The Complete Quantum Computing Course with Python [2025]

Explore correlated quantum particles, from classical correlations to entanglement and non-local Bell correlations, and see implications for quantum cryptography, computing, and teleportation.

Explore Bell states, four maximally entangled two-qubit states (EPR pairs) essential to quantum computing, cryptography, and teleportation, where measuring one qubit instantly determines the other.

Explore the Einstein-Podolsky-Rosen paradox, challenging local realism and hidden variables, and show how quantum entanglement leads to nonlocal correlations, Bell inequality tests, and quantum technology like teleportation and cryptography.

Learn how the Hadamard gate transforms a qubit into an equal superposition of 0 and 1, enabling quantum parallelism for global search and Shor factoring.

Learn how cirq, Google's open source quantum framework, designs and runs circuits on simulators and Sycamore hardware. Use Python-based syntax to work with devices and explore entanglement and error correction.

Explore the three Pauli gates (X, Y, Z) and their matrices. See how phase shifts and swaps transform qubits on Bloch sphere for state flipping, quantum teleportation, and error correction.

Install circle==0.1.0 to fix the library error, restart the notebook runtime, and ensure compatibility with numpy so the code runs smoothly; resources attached.

Install the circuit library, import it in Python, create a qubit, apply the Hadamard gate, build and run the circuit with a simulator to view the final state vector.

Implement Pauli gates in Python by defining a qubit, building a quantum circuit, applying Pauli X, Y, and Z gates, measuring, and simulating results.

Implement an advanced Hadamard gate on three qubits in Python, build and simulate the circuit, and observe superposition through measurement histograms.

Phase kickback causes a phase shift on a target qubit that kicks back to the control qubit, enabled by superposition, powering quantum phase estimation and Shor's algorithm.

Implement phase kickback in Python by building a two-qubit circuit with a Hadamard on the control, a controlled-Z, and measurement to reveal phase-induced bias in outcomes.

Implement eigenstates in Python using quantum circuits to generate z, x, and y eigenstates, apply Hadamard, S, and X gates, and measure outcomes in a simulator.

Explore the swap gate, a two-qubit gate that exchanges the states of two qubits while preserving superposition and entanglement, enabling circuit optimization and quantum teleportation.

Explore the Toffoli gate, a three-qubit quantum gate that flips the target qubit only when both control qubits are one, enabling reversible logic for quantum error correction and arithmetic.

Learn the cnot gate, a two-qubit operation that flips the target when the control is 1 and enables entanglement, quantum error correction, and algorithms like Shor and Grover.

Learn to implement CNOT gates in a circuit. Create a control qubit superposition with a Hadamard gate, apply CNOT to flip the target, and measure qubits in a Python simulator.

Explore the R3 gate, a single-qubit phase-shift that leaves |0⟩ unchanged while rotating the phase of |1⟩, a building block for phase estimation, quantum Fourier transform, and universal quantum computation.

Implement the rφ gate by installing circle==0.1.0 to ensure compatibility with numpy, restart the runtime, and run the code with the provided notebook resources.

Implement rx and ry gates on a grid qubit, defining x and y rotation angles pi/4 and pi/3, build and simulate circuits, and interpret measurements as probabilistic due to superposition.

Explore equal superposition states, where all basis states have equal probability, created by the Hadamard gate, and see how quantum parallelism and interference enable global search and other algorithms.

Explore entangled states where two qubits share a quantum state and show correlations upon measurement. See how Hadamard and cnot gates generate entanglement for quantum communication, teleportation, and Shor's algorithm.

Define and simulate a Bell state with NumPy and a quantum circuit, producing a superposition of zero zero and one one and extracting the final state vector via a simulator.

Implement swap using the circle library by creating two qubits and simulating the swap circuit. Decompose the swap into three cnot gates, implement the decomposed circuit, and compare state vectors.

Learn to build and represent quantum computational basis states for one and multiple qubits in Python using NumPy and the tensor product, with a function to generate n-qubit states.

Demonstrates creating a quantum superposition in Python by applying the Hadamard gate to zero and one, using alpha and beta amplitudes, and extending to two qubits with NumPy.

Construct complex state vectors in python by defining alpha and beta, building single-qubit and two-qubit superpositions, and extract measurement probabilities to verify normalization.

Explore complex superpositions with phase factors using numpy, building single- and two-qubit states with alpha and beta coefficients, and study how phase shifts affect interference patterns without changing probabilities.

Learn to create a quantum state with complex amplitudes using Hadamard-induced superposition, phase shifts, and entanglement, including Bell states and phase kickback for quantum phase estimation.

