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Indian Institute of Science (IISc)
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Lecture 5: Axiomatic Non-relativistic Quantum Mechanics
Quantum mechanics is formulated using linear algebra in Hilbert space. Definitions of states, tensor product, operators, measurement and evolution are given. The Bloch sphere representation for a qubit is introduced. The map from quantum to classical system is pointed out.
Просмотров: 268
Видео
Lecture 21: Quantum Search
Просмотров 2,5 тыс.2 месяца назад
Algebraic structure of Grover’s reflection operators is presented. With identification of the reflection operators with potential and kinetic energies, the effective Hamiltonian for each iteration is derived. Classical wave dynamics implementation of the algorithm using a coupled oscillator model is demonstrated. Implementation of the algorithm with elastic collisions of two blocks on a frictio...
Lecture 22: Extensions and Applications of Grover’s Algorithm
Просмотров 5272 месяца назад
Various extensions and applications of Grover’s algorithm are discussed: Wave dynamics implementations and energy transfer, search with multiple targets, logic circuit with the base encoded as uniform superposition of qubit states, generic amplitude amplification of any probabilistic algorithm, extracting properties of some distribution (mean, median, maximum, minimum, counting), the appointmen...
Lecture 23: Extensions and Applications of Grover’s Algorithm (contd.)
Просмотров 2492 месяца назад
Discussion of extensions and applications of Grover’s algorithm continues: Dimension dependence of spatial search, the collision problem, the element distinctness problem, quantum counting, fixed point search that converges to the target. The factorisation problem is introduced, with f(x)=a^x (mod N) as the periodic function.
Lecture 24: Introduction to the Factorisation Problem
Просмотров 3252 месяца назад
The factorisation problem is reduced to the period finding problem, and illustrated with simple instances. The infinite number of prime numbers is pointed out. Euclid’s efficient algorithm for finding GCD of two numbers is described. The finite probability of two randomly chosen numbers to be co-prime is derived. The need to rule out the number to be factored being a prime power as well as the ...
Lecture 25: Shor's Period Finding Algorithm using the Quantum Fourier Transform
Просмотров 1892 месяца назад
It is pointed out that checking for primality is a polynomial problem. Discrete Fourier transform is defined, and it is demonstrated how its factorisation yields the FFT. The same result, together with superposition of N inputs using log(N) qubits gives the QFT (Quantum Fourier Transform). The quantum logic gate circuit for QFT is constructed. Modular exponentiation is defined and used to const...
Lecture 13 Introduction to Computational Complexity: Problem Classification
Просмотров 1612 месяца назад
Concept of asymptotic scaling of resources for digitised problems is introduced, together with logical relations between problems. Hierarchy of computational complexity classes for decision problems is defined: P, NP, PP, PSPACE. NP-complete and BPP problems are defined. Quantum extensions to BQP and QMA are pointed out. Dependence of complexity on phrasing of the problem is emphasised. General...
Lecture 14: Boolean Logic Properties, Idea of Reversible Computation
Просмотров 1622 месяца назад
Boolean operations are described using binary as well as logical variables. General Boolean arithmetic function is a multilinear polynomial, and general Boolean logic function can be given either a conjunctive or a disjunctive normal form. The k-SAT problem is defined, and complexity distinction between k=2 and k greater than 2 is pointed out. Reversible computation is introduced as combination...
Lecture 15: Reversible Computation
Просмотров 1292 месяца назад
Properties of permutations, and universality of the Toffoli gate for Boolean algebra are explained. General reversible computing strategy with M and M-inverse described, identifying its free energy cost with the erasure of the output (Landauer’s principle). T time steps of Boolean algorithm are mapped to 2T time steps and O(T) extra space; it is explained how extra space can be reduced to O(log...
Lecture 16: Reversible Computation (contd.), Quantum Generalisation and Simplification
Просмотров 1012 месяца назад
Universality of Billiard ball model explained by construction of the SWITCH gate construction and reversible measurement. There is no thermodynamic constraint except the resetting free energy cost. Quantum generalisation introduced as linear superposition of basis states appearing in classical reversible computation. Quantum logic operations are simplified using SU(2) algebra: Euler angle rotat...
Lecture 17: Quantum Gates, Reachability and Efficiency
Просмотров 1282 месяца назад
Reachability of SU(2) group operations to construct general unitary evolution is explained. Hierarchy of group operations is described with their increasing capability: Boolean Z(2), Rebit U(1), Quaternion group, Clifford group, full SU(2) group. For multi-qubit systems, it is explained how Lie algebra properties of SU(n) give reachability, and the universal Deutsch gate can be reduced to C-NOT...
