Quantum Computing

Quantum Fourier Transform

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Fourier Transform – A method of transforming from one basis to another. Pair of bases can be position and momentum or time and frequency. Discrete Fourier Transform – While fourier transform is useful for signal processing applications, for real world application contexts, we usually want to transform a discrete set of data points, not a ... Read More

Quantum Error Correction Challenges – Quantum Computing

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Books References: Exploration in Quantum Computing by Colin P. WilliamsQuantum Computation and Quantum Information by Nielsen et. al Quantum error correction (QEC) is widely considered the “holy grail” of quantum computing and also its most formidable bottleneck. While classical computers can easily correct errors by copying data (redundancy), quantum computers are forbidden from doing this ... Read More

Quantum Error Correction – Quantum Computing

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Books References: In an idea set up, we assume that logical qubits evolves unitarily following Schrodinger’s equation from the moment quantum comptuer is prepared, go through some computations and measured. However, during this process, real quantum system couples with its environment causing information leak out of logical state of the qubits in the quantum memory ... Read More

What is quantum advantage actually?

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https://www.linkedin.com/posts/googleresearch_what-does-quantum-advantage-really-mean-activity-7411496236043808768-1fTo?utm_source=share&utm_medium=member_desktop&rcm=ACoAAFvtEp0B-fk768n2MQaWnQRVk0ixzjLJZV0 https://research.google/blog/a-verifiable-quantum-advantage/ https://www.nature.com/articles/s41586-025-09526-6 FUNDAMENTALS: Out-of-time-order correlators in quantummechanicshttps://arxiv.org/pdf/1703.09435

Quantum Information – Quantum Noise and Error

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Book Quantum Computation and Quantum Information, Nielson and Chuang. Cambridge, Page 353 and Page426 Systems can be either closed or open sytems. All systems somehow have to interact with outside environment. These unwanted interactions from outside world can introduce noie to the information processing system.

Deutsch’s Algorithm

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https://quantum.cloud.ibm.com/learning/en/courses/fundamentals-of-quantum-algorithms/quantum-query-algorithms/deutsch-algorithmhttps://en.wikipedia.org/wiki/Deutsch%E2%80%93Jozsa_algorithm Implementaion link: https://github.com/computingnotes/QuantumAlgorithmsUsingQiskit/blob/main/deutsch_algorithm_using_qiskit.ipynbGitHub: https://github.com/computingnotes deutsch_algorithm_using_qiskit (1) Source: https://quantum.cloud.ibm.com/learning/en/courses/fundamentals-of-quantum-algorithms/quantum-query-algorithms/deutsch-algorithm Deutsch’s Algorithm Implementation in Qiskit¶ In [45]: # --- 1. Installation and Setup --- # Install necessary libraries silently !pip install qiskit qiskit_aer pylatexenc -q In [46]: from qiskit import QuantumCircuit from qiskit_aer import AerSimulator In [47]: # Imports from qiskit import QuantumCircuit from qiskit_aer import AerSimulator from typing ... Read More

Quantum Parallelism

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Quantum Computation and Quantum Information, Machael A. Nielsen, Isaac L. Chuang Quantum Parallelism is foundational technique that gives quantum computers their potential speed advantage. It explains how a quantum computer can evaluate a function f(x) for many different input values x simultaneously, a feat impossible for a classical computer. The oracle Uf​ maps the basis ... Read More

Quantum Computing Fundamentals – Multiple Qubits

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Book source: Quantum Computation and Quantum Information by Michael A. Nielsen and Isaac L. Chuang Similar to classical qubits, 2 qubit systems have 4 computational basis states. One of the important state is Bell State. Correlation in measurements of qubits in bell state.

Quantum Computing Fundamentals – Qubits

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Source book: Quantum Computation and Quantum Information, Michael A. Neilsen and Isaac L. Chuang Analogy between classical bit and quantum bit (qubit).Classical bit has 0 or 1 value whereas qubit can have state $|0\rangle$ or $|1\rangle$ along with linear combination ot those states (superposition). While classical bit can be measured deterministically with value either 0 ... Read More
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