Quantum Computing in Python using Qiskit

Differentiate scalar quantities from vectors by magnitude alone versus magnitude and direction, using displacement, velocity, acceleration, and force; Note distance is scalar while others are vectors per Newton's second law.

Treat vectors as lists of numbers in matrix form, with two and three dimensional examples at the origin, then extend to infinitely dimensional sealed spaces for quantum computing.

Explore matrices in quantum mechanics by learning matrix notation, sizes, identity matrices, and the basic operations of addition, subtraction, scalar multiplication, transpose, and the conjugate transposition.

explore matrix multiplication, its dimension rules and dot-product computation, and see how unitary matrices representing quantum gates operate on quantum states in quantum computing.

Explain how the tensor product combines two matrices into a larger block matrix. Show how this operation underpins quantum computing, enabling complex states in qiskit.

Discover Dirac notation by using kets and bras to form inner products. See how complex conjugate transpose defines bras, and how orthogonal, unit-length vectors appear in various dimensions.

Explore qubits as two-level quantum systems, describe ground and excited states with amplitudes a and b, and explain measurement probabilities, normalization, and superposition.

Explain how global phase factors do not affect measurement probabilities, demonstrate state equivalence, and show that relative phase can influence physical observables.

Map a qubit’s state to the Bloch sphere using amplitudes a and b, include global phase, and connect Cartesian coordinates to spherical angles theta and phi to visualize pure states.

Explore density matrices as the general quantum-state description, distinguishing pure and mixed states, and linking probabilities and superposition to a Pauli-basis decomposition using I, X, Y, Z.

Explore purity in quantum states using density matrices and the purity measure Tr(ρ^2). Distinguish pure and mixed states, understand Bloch sphere intuition, and the maximally mixed state 1/D I.

Explore fidelity as a measure of how close the quantum state is to the initial state after applying a gate. See examples with the ground state |00> and a superposition.

Construct a quantum state by initializing qubits, apply single- or two-qubit unitary gates to reach a desired state, then measure to produce classical bits.

Download and install the Anaconda individual edition, set Python 3.9 as the default, and open Anaconda on your Windows computer. Use pip to install Qiskit and then update all packages.

Learn to set up linux for quantum computing with anaconda installation, environment activation, and pip installation of qiskit, then launch a notebook workspace for your quantum python projects.

Explore constructing the initial state's density matrix from a linear combination of gates with coefficients, verify a pure state via a unit-norm block vector and purity calculation.

Explore how the identity gate operates on the ground-state initial state and does nothing, yielding the same final state via the 2x2 identity matrix acting on the state vector.

Demonstrate how the identity gate leaves a single qubit in the ground state, building and executing a Qiskit circuit, and visualizing state, density matrix, and fidelity on an ideal simulator.

The Pauli X gate flips the qubit from |0> to |1> using its 2x2 matrix form and density matrix, and discusses purity and fidelity between states.

Apply Pauli X gate to the ground state, flipping |0> to |1>, producing a final state orthogonal to the initial with fidelity zero and measurement outcome |1> with probability one.

Apply the Pauli Y gate to the ground state |0> to obtain |1> up to a global phase, and analyze the resulting density matrix and state fidelity.

Explore how the Pauli Y gate operates on the ground state, including state transformation, density matrix, purity, and fidelity, and confirm measurement yields the |1> state with 100% probability.

The Pauli Z gate leaves the ground state unchanged, preserving the |0> density matrix as a pure state, with the Bloch vector pointing to the north pole.

The Pauli Z gate leaves the ground state unchanged, yielding the same density matrix; purity remains one and fidelity equals one, with measurements showing the state |0> with probability one.

This lecture explains how the hadamard gate acting on the ground state |0> creates the equal superposition |+> with coefficients 1/√2 for |0> and |1>, analyzes fidelity and measurement probabilities.

Apply the Hadamard operation to the ground state, generating a superposition of |0> and |1>, analyze the resulting density matrix and measurement probabilities, showing 50/50 outcomes.

Learn how the Rx rotation around the x-axis acts on a ground-state qubit, derive its matrix form, and analyze fidelity with the initial state.

Apply the rx rotation around the x axis to the ground state |0>, yielding equal |0> and |1> probabilities and a 3π/2 phase; fidelity to the initial state is 0.5.

Explore how the ry gate rotates a qubit about the y axis, derive its matrix, compute the final state and its density matrix, and evaluate measurement probabilities.

Apply Ry rotation around the y axis to the ground state, yielding a superposition with 0.75 probability for zero and fidelity of 0.75 with the initial state.

