Tutorials
Free quantum computing tutorials
Every tutorial on this site, in one index. Written to be worked through, not skimmed. No sign-up, no paywall, no trial.
- Tutorials
- 220
- Frameworks covered
- 21
- Written for beginners
- 50
- With an interactive
- 23
Showing all 220 tutorials
Start here
Hello World
Your first quantum program, once per framework. Fifteen minutes, start to finish. 15 tutorials
- Amazon Braket Amazon Braket Hello World Run your first quantum circuit with Amazon Braket. Build a Bell state on the local simulator, then learn how to submit jobs to real quantum hardware on AWS.
- Superstaq Getting Started with Superstaq Install Superstaq, set up an API key, and submit a Bell state circuit to IonQ and Quantinuum simulators to see how cross-platform compilation works in practice.
- Cirq Hello World in Cirq Write your first quantum program in Cirq, create a Bell state using GridQubits and Moments, run it on the Cirq simulator.
- D-Wave Ocean Hello World in D-Wave Ocean Write your first quantum annealing program with D-Wave Ocean, formulate a simple QUBO problem and solve it with the simulated annealing sampler.
- OpenQASM Hello World in OpenQASM Write your first quantum program in OpenQASM 3, the universal quantum assembly language used by IBM Quantum, Qiskit, and cross-platform toolchains.
- PyQuil Hello World in PyQuil Write your first quantum program in PyQuil, build a Bell state using Quil instructions, run it on the QVM simulator, and understand the output.
- Q# Hello World in Q# Write your first quantum program in Q#, put a qubit in superposition, build a Bell state, and run it from Python using the qsharp package.
- Qiskit Hello World in Qiskit Interactive Write your first quantum program in Qiskit, build a Bell state, run it on a local simulator, and interpret the results.
- tket Hello World in tket (pytket) Your first quantum program using pytket, Quantinuum's high-performance quantum SDK with built-in circuit compilation and multi-backend support.
- CUDA-Q Hello World with CUDA Quantum Your first quantum circuit with NVIDIA's CUDA Quantum framework - create a Bell state, run on CPU and GPU simulators, and compute expectation values.
- PennyLane PennyLane Hello World Run your first differentiable quantum circuit in PennyLane. Build a Bell state, compute gradients, and see why PennyLane is the go-to framework for quantum ML.
- Strawberry Fields Hello World in Strawberry Fields Your first photonic quantum program using Xanadu's Strawberry Fields, a fundamentally different model of quantum computing based on light and continuous variables.
- Bloqade Hello World with Bloqade (Neutral Atom Computing) Program neutral atom quantum hardware with QuEra's Bloqade framework - define atom arrays, drive Rydberg transitions, and run analog Hamiltonian simulations.
- Perceval Hello World with Perceval (Photonic Quantum Computing) Build your first photonic quantum circuit with Quandela's Perceval framework - create a beam splitter circuit, demonstrate the Hong-Ou-Mandel effect, and understand how photons encode quantum information.
- TF Quantum Hello World with TensorFlow Quantum Build your first hybrid quantum-classical machine learning model with TensorFlow Quantum - create a parameterized circuit, wrap it as a Keras layer, and train it with gradient descent.
Then
Getting Started Guides
Install, set up, and write something real in the framework you picked. 12 tutorials
- Amazon Braket Getting Started with Amazon Braket Set up Amazon Braket, run circuits on the local simulator, and learn how to submit jobs to real quantum hardware on AWS.
- Cirq Getting Started with Cirq Learn Google's Cirq framework, build quantum circuits with fine-grained control over qubit placement and gate timing, and run them on Google's quantum hardware.
- D-Wave Ocean Getting Started with D-Wave Ocean SDK Install the D-Wave Ocean SDK, formulate a simple optimization problem as a QUBO, and solve it using D-Wave's quantum annealer or simulator.
- PyQuil Getting Started with PyQuil (Forest SDK) Learn Rigetti's PyQuil framework, write quantum programs in the QUIL instruction language and run them on Rigetti's superconducting quantum processors via Quantum Cloud Services.
- Q# Getting Started with Q# Learn Microsoft's Q# quantum programming language, a purpose-built language for quantum algorithms with built-in classical-quantum integration and Azure Quantum access.
- Qiskit Getting Started with Qiskit Install Qiskit, build your first quantum circuit in Python, and run it on a real IBM quantum computer, all in under 30 minutes.
- IonQ SDK Getting Started with the IonQ Python SDK Install the IonQ Python SDK, build a circuit using native GPi and MS gates, run it on the IonQ simulator, and understand when to use the native SDK versus cirq-ionq or Qiskit on Azure.
