantum Fourier transform, this is an important advancement. This algorithm has been integrated into leading quantum computing platforms, with both IBM’s Qiskit and Google’s Cirq introducing it as the UniformSuperpositionGate to facilitate the incorporation of uniform superposition states into quantum circuits. For more details, see the UniformSuperpositionGate Documentation - Cirq and the Qiskit Release Notes.

1. Hybrid classical-quantum image processing via polar Walsh basis functions (2024)
   Authors: Mohit Rohida, Alok Shukla, Prakash Vedula
   Journal: Quantum Machine Intelligence, 6, 72 (2024. DOI: 10.1007/s42484-024-00205-9
   Preprint: https://arxiv.org/abs/2403.16044.pdf  
2. An efficient quantum algorithm for preparation of uniform quantum superposition states (2024)
   Authors: Alok Shukla, Prakash Vedula
   Journal: Quantum Information Processing, 23, 38 (2024). DOI: 10.1007/s11128-024-04258-4
   Preprint: https://arxiv.org/pdf/2306.11747.pdf  
3. A quantum approach for digital signal processing (2023)
   Authors: Alok Shukla, Prakash Vedula
   Journal: The European Physical Journal Plus, 138(12), DOI: 10.1140/epjp/s13360-023-04730-7
   Preprint: https://arxiv.org/pdf/2309.06570.pdf
4. A generalization of Bernstein–Vazirani algorithm with multiple secret keys and a probabilistic oracle (2023)
   Authors: Alok Shukla, Prakash Vedula
   Journal: Quantum Information Processing,  22(6), DOI: 10.1007/s11128-023-03978-3
   Preprint: https://arxiv.org/pdf/2301.10014
5. Tiling proofs of Jacobi triple product and Rogers-Ramanujan identities (2023)
   Author: Alok Shukla
   Journal: Journal of the Ramanujan Mathematical Society, 38.2 (2023): 157-176
   Preprint: https://arxiv.org/pdf/2006.03878.pdf
6. A hybrid classical-quantum algorithm for the solution of nonlinear ordinary differential equations (2023)
   Authors: Alok Shukla, Prakash Vedula
   Journal: Applied Mathematics and Computation, 442, 127708, DOI: 10.1016/j.amc.2022.127708
   Preprint: https://arxiv.org/pdf/2112.00602.pdf
7. A hybrid classical-quantum algorithm for digital image processing (2023)
   Authors: Alok Shukla, Prakash Vedula
   Journal: Quantum Information Processing, 22, 3 (2023), DOI: 10.1007/s11128-022-03755-8
   Preprint: https://arxiv.org/pdf/2208.09714.pdf
8. 106.20 When do we have 1 + 1 = 11 and 2 + 2 = 5? (2022)
   Authors: Padmanabhan, R., Alok Shukla
   Journal: Mathematical Gazette, 106(566), 319-323, DOI: 10.1017/mag.2022.74
   Preprint: https://arxiv.org/pdf/1906.02324.pdf
9. Pullback of Klingen Eisenstein series and certain critical L-values identities (2021)
   Author: Alok Shukla
   Journal: The Ramanujan Journal, 55(2), DOI: 10.1007/s11139-019-00246-w
   Preprint: https://arxiv.org/pdf/2006.05273
10. Orchards in elliptic curves over finite fields (2020)
    Authors: R. Padmanabhan, Alok Shukla
    Journal: Finite Fields and Their Applications, 68,  DOI: 10.1016/j.ffa.2020.101756
    Preprint: https://arxiv.org/pdf/2003.07172
11. Means compatible with semigroup laws (2019)
    Authors: Ranganathan Padmanabhan, Alok Shukla
    Journal: Quasigroups and Related Systems, 27(2),
    Preprint: https://arxiv.org/pdf/1902.10809
12. On Klingen Eisenstein series with level in degree two (2019)
    Authors: Ralf Schmidt, Alok Shukla
    Journal: Journal of the Ramanujan Mathematical Society, 34(4)
    Preprint: http://www2.math.ou.edu/~ashukla/OnKlingenEisensteinSeriesWithLevelInDegreeTwo.pdf
13. Trajectory optimization using quantum computing (2019)
    Authors: Alok Shukla, Prakash Vedula
    Journal: Journal of Global Optimization, 75(1), DOI: 10.1007/s10898-019-00754-5
    Preprint: https://arxiv.org/pdf/1901.04123
14. A Short Proof of Cayley's Tree Formula (2018)
    Author: Alok Shukla
    Journal: The American Mathematical Monthly, 125(1), DOI: 10.1080/00029890.2017.1404142
    Preprint: https://arxiv.org/pdf/0908.2324
15. Codimensions of the spaces of cusp forms for Siegel congruence subgroups in degree two (2018)
    Author: Alok Shukla
    Journal: Pacific Journal of Mathematics, 293(1), DOI: 10.2140/pjm.2018.293.207
16. On Klingen Eisenstein series with levels (2018)
    Author: Alok Shukla
    PhD Dissertation: Department of Mathematics, University of Oklahoma, Norman, https://shareok.org/bitstream/handle/11244/299326/2018_Shukla_Alok_Dissertation.pdf

Preprint:

1. On sequency-complete and sequency-ordered matrices (2024)
   Author: Alok Shukla and Prakash Vedula
   Arxiv link: https://arxiv.org/abs/2402.11003
2. Efficient Implementation of a Quantum Search Algorithm for Arbitrary N (2024)
   Author: Alok Shukla and Prakash Vedula
   Arxiv link: https://arxiv.org/abs/2406.13785
3. A quantum approach for optimal control (2024)
   Author: Hirmay Sandesara, Alok Shukla and Prakash Vedula
   Arxiv link: https://arxiv.org/abs/2407.02864
4. Efficient quantum algorithm for weighted partial sums and numerical integration (2024)
   Author: Alok Shukla and Prakash Vedula
   Arxiv link: https://arxiv.org/pdf/2411.10986

Monsoon 2024

• CSC210 - Introduction to Data Structures and Algorithms

Winter 2024

• FDP - Foundation Programme (ECC Module - I)

Monsoon 2023

• MAT256 - Differential Equations
• MAT485 / MAT585 - Introduction to Quantum Computing
• MAT775 - Lie Algebras and their applications in Quantum Physics

Winter 2023

• MAT248 - Applied Linear Algebra
• MAT334 - Introductory Real Analysis

Monsoon 2022

• MAT142 - Introductory Calculus
• MAT465 / MAT565 - Fourier Analysis and Its Applications
• PHY798 Research Project - II

Winter 2022

• MAT248 - Applied Linear Algebra
• MAT442 - Complex Analysis
• MAT485 / MAT585 - Introduction to Quantum Computing

Monsoon 2021

• MAT256 - Differential Equations

Winter 2021

• MAT246 - Introduction to Linear Algebra 
• FDP - Foundation Programme (ECC Module - II)

Monsoon 2020

• MAT142 - Introductory Calculus