Ph.D. in Science and Engineering (2024 admissions)

Under the aegis of the TCG CREST-AcSIR Agreement for promoting research and academic collaboration in quantum sciences and technologies, CQuERE is inviting applications from interested candidates for the PhD in Science and Engineering on quantum sciences and technologies with emphasis on quantum computing, quantum information, and quantum sensing. The Ph.D. degree will be awarded by Academy of Scientific and Innovative Research (AcSIR) and the PhD program shall be guided by the rules and regulations of AcSIR Ph.D. ordinances.

The CQuERE Ph.D. Program at TCG CREST was initiated in 2022 and combines coursework and original research. The program is thesis based. At present eleven research fellows are pursuing their PhD at CQuERE.

**Important Updates on the Interview:**

List of candidates selected for the Interview in Physical Sciences (PS) and Engineering has been published. The complete list, date and time of the interview, and all instructions can be found below. All the selected candidates must follow all the instructions given in the document.

**Research Focus:**

**The link for online test along with instructions have been sent to the shortlisted candidates. Please check your mailbox and spam as well. In case you have not received the mail please send mail to academic.coordinator@tcgcrest.org **

Why join Ph.D. at CQuERE?

The CQuERE PhD program trains you to become the next generation research leader in the field of Quantum Sciences. The cornerstone of the doctoral experience at the CQuERE of TCG CREST is the research coursework that all students undertake, typically under the guidance of a group of academic advisors, but often with other external eminent faculty as well.

Research Focus

The areas of research currently being pursued at CQuERE are** quantum computation (theory), quantum information (theory), quantum computing using superconducting quantum circuits, photonic integrated circuits and NV centres for sensing and computing, quantum sensing using cold atoms**, as well as **quantum algorithms and machine learning**.

Eligibility

MSc in Physics / Chemistry (preferably Physical Chemistry), ME / MTech or other equivalent degree in Engineering Physics or other similar streams, MS in Computer Science, (preferably the students have taken some courses in MSc level Quantum Mechanics). Candidates who have already qualified CSIR (NET) JRF will be directly considered for the interview, all others need to appear for the national level test organized by CQuERE, TCG-CREST and only the shortlisted candidates will be called for the interview. Candidates having 60 percent (throughout their academic career: 10, 12, graduation, and Masters) will be shortlisted. Both the written test and the interviews will be held in online mode.

Important Information

-TCG CREST does not provide any hostel facilities. However, we will organise managed and secured hostel facilities at a competitive rate for you in the vicinity. We will also help you to find secured accommodation in the vicinity. TCG CREST will not bear the rent nor the hostel charges.

-For selection of candidates UGC and/or AcSIR guidelines may be adopted.

-Reservation Policy as per the norms of Government of India will be followed.

-Selection procedure: written test (separate tests for Physical Sciences and Engineering streams) followed by interview. Entrance exam date: 26th May 2 to 4 pm.

**-Syllabus and details of entrance exam: **

**A. Physical Sciences stream:**

The entrance exam is of 2 hours duration. The questions would require answers to be descriptive in nature. The question paper would contain a total of 15 questions, and are divided into two sections:

a. One compulsory with 5 questions on quantum mechanics and mathematical physics, and

b. One where a student can choose 5 out of 10 questions from a. Electronics (2 questions), b. Condensed matter physics (2 questions), nuclear and particle physics (1 question), c. Atomic & molecular physics (1 question), d. statistical mechanics (2 questions), and e. Electricity and magnetism (2 questions).

Questions would typically be at the level of standard MSc Physics courses, and we list below some representative topics under each of the subjects:

**Quantum mechanics: **Basic linear algebra relevant to quantum mechanics (for example: vector spaces, direct sum, tensor product, hermitian and unitary operators, etc), postulates of quantum mechanics, Schrodinger equation and its applications, quantum harmonic oscillator, symmetries, angular momentum, variational principle, and approximation methods.

**Mathematical physics: **Differential equations, integrals, Fourier transforms, and complex analysis.

**Atomic and Molecular physics: **Hydrogen atom, helium atom, H2+ molecular ion, Zeeman effect, and Stark effect.

**Statistical Mechanics: **Microcanonical, canonical, and grand canonical ensembles, partition function, laws of thermodynamics, Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein statistics.