- D-Wave Ocean Getting Started with D-Wave Ocean SDK Learn D-Wave's Ocean SDK for quantum annealing, formulate combinatorial optimisation problems as QUBO models and solve them on the world's largest quantum annealing processors.
- Amazon Braket Getting Started with IonQ Aria: Trapped Ion Quantum Computing IonQ Aria's 25-qubit trapped ion architecture, native gate set (GPi, GPi2, MS), cloud access options including Braket and Azure Quantum, circuit construction with native gates and transpilation, Aria vs Forte performance, and when trapped ion platforms beat superconducting alternatives.
- tket Getting Started with Quantinuum H-Series Run circuits on Quantinuum's H-series trapped-ion processors using pytket. Covers hardware access, qubit connectivity, mid-circuit measurement, and error mitigation strategies that exploit H-series strengths.
- Strawberry Fields Getting Started with Strawberry Fields Set up Strawberry Fields, learn the continuous-variable gate model, and run your first photonic quantum circuit using the Fock and Gaussian backends.
- OpenFermion Quantum Chemistry with OpenFermion Set up molecular Hamiltonians in OpenFermion, apply Jordan-Wigner mapping to convert fermionic operators to Pauli strings, and build a VQE circuit in Cirq.
The library
Beginner
Concepts and first programs. No prior quantum background assumed. 32 tutorials
- Concepts Bra-Ket Notation Explained Interactive A practical guide to Dirac bra-ket notation as used in quantum computing: kets, bras, inner products, outer products, and how to read quantum circuit diagrams.
- Qiskit Build Your First Quantum Circuit in Qiskit (Complete Beginner Guide) Interactive Step-by-step guide to installing Qiskit, building your first quantum circuit, creating a Bell state, simulating it locally, and running it on a real IBM Quantum device.
- Qiskit Building a Quantum Random Number Generator Build a true quantum random number generator using superposition and measurement in Qiskit, and understand why quantum randomness is fundamentally different from classical pseudo-randomness.
- Concepts Careers in Quantum Computing: Roles, Skills, and How to Get Hired A practical guide to quantum computing job categories, required skills per role, salary ranges, companies hiring, and how to build a portfolio that gets you in the door.
- Concepts Complex Numbers in Quantum Computing Interactive Why quantum computing uses complex numbers, how quantum amplitudes work, and the role of phase in quantum interference.
- Qiskit Debugging Quantum Circuits with Qiskit's Statevector Simulator Use the statevector simulator to debug quantum circuits: print amplitudes, plot probability distributions, probe mid-circuit state, and catch common bugs.
- Concepts Hadamard, S and T on the Bloch Sphere Interactive The Hadamard gate is a half-turn about a diagonal axis, and S and T are partial twists about the vertical one. Seen on a live Bloch sphere, the H, S and T gates stop being matrices and start being furniture-moving.
- Concepts How Quantum Algorithms Work A conceptual guide to how quantum algorithms actually work: using superposition to explore many paths, interference to amplify correct answers, and measurement to extract results.
- Concepts How to Read the Bloch Sphere Interactive A guided tour of the Bloch sphere using a live simulator: what the poles, the equator and the two angles actually mean, and why two states with identical measurement odds can sit on opposite sides of the ball.
- Concepts Linear Algebra for Quantum Computing Interactive The essential linear algebra you need for quantum computing: vectors, matrices, tensor products, and inner products, explained with quantum computing in mind.
- Concepts Linear Algebra for Quantum Computing: Vectors, Matrices, and Inner Products Master the linear algebra underlying quantum computing: Dirac notation, inner products, tensor products, Hermitian and unitary matrices, eigenvalues, and partial trace, all with numpy examples.
- OpenQASM OpenQASM 3 and Qiskit Interoperability How to convert between Qiskit QuantumCircuit objects and OpenQASM 3 strings for sharing, archiving, and cross-platform workflows.
- Concepts Pauli Gates as Rotations: X, Y and Z on the Bloch Sphere Interactive Watch the X, Y and Z gates run on a live Bloch sphere. All three are half-turns around an axis, which explains why X flips a qubit, why Z appears to do nothing, and why applying any of them twice gets you back where you started.
- Concepts Python for Quantum Computing: A Practical Setup Guide Interactive Everything you need to set up Python for quantum computing: virtual environments, NumPy fundamentals, and your first quantum program from scratch.