Lecture 18: Quantum Error Bounds, Deutsch and Deutsch-Jozsa Algorithms
Просмотров 1232 месяца назад
Growth of errors in unitary evolution is quantified, emphasising efficiency of BQP over BPP. The Deutsch algorithm illustrates quantum advantage in identifying 1-to-1 vs. balanced function for a single qubit, and then the Deutsch-Jozsa algorithm extends it to multiple qubits demonstrating exponential quantum advantage.
Lecture 19: Deutsch-Jozsa Algorithm (cntd.), Bernstein Vazirani Problem, Simon’s Algorithm
Просмотров 1262 месяца назад
Error analysis of Deutsch-Jozsa algorithm is carried out to quantify exponential quantum advantage. The particular choice for the binary function, f(x)=a.x, defines the Bernstein-Vazirani problem. Then the solution of “n” simultaneous linear equations determining “a” has quantum advantage Theta(n). Simon’s algorithm for solving the binary periodicity problem, f(x) = f(x a), is worked out using ...
Lecture 20: Database Search, Grover’s Algorithm
Просмотров 1242 месяца назад
Lecture 20: Database Search, Grover’s Algorithm
Lecture 26: Shor's Factorisation Algorithm (contd.)
Просмотров 1062 месяца назад
Lecture 26: Shor's Factorisation Algorithm (contd.)
Lecture 27: Quantum Features underlying Algorithms, Properties of Quantum Correlations
Просмотров 752 месяца назад
Lecture 27: Quantum Features underlying Algorithms, Properties of Quantum Correlations
Lecture 28: Tests and Interpretations of Quantum Correlations: Spatial and Temporal
Просмотров 892 месяца назад
Lecture 28: Tests and Interpretations of Quantum Correlations: Spatial and Temporal
Lecture 29: Tests and Interpretations of Quantum Correlations (contd.)
Просмотров 942 месяца назад
Lecture 29: Tests and Interpretations of Quantum Correlations (contd.)
Lecture 30: Interpretation of Quantum Correlations: Wigner functions
Просмотров 1332 месяца назад
Lecture 30: Interpretation of Quantum Correlations: Wigner functions
Lecture 31: Clifford Group Operations, Quantum Error Correction Framework
Просмотров 1322 месяца назад
Lecture 31: Clifford Group Operations, Quantum Error Correction Framework
Lecture 32: Classical and Quantum Error Correction: Simple Example
Просмотров 2512 месяца назад
Lecture 32: Classical and Quantum Error Correction: Simple Example
Lecture 13: Introduction to Computational Complexity Problem Classification
Просмотров 1662 месяца назад
Lecture 13: Introduction to Computational Complexity Problem Classification
Lecture 12: Introduction to Computational Complexity: Resources and Optimisation
Просмотров 1582 месяца назад
Lecture 12: Introduction to Computational Complexity: Resources and Optimisation
Lecture 11: Superoperator Evolution of Quantum Systems and its Special Cases
Просмотров 1442 месяца назад
Lecture 11: Superoperator Evolution of Quantum Systems and its Special Cases
Lecture 10: Implications of Schmidt Decomposition, Evolution of Open Quantum Systems via CPTP maps
Просмотров 1742 месяца назад
Lecture 10: Implications of Schmidt Decomposition, Evolution of Open Quantum Systems via CPTP maps
Lecture 9: Reduced Density Matrix, Gleason’s Theorem, Schmidt Decomposition and its Implications
Просмотров 1812 месяца назад
Lecture 9: Reduced Density Matrix, Gleason’s Theorem, Schmidt Decomposition and its Implications
Lecture 8: Quantum Uncertainty Principle, Multi-component and Open Quantum Systems
Просмотров 3042 месяца назад
Lecture 8: Quantum Uncertainty Principle, Multi-component and Open Quantum Systems
Lecture 7: Mixed States as Ensembles of Quantum States, Important Consequences of Unitary Dynamics
Просмотров 2372 месяца назад
Lecture 7: Mixed States as Ensembles of Quantum States, Important Consequences of Unitary Dynamics
Lecture 6: Bloch Sphere for a Qubit, Density Matrix Formalism for Quantum Mechanics
Просмотров 6032 месяца назад
Lecture 6: Bloch Sphere for a Qubit, Density Matrix Formalism for Quantum Mechanics
5984 Carter Plaza