Learn how to build multi-qubit states by tensoring basis states, create superpositions with Hadamard gates, and generate entangled states such as Bell, GHZ, and W states using Python simulations.

Extract a two-qubit quantum state in python with numpy, normalize the state vector, and obtain real and imaginary parts; then use a hadamard gate to create entanglement and reveal the bell state (|00>+|11>)/√2.

Resize single-qubit gates in Python by embedding them into multi-qubit systems with the Kronecker product, shown by expanding Hadamard gate to two qubits and adjusting rotation angle of parameterized gates.

Explain bit-flip errors in qubits caused by decoherence and noise, modeled by the Pauli X gate, and introduce a three-qubit repetition code for detection and correction via majority voting.

Demonstrates bit-flip error correction with a three-qubit encoding, applying cnot encoding and an x gate on q1, then decoding and simulating to obtain the final state vector.

Explore phase flip errors in quantum computing, how a qubit’s phase flips while its bit value stays the same, and how three-qubit encoding with CNOT and Hadamard gates enables correction.

Implement phase flip error in a three-qubit circuit, encode the qubits, apply phase flip on q1, decode with Hadamard and CNOT, and simulate the final state vector.

Explore how quantum error correction protects qubits from decoherence, gate and measurement errors, and no cloning limits by encoding across multiple qubits, using redundancy, syndrome measurements, and error correction.

Implement quantum error correction by encoding a logical qubit across three qubits and using parity checks with an ancilla qubit to detect and correct bit-flip errors. Measure to verify recovery.

Explore Shor code, a nine-qubit quantum error correction scheme that protects a single logical qubit from bit flip and phase flip errors by encoding, parity checks, and ancilla-based correction.

Implement the Shor code by encoding a qubit into nine qubits, protecting against bit-flip and phase-flip errors, and detecting and correcting introduced errors with ancilla qubits.

Explore how quantum fault tolerance protects computations via quantum error correction across layers, using fault-tolerant gates like Toffoli, CNOT, and Hadamard, with logical qubits and threshold theorem to prevent errors.

Explore variational quantum circuits within hybrid quantum‑classical algorithms like VQE and QAOA. Learn how quantum error correction protects variational states against hardware noise and preserves the trainable parameter.

Explore the classical oracle in quantum computing, a black box classical function encoded as a reversible unitary that maps x to f(x) and enables quantum query.

Implement a classical oracle for x mod two by flipping the ancilla with a CNOT when the input qubit is one, then simulate the circuit to observe the state change.

Explore how a phase oracle marks quantum states by applying a phase shift rather than flipping a qubit, encoding information in the phase for global search and quantum phase estimation.

Implement a phase oracle in Cirq with two qubits q1 and q2, applying a controlled Z gate to induce a -1 phase on the |11> state, and run the circuit.

Explore how a quantum oracle encodes a function into a unitary transformation u_f in circuit, acting as a black box with input x and output y for Deutsch-jozsa and Simon.

Implement a quantum oracle by building a circuit with two input qubits and an output qubit, encoding x1 and x2, and applying two cnot gates to flip the output.

Explore how quantum oracles encode classical functions into reversible circuits, enabling exponential speedups and factoring via quantum Fourier transform with interference and superposition.

Explore quantum phase estimation, a fundamental algorithm that extracts eigenvalue phase theta from a unitary operator and powers of U, enabling Shor's algorithm, factoring, solving linear equations, and quantum chemistry.

Implement quantum phase estimation with a three-qubit register, define controlled powers of U, apply inverse quantum Fourier transform, simulate the circuit, and read out the estimated eigenphases from measurements.

Explore amplitude amplification, a core quantum technique that boosts the probability of measuring a desired state with an oracle and diffusion operator, starting from a Hadamard superposition.

Implement amplitude amplification by defining qubits, creating an oracle, and applying the diffusion operator in a quantum circuit. Simulate the circuit and observe the histogram showing the amplified state.

Explore the Deutsch-Jozsa algorithm, a quantum method to decide if a function is constant or balanced with one quantum query, using qubits and a Hadamard transform across five steps.

Explore Grover’s algorithm, a quantum search that speeds up unstructured database searches using equal superposition, an oracle, diffusion, and O(sqrt(n)) iterations.

Explore the quantum Fourier transform, the quantum analogue of the discrete Fourier transform, mapping n-qubit states to the Fourier basis with a circuit of Hadamard and controlled phase gates.

Implement the quantum Fourier transform by applying Hadamard gates, encoding phase information with control phase rotations, and swapping qubits to correct order, demonstrated with code and simulation.

Implement the Deutsch-Jozsa algorithm in Python by building a quantum circuit, defining a constant or balanced oracle, applying Hadamard gates, and measuring qubits to decide constant or balanced.

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