- Qiskit Qiskit Basics: Quantum Gates, Circuits, and Measurements Interactive A comprehensive beginner guide to Qiskit covering single-qubit gates, two-qubit gates, circuit drawing, statevector simulation, measurement, and histograms, with 20+ code examples.
- Concepts Quantum Annealing vs Gate-Based Quantum Computing A clear comparison of quantum annealing and gate-based quantum computing: how they work, what problems they solve best, and when to choose each approach.
- Concepts Quantum Computing Applications: What Problems Can It Solve? A practical overview of what quantum computers can actually do today and in the near future: chemistry simulation, optimisation, cryptography, and machine learning.
- Concepts Quantum Entanglement Explained Interactive What entanglement actually is, why Einstein hated it, and why it's essential for quantum computing and quantum communication.
- Concepts Quantum Gates as Matrices: The Linear Algebra Behind Quantum Computing Interactive Understand quantum gates as 2x2 unitary matrices, see the explicit matrices for X, Y, Z, H, S, and T gates, and learn how matrix multiplication corresponds to running gates sequentially.
- Concepts Quantum Gates: Hadamard, Pauli, CNOT, Toffoli (with Diagrams) Interactive What each quantum gate actually does to a qubit state, with circuit diagrams and matrix forms for Hadamard, Pauli-X/Y/Z, CNOT, Toffoli, and the rotation gates.
- Concepts Quantum Measurement Explained Interactive How quantum measurement works: the Born rule, wavefunction collapse, measurement bases, and why measurement is irreversible in quantum computing.
- Concepts Quantum vs Classical Computing: What's Actually Different? Cut through the hype and understand what actually separates quantum computers from classical ones, what problems they genuinely help with, and what realistic expectations look like.
- Concepts Qubits vs Classical Bits: The Key Differences Interactive A side-by-side comparison of classical bits and qubits: what makes a qubit fundamentally different, what it can and cannot do, and common misconceptions.
- D-Wave Ocean Simulated Annealing with D-Wave Ocean Use D-Wave Ocean's SimulatedAnnealingSampler to test QUBO formulations locally before committing to quantum hardware.
- Concepts Simulating BB84 Quantum Key Distribution in Python Implement the BB84 quantum key distribution protocol from scratch in Python, simulating qubit encoding, eavesdropping detection, and secure key sifting.
- Concepts The Bernstein-Vazirani Algorithm: Implementing a Hidden String Finder in Qiskit Interactive Implement the Bernstein-Vazirani algorithm in Qiskit: find a hidden bit string in a single query using superposition and phase kickback, versus N queries classically.
- Qiskit The Deutsch-Jozsa Algorithm: Quantum's First Speedup Explained Interactive Learn how the Deutsch-Jozsa algorithm solves in a single query a problem that requires exponentially many classical queries, and implement both constant and balanced oracles in Qiskit.
- Qiskit Visualizing Quantum Circuits and States in Qiskit How to visualize quantum circuits, measurement histograms, statevectors, and Bloch sphere representations using Qiskit's built-in tools.
- Concepts What Is a Quantum Algorithm? How Quantum Programs Work Understand the structure of quantum algorithms through state preparation, oracles, interference, and measurement, using Deutsch's algorithm as the clearest possible example.
- Concepts What is a Qubit? Interactive A plain-English explanation of qubits, what makes them different from classical bits and why that matters for computing.
- Concepts What is Quantum Entanglement? A clear explanation of quantum entanglement: what it is, what it is not, how it differs from classical correlations, and why it is a resource in quantum computing.
- Concepts Why Are Quantum Computers Faster? Superposition, Interference, and Entanglement Explained Understand the real mechanism behind quantum speedup: not 'exploring all paths at once,' but engineering interference to amplify right answers and cancel wrong ones.
Intermediate
Algorithms, simulation and hardware, for readers who can already build a circuit. 101 tutorials
- D-Wave Ocean Advanced D-Wave: Hybrid Solvers and Leap Use D-Wave's Leap hybrid solver service to solve large optimization problems that are too big for the QPU alone: LeapHybridSampler, problem formulation, and interpreting solutions.
- Cirq Advanced Gates and Custom Unitaries in Cirq Define custom quantum gates in Cirq from unitary matrices, use the fermionic simulation gate (FSimGate), and build parameterized custom operations.
- Concepts Bell Inequalities and the CHSH Test: How We Know Entanglement Is Real Derive the CHSH inequality, understand why classical correlations cannot violate it, and verify that quantum entanglement does, with working Qiskit code that reproduces Bell test results.
- Concepts Bloch Sphere Math: State Vectors to Rotations Interactive The mathematics behind the Bloch sphere: how the angles θ and φ map to quantum state vectors, why single-qubit gates are rotations, and how to read any single-qubit state geometrically.