Invent a device that integrated into the human body that enables us to seamless multitasking, invent a device that integrated into the human body that stops overthinking side effects like migraine, memory power loss, heart pain, acid reflux, testosterone level low in male etc, invent a device that integrated into the human body that stops stress, depression, anxiety side effects like migraine, memory power loss, heart attack risk increase, low testosterone level in male, acid reflux, hair loss, vision loss, hearing loss, tinnitus, periods problem, obesity,hernia disease chance increase,lungs damage,kidney damage etc, invent a device that integrated into the human body that stops excessive sleep side effects like death chance increase, stroke, anorexia, back pain, concentration problem etc, invent a device that integrated into the human body that stops late night sleep side effects like dark circles in eyes, periods problem, hair loss, obesity, heart disease,low eyesight, mental health problems etc, invent a device that integrated into the human body that stops cigarette smoking side effects like stroke, vision loss, hearing loss, dental health problem, infection, cancer like throat cancer, breast cancer, stomach cancer, mouth cancer etc, invent a device that is integrated into the human body that stops alcohol consumption side effects like headache, heart disease, stroke, cancer, impair judgement, memory power loss, nervous system damage, liver damage, disrupt sleep,bad dream, vomiting etc but notice that these all devices have no side effects.
When possible please provide all faculty lecture online to helps all indian student's
"You will not be here but your work will be here." The dream of every fellow researcher. Well put into words brother.
How to join the m tech online program?
AIM is iisc
Innovation 💡
how to appy for online M.Tech?
All Motivation in a single line🙂↔️🙂↔️🙇🏻🙇🏻🙏🏻🙏🏻
Congratulations KVNS CHINNI
Congratulations CHINNI,KVNS. WE all very much proud of you.keep it up❤
Congratulations Prashant 🎉❤
Mr Naren it's an ecstatic moment, congratulations. After a long gap of studies, you have come back with a bang.. highly appreciable and inspiring. Thankyou. ❤🎉🎉
Congratulations Naresh Anna🎉🎉🎉
Congrats sanjay
🎉
Congratulations Pooja beta🎉
Congrats Sanjay 🔥
Where the rest?? live stream???
Hearty congratulation all. The faculties students and other. Workers.
Congratulations beta proud of you
Please livestream the rest...
Where is the rest?
Hearty congratulations to all the gold medal winners.
Congratulations beta..wish you all the best for your future endeavors...proud of you 🎉❤
Many Many Congratulations all of Students With Her Parents..
Congratulations all of u beta
This is great inspiration Shilpa !!
WOW EVEN GALGOTIA UNIVERSITY CLAIMS AS NO. 1 UNIVERSITY IN INDIA
i will be at IISC in 2027
THIS LOOKS MORE MAJESTIC THAN ANY OF THE IITS 😮💨
Laura ka college hai. Jhaat bhar placement nahi hai
Yes pls allow second dropers for iisc bs course via IAT
Bro casually dropped the hardest line at the end
I request IISc to podcast discussions with eminent scientists on topics of science.
Please organize a discussion with her on 'Humanitarian Technology'
Please organize a discussion with her on 'Machine Learning, Deep Learning and Soft Computing'
Kya fayda second dropper ko elligible krke jbvo ye branch choose hi nhi kar sakta...qki 2nd dropper jee advanced nhi de sakta to vo ye branch kaise opt kar sakega.... 2nd dropper valo ko iat ke score se v ye branch mile aisa criteria me mention krna chahiye
Yes pls allow second dropers for iisc bs course via IAT.
Yes pls allow second dropers for iisc bs course via IAT
Kya fayda second dropper ko elligible krke jbvo btech in mathematics and computing branch choose hi nhi kar sakte...qki 2nd dropper jee advanced nhi de sakta to vo ye branch kaise opt kar sakenge.... 2nd dropper valo ko iat ke score se v ye branch mile aisa criteria me mention krna chahiye
True words
Well said 💯
Sir placement 35+lpa ho ga ya nahi
Wow! Such a bright mind
Btech student ko nahi mila kya
Best is best
It's great interview
Congratulations Naren for this milestone and proud to be your colleague in Samsung.💐💐💐
Congratulation Shilpa
why no scholarship ...only for bsc why not btech???
IISC's marketing team sucks