Apply the rz gate to the ground state to rotate about the z axis, using its rotation matrix, with the final state equivalent to |0> up to a global phase.

Explore how the Rz rotation gate around the z-axis acts on the ground state, revealing a global phase while keeping the state and yielding a probability of 1 for |0>.

Learn how the identity gate leaves a single qubit's excited state unchanged, visualize state vectors and density matrices, and verify unity fidelity between initial and final states.

Demonstrates how the Pauli X gate flips the excited state from |1> to |0> in Qiskit, and analyzes the final state, density matrix, purity, and measurement outcomes.

Show how the Pauli Y gate maps the excited state |1> to |0> (up to a global phase) and confirm zero fidelity with initial state, yielding zero probability for |1>.

Demonstrate how the Pauli Z gate acts on a quantum state, yielding the same state up to a global phase of -1 and a measurement of 1 with probability one.

Apply the Hadamard gate to the initial state |0>, yielding a superposition of |0> and |1> with 0.5 probability for each outcome, and discuss the density matrix and fidelity.

Dissect how the Rz gate rotates around the z-axis on a qubit in the excited state, revealing global phase factors and preserved measurement probabilities.

Discover single qubit identities to simplify quantum circuits using X, Y, Z gates and the identity gate, with 2x2 matrices and global phase considerations.

Explore single-qubit identities in Qiskit by building two circuits, applying X, Z, and the wide gate, and proving gate equivalences such as XZ equals minus Y via state vectors.

Derive the most general single-qubit gate using a unitary with a global phase. Demonstrate how the gate decomposes into rotations around the x, y, and z axes.

Explore building a one-qubit circuit in Qiskit, applying the U gate with different theta, phi, lambda parameters, and observe how it reproduces identity, hadamard, and related gates via state vectors.

Explore how a quantum state with relative amplitudes evolves from the initial |0⟩ under a phase gate in county interferometry, and how relative phase affects zero-or-one measurement probabilities.

Create a one-qubit quantum circuit, build a superposition with a Hadamard gate, apply a phase gate to induce a relative phase, and measure outcomes to compare with theory.

Explore multi-qubit states, tensor products, and amplitudes for two and three qubits, using |00>, |01>, |10>, |11> basis, and how classical computers store amplitudes as complex numbers with memory growth.

Explore applying gates to two- and three-qubit systems, turning initial states into final tensor-product states using X, Hadamard gates, and a rotation around the y axis.

Demonstrate two-qubit gates and their representations with unitary matrices, including swap gates and controlled gates, and decompose complex gates using multiple control operations.

Explore two-qubit gate operations using controlled rotation around the y axis and controlled r x gates, starting from the ground state and analyzing the resulting two-qubit state vector.

Explore entanglement in quantum computing through Bell states, including the plus and minus states, and show how certain two-qubit states cannot be decomposed into simple product states.

Construct the Bell states with a two-qubit quantum circuit using superposition and a cnot gate, visualize the state vectors, and analyze entanglement and purity in the Hilbert space.

Compute reduced density matrices from a pure two-subsystem state using a partial trace, showing that each subsystem is completely mixed with purity 0.5.

Explore the Toffoli gate, a three-qubit controlled gate that flips the target qubit when control qubits meet specific conditions, and learn to build quantum circuits with multiple qubits.

This lecture builds a quantum circuit for the Toffoli gate with multiple controls, initializes qubits to the ground state, and analyzes the state vector without measurements.

Build a five-qubit quantum circuit with a five-bit classical register in Qiskit, apply gates in loops, initialize qubits to the ground state, and explore reversing gate order with reverse weights.

visualize the results of two quantum experiments in a single figure by building a circuit, creating superposition, measuring the state, and plotting a histogram with colors and a title.

learn how to initialize a three-qubit state by specifying an amplitude vector using the initialization function in qiskit, and compare it with gate-based construction to verify identical outcomes.

Define a custom two-qubit unitary as an identity gate, initialize two qubits to the ground state, apply the unitary, and verify the final state equals the initial state.

Construct a five-qubit quantum circuit without measurements or classical bits, apply swap and controlled gates, and build a seven-qubit gate in Qiskit.

demonstrates constructing a quantum circuit with quantum and classical registers, applying x and control-not gates, and defines depth as the longest path and width as qubits plus classical bits.

Learn how to query backend information in qiskit, comparing simulated and IBM backends and examining qubits, decoherence times, coupling maps, error sources, and circuit optimization.

Learn to run quantum experiments on real quantum computers using Qiskit, build and measure a multi-qubit state, and compare results from simulation and real devices on IBM Quantum backends.