- Strawberry Fields Boson Sampling Applications with Strawberry Fields Use Gaussian Boson Sampling in Strawberry Fields for molecular vibronic spectra simulation and graph similarity, with practical examples from the sf.apps module.
- PennyLane Building a Variational Quantum Classifier from Scratch Build a complete binary quantum classifier with angle encoding, strongly entangling layers, BCE loss, and Adam optimizer, trained on the moons dataset, with decision boundary visualization and comparison to logistic regression.
- PyQuil Building Quantum Programs with PyQuil and Quilbase Use PyQuil's Quilbase API to construct parameterized Quil programs, manage classical memory, and execute on Rigetti QCS. Covers the modern PyQuil 4.x API with QCSClient.
- tket Circuit Optimisation with tket How to use tket (pytket) to optimise quantum circuits, reduce gate counts, and compile for specific hardware backends without rewriting your circuits.
- Qiskit Circuit Transpilation in Qiskit How Qiskit's transpiler transforms abstract circuits into hardware-executable form: qubit mapping, SWAP insertion, gate decomposition, and optimization passes.
- Cirq Cirq QFT From Scratch: Controlled-Phase Rotations Step by Step Build the Quantum Fourier Transform in Cirq one rotation at a time. Verifies against the classical DFT, explains the bit reversal, and shows where the speedup actually comes from.
- OpenQASM Classical Control Flow in OpenQASM 3 Use OpenQASM 3's classical control flow features: if/else on measurement outcomes, for loops, while loops, and real-time classical computation for dynamic quantum circuits.
- Amazon Braket Comparing Quantum Hardware on Amazon Braket: IonQ vs Rigetti vs IQM vs QuEra Run the same benchmark circuit across multiple Braket hardware providers, compare noise levels, gate sets, connectivity, pricing, and latency.
- tket Connecting tket to Real Quantum Hardware How to connect tket circuits to IBM Quantum, Quantinuum H-Series, and AWS Braket backends using pytket extension packages.
- D-Wave Ocean Constrained Optimization with D-Wave's CQM Sampler Use D-Wave's Constrained Quadratic Model (CQM) sampler to solve optimization problems with explicit constraints, eliminating the need for manual QUBO penalty encoding.
- D-Wave Ocean D-Wave Hybrid Workflows: Combining Classical and Quantum Solvers Learn the full D-Wave hybrid workflow: define optimization problems as BQMs and CQMs, use LeapHybridSampler for large-scale solving, apply SteepestDescentSolver for local refinement, and decide when hybrid outperforms pure classical or QPU-only approaches.
- OpenQASM Defining Custom Gates in OpenQASM 3 How to define reusable custom gates in OpenQASM 3 using the gate keyword, angle parameters, and inline gate modifiers.
- Concepts Density Matrices and Mixed States in Qiskit Understand density matrices, mixed states, and the partial trace. Essential for reasoning about noise, decoherence, and real hardware, with working Qiskit examples.
- Qiskit Designing Grover's Algorithm Oracles How to design and implement oracles for Grover's search algorithm: from Boolean functions to quantum circuits, phase kickback, and multi-target search.
- Qiskit Dynamic Quantum Circuits: Mid-Circuit Measurement and Classical Feedforward in Qiskit Implement quantum teleportation using Qiskit's dynamic circuit primitives: mid-circuit measurement, classical feedforward with if_else, and comparison to the static circuit approach. Includes repeat-until-success gates.
- Amazon Braket Error Mitigation on Amazon Braket Apply zero-noise extrapolation and measurement error mitigation techniques on Amazon Braket using local and density matrix simulators.
- Mitiq Error Mitigation with Mitiq: Zero-Noise Extrapolation Use Mitiq's zero-noise extrapolation to reduce the impact of hardware noise on expectation values without full quantum error correction.
- PennyLane Finite-Shot Optimization in PennyLane Optimize variational circuits using finite shots in PennyLane. Compare parameter-shift, SPSA, and natural gradient estimators for shot-limited hardware settings.
- D-Wave Ocean Graph Coloring with D-Wave Ocean Formulate the graph coloring problem as a QUBO and solve it on D-Wave using the Ocean SDK.
- Concepts Grover's Algorithm Explained Interactive How Grover's algorithm searches an unsorted database in √N steps, and why that matters for cryptography and optimization.
- Qiskit Grover's Algorithm with Multiple Solutions Extend Grover's algorithm to handle multiple marked items. Derive the optimal number of iterations, implement multi-solution oracles in Qiskit, and use quantum counting to find the solution count.
