Quantum Computing Talks

PAST The Case Against Hidden Variables in Quantum Entanglement [Columbia Undergraduate Quantum Computing Club]

Wednesday, October 18 at 6:00-7:00pm ET

Zoom + CSB 453, Columbia University

Quantum entanglement is one of the most important and fundamental phenomena in physics. It's applications to computer science would revolutionize computations, cryptography, and methods of communication. In this talk, we understand entanglement through the lens of quantum bits -- two-level systems whose measurements are determined probabilistically. Our key focus will be on use of entanglement and the CHSH inequality in disproving the existence of Bell's class of local hidden variables in our description of quantum mechanics. Finally, we will explore an application of entanglement to a data transfer protocol called quantum teleportation -- this will be done without any equations!

This talk requires almost no knowledge of quantum mechanics, and will be accessible to all undergraduates.


PAST An Introduction to Qubit Geometry using Hopf Bundles and Hopf Fibrations [Columbia Undergraduate Quantum Computing Club]

Wednesday, April 12, 2023 at 7:00-8:00pm ET

CSB 488, Columbia University

We commonly refer to qubits as two-level systems whose states a|0> + b|1> are specified by two complex numbers a and b. Normalization of qubit states restricts the complex numbers a and b, allowing us to map qubit states onto the 3-sphere. However, the Bloch sphere representation of a qubit is a map of qubit states onto the 2-sphere. In this talk, we explain this descent in qubit state-representation from the 3-sphere to the 2-sphere using objects in algebraic geometry: Hopf bundles and Hopf fibrations. Surprisingly, we will observe how Hopf fibrations from higher dimensional spheres map entangled qubit states onto sub-spheres of lower dimensional spheres. In this way, Hopf fibrations are entanglement sensitive!  Ultimately, understanding the geometry of qubits will reveal new ways to store, process, and manipulate information in physical quantum systems.

This talk requires almost no knowledge of quantum mechanics or differential geometry, and will be accessible to all undergraduates.

PAST Entanglement, Teleportation, and Quantum Computing [Society of Physics Students]

Thursday, October 27, 2022 at 7 PM

Center for Theoretical Physics, 8th Floor of Pupin Hall, Columbia University

Quantum entanglement is an incredibly impactful and exciting topic of study in physics, mathematics, and computer science. Entanglement has been used to prove the nonlocality of quantum mechanics, to enable quantum cryptography, and to demonstrate quantum teleportation. Demonstrations of photon entanglement via the violation of Bell inequalities resulted in Aspect, Clauser, and Zeilinger being awarded the 2022 Nobel Prize in Physics.

In my talk, I will discuss four topics: 

1) The physics behind quantum entanglement. 

2) The photon-entanglement experiment itself. This experiment can be conducted at Columbia University (by undergraduate students). I will briefly describe results from my own execution of the experiment this Fall. 

3) Encoding quantum entanglement onto a quantum computer. I will demonstrate this on Qiskit, IBM's cloud quantum computing service.

4) An application of entanglement to quantum teleportation. To understand its true nature, I will discuss quantum teleportation without any equations! This too will be demonstrated on Qiskit.

SPS will provide free pizza at this talk! Join the SPS mailing list to receive notifications about this and future talks.

Photo credit: Aswath Suryanarayanan

Post-Talk Posts

Slides + Video

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Experiment Paper

Paper: https://columbia.edu/~ask2262/CourseProjects/KudinoorEntanglementExperiment.pdf

I conducted an experiment to violate the CHSH-Bell inequality using entangled photons at Columbia University. I was lucky enough to conduct this experiment as the 2022 Nobel Prize in Physics was announced for experiments violating Bell inequalities using entangled photons!

Code

I wrote the below code (at the links) on IBM's cloud quantum computing service, Qiskit. I would recommend creating an account at https://quantum-computing.ibm.com/ to implement this code.

Quantum Entanglement (link):  I wrote an algorithm to entangle two qubits. This algorithm is tested on IBM's statevector_simulator and quantum hardware. Additional Reference: Qiskit Textbook

Quantum Teleportation (link): I wrote a protocol to teleport a qubit using an entangled pair of qubits. The mathematics of this protocol are also worked out. Additional Reference: Qiskit Textbook

Questions

Any system that has a two distinguishable and identifiable quantum states can implement a qubit, or quantum bit. There are multiple physical implementations like transmons, ion traps, etc. Transmons are superconducting charge qubits that use an anharmonic oscillator to distibguish between two states. The anharmonicity of the oscillator splits energy levels with nonuniform spacing between each other -- this makes the energy states of the system distinguishable and identifiable.

The simplest transmon consists of two superconducting electrodes that are interconnected by a a capacitor and inductor, much like an LC circuit. However, an LC circuit has equally spaced energy levels since it follows the Hamiltonian of a harmonic oscillator. Equally spaced energy levels will not allow us to identify exactly whcih state an electron in our system is in. So, instead of connecting the electrodes with a simple capacitor and inductor, we connect them using a Josephson junction. This system now follows the Hamiltonian of an anharmonic oscillator, allowing us to distinguish between all states of the system, and to isolate the 0th and 1st energy levels. Therefore, a transmon -- two superconducting elctrodes that are interconnected by a Josephson junction -- forms a qubit.

There is a manual that students can follow to align the components of the QuTools apparatus. This process is quite tedious and time-consuming. However, it is iterative -- so, if done correctly, alignment should improve with each repetition of the alignment procedure.