Quantum Computing and Quantum Machine Learning - Part 3

Explore quantum gates as unitary operators, including the identity matrix and adjoint concepts, and examine reversibility, noting quantum gates are reversible while classical computing is not, except the not gate.

Explore why a quantum gate must be a unitary operator, preserving the length of the qubit's state on Bloch sphere as it maps to another state within the same sphere.

Show how any matrix is a linear combination of the identity and Pauli X, Y, Z, and explain the phase flip and selective phase gates alongside the T-gate.

Apply a two-by-two unitary matrix to a two-by-one Cubitt state to produce a two-by-one output, preserving the original dimension.

Explore CCNOT, swap, and CSWAP gates in quantum computing and quantum machine learning, showing how control qubits enable conditional flips and state swaps.

Compare quantum circuits with classical circuits, where qubits serve as inputs and outputs and time flows forward. Prevent fan-out; copying is forbidden by the no cloning theorem.

Demonstrates a quantum half adder that sums two qubits and computes the carry using quantum logic gates, including CNOT and XOR.

Explore a quantum oracle as a black box that applies a circuit to x, flipping x when y is one and leaving it unchanged when y is zero.

Discover how uniform superposition of n qubit basis enables parallel evaluation in quantum computing, using an oracle blackbox to create a linear combination of basis states and reveal the output.

Explore the no cloning theorem in quantum computing and quantum machine learning—part 3, showing no unitary transformation can copy an arbitrary state onto a blank state, with a Xerox analogy.

Learn how quantum teleportation transfers a qubit from Alice to Bob using an entangled pair, Bell measurement outcomes B1 and B2, and a final rotational unitary transformation.

Explore quantum teleportation where Alice and Bob use unitary operations, CNOT, and Hadamard measurements to transfer a qubit and recover the original state with conditional gates.

Explain the complete quantum teleportation protocol: share a Bell state, apply Hadamard and CNOT, perform Alice's measurement, and Bob applies X or Z to recover alpha|0>+beta|1>.

Demonstrate reversible computation in quantum circuits by using unitary transformations and their inverses to compute on a target qubit B initialized to zero, then reverse to recover the input X.

Explore reversible computation by translating classical circuits to quantum equivalents, examining how unitary quantum circuits output C(X) with junk bits and zero bits, and why removing junk matters.

Discover why removing junk bits prevents quantum interference from corrupting outcomes, and see a reversible quantum circuit using unitary transformations to preserve qubits and information.

Explain how super dense coding uses a Bell state to turn a qubit into two classical bits, inverse of quantum teleportation, with applications in quantum cryptography.

Describe how density matrices represent pure and mixed states, quantify populations and coherences, and use the Liouville equation to model their time evolution under a Hamiltonian.

Explore the quantum version of classical registers and learn to simulate quantum states in Python, covering entanglement, measurement, and decoherence with open system concepts.

Explore representing quantum gates and states in a notebook, measure in the 01 basis, visualize Bloch sphere behavior, and study Pauli, Hadamard, and CNOT gates, decoherence, and dagger notation.

Represent and visualize quantum circuits using quantum gate theory, applying gates and measurements in a Kaskade-based Biton workflow to illustrate reversible, unitary circuitry.

Wrap up part three by reviewing quantum gadgets and circuits, the no cloning theorem, and quantum teleportation; preview four with Shor's, Grover's, and Simmons' algorithms and quantum cryptography.