- Classiq High-Level Quantum Circuit Synthesis with Classiq Learn how Classiq's synthesis engine lets you describe quantum algorithms at a functional level and automatically optimizes circuits for depth, width, or hardware constraints, with a complete Grover's search example.
- Qiskit How to Build a Realistic Qiskit Noise Model (T1, T2, Depolarizing) Step-by-step Qiskit noise model with depolarizing channels, T1/T2 decay, and readout error. Includes importing real IBM backend calibrations so simulations match hardware.
- PennyLane Hybrid Quantum-Classical Optimization Loops with PennyLane and PyTorch Build a complete hybrid quantum-classical optimization pipeline: PennyLane QNode wrapped as a PyTorch layer, automatic differentiation through quantum circuits, Adam optimizer training on a binary classification task, and comparison to classical logistic regression.
- Q# Implementing Grover's Algorithm in Q# Build a complete implementation of Grover's quantum search algorithm in Q#, including oracle design, reflection operations, and execution on the Azure Quantum Resource Estimator and full-state simulator.
- Qiskit Implementing Quantum Teleportation in Qiskit Build a working quantum teleportation circuit in Qiskit - create an entangled pair, perform a Bell measurement, apply classical corrections, and verify the teleported state.
- Qiskit Introduction to Quantum Error Correction: The Bit-Flip Code Learn how quantum error correction works by implementing the 3-qubit bit-flip code in Qiskit - encode a logical qubit, introduce an error, detect it with syndrome measurement, and correct it.
- Concepts Introduction to Quantum Error Models A practical introduction to the main quantum error models: bit flip, phase flip, depolarizing, and amplitude damping. Understand how these map onto real hardware noise and how error correction addresses each.
- PennyLane Introduction to Quantum Machine Learning A conceptual and practical introduction to quantum machine learning: what QML is, data encoding strategies, parameterized quantum circuits, and a complete classification example.
- Concepts Measurement, Decoherence and What the Bloch Sphere Cannot Show You Interactive The Bloch sphere is a map with edges. This final part covers what measurement does to the arrow, why real qubits drift inside the ball, and why an entangled qubit has no arrow at all.
- Concepts Measuring Quantum Advantage: Benchmarks, Metrics, and What They Really Mean Understand quantum volume, CLOPS, randomized benchmarking, and cross-entropy benchmarking: what each metric actually measures, why they are sometimes gamed, and what genuine quantum advantage requires beyond laboratory demonstrations.
- Qiskit Measuring Quantum Volume: A Step-by-Step Guide with Qiskit Implement quantum volume measurement from scratch using random SU(4) circuits, ideal vs noisy simulation, and the heavy output generation problem.
- OpenQASM Mid-Circuit Measurement and Classical Feedforward in OpenQASM 3 How to use mid-circuit measurements, classical conditionals, and real-time feedback in OpenQASM 3 dynamic circuits.
- Qiskit Migrating from Qiskit 0.x to Qiskit 1.0 A practical guide to porting Qiskit 0.x code to Qiskit 1.0: deprecated APIs removed, primitives V2 migration, backend changes, and transpiler updates.
- Concepts Neutral Atom Quantum Computing: How It Works How neutral atom quantum computers work: optical tweezers, Rydberg interactions, programmable connectivity, and how platforms like QuEra and Pasqal compare to superconducting and trapped ion approaches.
- Mitiq Noise Mitigation with Mitiq How to reduce the effect of quantum hardware noise using Mitiq's zero-noise extrapolation and probabilistic error cancellation techniques without full error correction.
- Cirq Noise Modeling in Cirq Model realistic quantum hardware noise in Cirq: depolarizing channels, amplitude damping, bit-flip channels, and using DensityMatrixSimulator for noisy circuit simulation.
- PyQuil Noise Simulation in PyQuil Learn to simulate realistic quantum noise in PyQuil using Kraus operators, depolarizing channels, and T1/T2 decoherence models. Compare ideal and noisy Bell state results on the QVM.
- PyQuil Parametric Quantum Programs and Compilation with pyQuil Learn how to write and compile parametric quantum programs in pyQuil using DECLARE memory regions and runtime memory maps, compile for Rigetti's Ankaa topology with Quilc, and execute on the QVM and Rigetti QCS.
- PennyLane PennyLane Error Mitigation: ZNE and PEC for NISQ Circuits Cut noise on NISQ devices with PennyLane: implement zero-noise extrapolation and probabilistic error cancellation, with a working example that beats the unmitigated baseline.