**Electricity and Magnetism: **Electrostatics, magnetostatics, electrodynamics, Maxwell’s equations, electromagnetic waves.

**Electronics: **Basic electronics, digital electronics, analog and digital modulation, microcontroller and processor

**Condensed matter: **Symmetry in Solids, X-ray Diffraction Methods, Free Electron Theory of Metals, Thermal Conductivity of Metals, Theory of Specific Heat, Lattice Vibrations, Dielectrics, Magnetism, Superconductivity: Type I and Type II Superconductors, BCS Theory, Josephson Tunneling, Energy Bands in Solids, Semiconductors, Defects in Solids

**Nuclear and particle physics: **Spin, parity and iso-spin, and nuclear forces, Deuteron problem, Shell model, Nuclear reactions, Fusion and fission, Nuclear decay, Particle accelerator, classification of elementary particles.

B. Engineering stream:

There will be a total of 16 questions divided into three groups (4 + 6 + 6 = 16). Each question will carry 20 marks. A candidate is required to answer 5 questions, with a minimum of 2 questions from Group A and the remaining from Group B or Group C.

**Group A: General Mathematics **

**Basic Algebra:** Theory of Equations, Complex Numbers, Basic understanding of Group Theory.

**Elementary Linear Algebra:** Determinants and their properties, Cramer’s Rule, Systems of linear equations, Rank, matrices and matrix algebra, Eigen values and Eigen vectors, orthogonal bases, vector spaces, inner products, Gram-Schmidt procedure.

**Basic Statistics:** Mean, median, mode, standard deviation, skewness and kurtosis, moment, correlation and regression.

**Discrete Mathematics:** Basics of set theory, functions and relations, basic combinatorics (basic counting, inclusion-exclusion principle, pigeonhole principle), permutation and combination, recurrence relations, generating functions.

**Elementary Probability:** Basic definitions, random variables, distribu- tions, Standard discrete distributions (uniform, binomial, Poisson, geometric, hypergeometric); Expectation, Variance and moments; Conditional probability and Bayes’ theorem.

**Basic Number Theory:** Divisibility, GCD, Modular arithmetic, Chinese Remainder Theorem.

**Elementary High School Level Calculus:** Limit, continuity, differentiation and integration.

**Group B: Technical Topics in Computer Science**

**Graph theory:** Paths and cycles, Connected components, Tree, Digraphs, Eulerian trails, Hamiltonian paths, Planar graphs, Graph coloring.

**Elements of computing:** Basics of programming (using pseudo-code and any one of the languages from C, C++, Java, Python), Procedure call and parameter passing.

**Data Structures:** Array, Linked list, Stack, Queue, Binary tree, Heap, AVL tree, B-tree.

**Design and Analysis of Algorithms:** Asymptotic notation, Searching, Sorting, Selection, Graph algorithms: Breadth First Search, Depth First Search, Shortest Path

**Circuits and systems:** Analysis of elementary high school level circuits involving resistance, capacitance and inductance; analog electronic circuits involving transistors, Boolean algebra, Minimization of Boolean functions, Gates and logic circuits, Combinational and sequential circuits; Signals and systems, Convolution, Fourier transform, and z-transform.

**Formal Languages and Automata Theory:** Finite automata and regular languages. Pushdown automata and context-free languages. Turing machines and recursively enumerable languages. Undecidability.

**Group C: Physics and Engineering Aspects of Physics**

**Quantum mechanics:** Basic linear algebra relevant to quantum mechanics (for example: vector spaces, direct sum, tensor product, hermitian and unitary operators, etc), postulates of quantum mechanics, Schrodinger equation and its applications, quantum harmonic oscillator, symmetries, angular momentum, variational principle, and approximation methods.

**Electronics:** Basic electronics, digital electronics, analog and digital modulation, microcontroller and processor.

**Condensed matter:** Symmetry in Solids, X-ray Diffraction Methods, Free Electron Theory of Metals, Thermal Conductivity of Metals, Theory of Specific Heat, Lattice Vibrations, Dielectrics, Magnetism, Superconductivity: Type I and Type II Superconductors, BCS Theory, Josephson Tunneling, Energy Bands in Solids, Semiconductors, Defects in Solids.