- PennyLane PennyLane QAOA Tutorial: Solve Max-Cut on a 5-Node Graph Run QAOA on Max-Cut in PennyLane end to end: encode the graph as a cost Hamiltonian, parameterize the variational circuit, and optimize toward the maximum partition.
- Strawberry Fields Photonic Quantum Computing with Strawberry Fields A hands-on guide to continuous-variable quantum computing with Strawberry Fields, covering the program model, Gaussian and Fock backends, Gaussian boson sampling, and a full CV teleportation circuit.
- Qiskit Portfolio Optimization with Qiskit and QAOA Formulate mean-variance portfolio optimization as a QUBO, solve it with QAOA using Qiskit Optimization, and compare results against the classical Markowitz efficient frontier.
- Bloqade Programming Neutral Atom Quantum Computers with Bloqade Learn how neutral atom quantum computers use optical tweezers and Rydberg blockade to implement quantum logic, how to define pulse sequences with Bloqade's Python SDK, and how to run simulations and submit to QuEra's Aquila QPU via Amazon Braket.
- Cirq QAOA for Max-Cut in Cirq Implement the Quantum Approximate Optimization Algorithm to solve a small Max-Cut problem using Cirq, with parameterized circuits and classical optimization.
- Qiskit QAOA for MaxCut: A Complete Qiskit Walkthrough Build the Quantum Approximate Optimization Algorithm from scratch in Qiskit to solve MaxCut on small graphs. Understand the circuit structure, cost function, and how to tune the depth parameter p.
- PennyLane QAOA: Quantum Approximate Optimisation Algorithm with PennyLane Implement the Quantum Approximate Optimisation Algorithm to solve the MaxCut graph problem using PennyLane, and understand how QAOA bridges quantum computing and combinatorial optimisation.
- Qiskit Qiskit Patterns: A Structured Workflow for Quantum Algorithms Learn IBM's 4-step Qiskit Patterns methodology and implement a complete VQE using SparsePauliOp, parametric ansatz, ISA transpilation, and RuntimeEstimator.
- Qiskit Qiskit Runtime Primitives: Sampler and Estimator How to use Qiskit Runtime's Sampler and Estimator primitives to run circuits on IBM quantum hardware efficiently, replacing the deprecated execute() API.
- Qiskit Qiskit Runtime Sessions and Primitives: A Production Guide A production-oriented guide to Qiskit Runtime's Session and Batch modes, the Estimator and Sampler primitives, Primitive Unified Blocs (PUBs), ISA circuits, and cost optimization strategies for IBM Quantum hardware.
- Stim Qiskit Sampler and Estimator: The Primitives API How to use Qiskit's Sampler and Estimator primitives for efficient quantum circuit execution on real hardware and simulators.
- Qiskit Qiskit Serverless: Scaling Quantum Workloads on IBM Quantum Platform Learn to use Qiskit Serverless to parallelize quantum workloads on IBM Quantum. Run parameter sweeps in parallel, coordinate classical and quantum compute, aggregate results, and choose between Session, Batch, and Serverless execution modes.
- Qiskit Qiskit SparsePauliOp Tutorial: Build Hamiltonians Build and manipulate Hamiltonians efficiently using Qiskit's SparsePauliOp class for variational algorithms and quantum chemistry simulations.
- Stim Quantum Amplitude Estimation: From Theory to Finance Applications Implement canonical QAE and Iterative QAE in Qiskit, understand the connection to Grover and QPE, and apply amplitude estimation to European call option pricing.
- Concepts Quantum Chemistry on Quantum Computers: The Basics How quantum computers simulate molecular systems: from second quantization and fermion-to-qubit mappings to VQE and the active space approximation.
- Concepts Quantum Computing in Julia with Yao.jl Write your first quantum programs in Julia with Yao.jl: build a Bell state, apply gates and rotations, measure, and compute expectation values. Every snippet is run on Yao 0.9.
- Concepts Quantum Decoherence Explained: Why Qubits Lose Their Quantum Nature What decoherence is physically, how T1 and T2 times characterise it, and why it is the central engineering problem of quantum computing. Includes Qiskit simulation of decoherence effects.
- Q# Quantum Error Correction in Q# Implement the 3-qubit bit flip code and phase flip code in Q#, covering encoding, error injection, syndrome measurement, and correction.
- Qiskit Quantum Error Correction: Building a 3-Qubit Repetition Code in Qiskit Implement a 3-qubit bit-flip repetition code from scratch in Qiskit: encoding, error injection, syndrome measurement with ancilla qubits, decoding logic, and fidelity benchmarking across error rates.
- Qiskit Quantum Fourier Transform in Qiskit Build the quantum Fourier transform circuit from scratch in Qiskit, understand why it works, and see how it underpins Shor's algorithm and quantum phase estimation.
- PennyLane Quantum Kernels and Support Vector Machines with PennyLane Learn how to build quantum kernel functions with PennyLane, use them with scikit-learn's SVM, and understand when quantum kernels might offer an advantage over classical kernels, with a full working classification example.
- Amazon Braket Quantum Machine Learning on Amazon Braket Train a variational quantum classifier on the Iris dataset using PennyLane with the Amazon Braket backend, including local simulation, SV1 managed simulator, and Hybrid Jobs for persistent classical-quantum training loops.
- PennyLane Quantum Machine Learning with PennyLane: Your First Classifier Build a quantum classifier using PennyLane's parameterized circuits and train it to classify a simple dataset using gradient descent.
- Qiskit Quantum Monte Carlo for Options Pricing Learn how quantum amplitude estimation delivers a quadratic speedup over classical Monte Carlo for pricing European call options, using Qiskit Finance's built-in circuits and AerSimulator.
- Concepts Quantum Networking: Entanglement Swapping and Quantum Repeaters Learn how entanglement swapping extends quantum correlations across arbitrary distances, why quantum repeaters are essential for a quantum internet, and how fiber loss rates drive the engineering challenge, with a Python simulation of fidelity degradation.
- Stim Quantum Phase Estimation in Q# Implement the Quantum Phase Estimation algorithm in Q# to estimate eigenvalues of unitary operators, with a worked example using the T gate.
- Stim Quantum Phase Estimation in Qiskit How quantum phase estimation works and how to implement it in Qiskit: circuit construction, ancilla register sizing, and reading the phase from measurement results.
- Concepts Quantum Sensing: How Quantum Systems Detect the Undetectable Explore how quantum superposition and entanglement enable sensors that exceed classical noise limits, from NV center magnetometers to atomic clocks, with a Qiskit simulation of the Ramsey spectroscopy protocol.
- Q# Quantum Teleportation in Q# Implement quantum teleportation in Q# using Bell state preparation and classical communication. Run on Azure Quantum simulators and understand the protocol step by step.
- PennyLane Quantum Teleportation with PennyLane Implement quantum teleportation in PennyLane: creating the entangled pair, Bell measurement, classical correction, and verifying the teleported state.
- Qiskit Quantum Teleportation: Transferring Quantum States Without Moving Particles Interactive Understand the quantum teleportation protocol from first principles, learn why it does not violate relativity or the no-cloning theorem, and implement a working teleportation circuit using Qiskit dynamic circuits.
- Concepts Quantum Walks and the Search Algorithm How quantum walks on graphs achieve quadratic speedup for search problems, with the Szegedy framework explained and a Qiskit implementation of discrete-time quantum walk search.
- Qiskit Quantum Walks: How Quantum Computers Explore Graphs Implement discrete-time quantum walks on a line and cycle graph in Qiskit, visualize the quadratic spreading advantage over classical random walks, and understand the deep connection to Grover's algorithm.
- Amazon Braket Quantum-Classical Hybrid Jobs on Amazon Braket Run variational quantum algorithms using Amazon Braket Hybrid Jobs: managed classical compute + quantum access in one job, with checkpointing and cost tracking.
- D-Wave Ocean QUBO Formulation: Translating Problems for D-Wave Learn how to formulate combinatorial optimization problems as QUBO matrices for D-Wave, including penalty terms for constraints and a worked number partitioning example.
- Qiskit Running Qiskit on Real IBM Quantum Hardware: Tips and Pitfalls A practical guide to running Qiskit circuits on real IBM quantum processors: account setup, backend selection, ISA transpilation, session management, reading results, and avoiding common errors on noisy hardware.
- Concepts Rx, Ry and Rz: Reaching Any Point on the Bloch Sphere Interactive Give a rotation a dial instead of a fixed angle and you can steer a qubit anywhere on the Bloch sphere with two gates. This is the Euler decomposition, and it is what your transpiler does to every circuit you run.
- Concepts Shor's Algorithm Explained How Shor's algorithm breaks RSA encryption by factoring large numbers exponentially faster than any classical computer, and what this means for cybersecurity.
- PennyLane Shot-Adaptive Optimization in PennyLane Use PennyLane's shot-adaptive optimizer to allocate measurement shots intelligently across circuit parameters.
- Qiskit Simon's Algorithm: Exponential Quantum Speedup for Period Finding Understand Simon's algorithm, the first proof of exponential quantum speedup, covering the hidden period problem, quantum circuit, classical post-processing over GF(2), and a complete Qiskit implementation.
- Qiskit Simulating the Transverse-Field Ising Model with Qiskit Simulate the 1D transverse-field Ising model using Trotterized time evolution in Qiskit. Measure magnetization dynamics, scan the quantum phase transition, and compare to exact diagonalization.
- Qiskit Solving Max-Cut with QAOA in Qiskit: A Practical Guide Build a complete Max-Cut solver using QAOA in Qiskit Optimization. Covers graph construction with NetworkX, QuadraticProgram formulation, QAOA via MinimumEigenOptimizer, and how solution quality changes with circuit depth p.
- D-Wave Ocean Solving Network Problems with D-Wave Ocean: TSP and Graph Coloring Learn how to formulate the Traveling Salesman Problem and graph coloring as QUBOs and BQMs using D-Wave Ocean SDK, then solve them with LeapHybridSampler and interpret the results.
- Qiskit Solving Optimization Problems with Qiskit Optimization Use Qiskit's optimization module to formulate and solve combinatorial problems: Max-Cut, knapsack, and TSP using QAOA and the MinimumEigenOptimizer.
- Strawberry Fields Squeezed States and Quadrature Measurements in Strawberry Fields Learn to create squeezed, displaced, and rotated states in Strawberry Fields, measure position and momentum quadratures via homodyne detection, and visualize the results with Wigner functions.
- OpenQASM Subroutines and Reusable Gates in OpenQASM 3 Define reusable gate subroutines and parameterized gates in OpenQASM 3. Learn the gate declaration syntax, scoping rules, and how to build modular circuit libraries.
- Qiskit Testing Quantum Circuits with Qiskit Fake Backends Use Qiskit fake backends to simulate real IBM quantum device noise locally, enabling fast and realistic circuit testing without using hardware credits.
- Concepts The Quantum Fourier Transform: How and Why It Works A step-by-step explanation of the quantum Fourier transform: the circuit construction, why it is exponentially faster than the classical FFT, and its role in phase estimation and Shor's algorithm.
- Concepts Turing Machines, Computability, and What Quantum Computing Actually Changes A quantum computer computes exactly the same set of functions as a Turing machine, no more and no fewer. It cannot solve the halting problem. What it changes is efficiency, not computability, and this tutorial draws the line precisely.
- PyQuil Understanding Quil: PyQuil's Quantum Assembly Language Deep dive into the Quil quantum assembly language underlying PyQuil. Learn DEFGATE, DECLARE, classical control flow, DEFCIRCUIT, and how PyQuil programs compile to Quil strings.
- D-Wave Ocean Using D-Wave Leap Hybrid Solvers Solve large optimization problems with D-Wave Leap hybrid solvers that combine classical heuristics and quantum annealing.
- Amazon Braket Using PennyLane with Amazon Braket Connect PennyLane to Amazon Braket backends to run hybrid quantum-classical workflows, from local simulation to IonQ trapped-ion hardware.
- tket Variational Quantum Algorithms with tket How to implement the Variational Quantum Eigensolver (VQE) using tket's parameterized circuits and scipy optimization.
- Qiskit Variational Quantum Eigensolver (VQE) Explained How VQE works: the variational principle, ansatz design, classical optimizer loop, and a complete Qiskit implementation for finding the ground state of a simple Hamiltonian.
- PennyLane Variational Quantum Eigensolver with PennyLane Implement the Variational Quantum Eigensolver to find the ground state energy of a hydrogen molecule using PennyLane and gradient-based optimization.
- Qiskit VQE for H2 Molecule: Complete Worked Example in Qiskit A complete walkthrough of VQE for the hydrogen molecule in Qiskit Nature, from PySCF driver and Jordan-Wigner mapping through UCCSD ansatz and classical optimization.
- OpenQASM Writing Quantum Circuits in OpenQASM 3 OpenQASM 3 syntax for describing quantum circuits: gate definitions, classical control flow, real-time feedback, and how QASM 3 differs from QASM 2.
Advanced
Error correction, compilation and research-level technique. 60 tutorials
- CUDA-Q Accelerating Quantum Simulation with CUDA Quantum and GPU Learn how NVIDIA's CUDA Quantum platform enables GPU-accelerated quantum circuit simulation using custatevec, kernel syntax, noise models, and multi-GPU scaling for 30+ qubit circuits.
- PennyLane Active Space Methods for Quantum Chemistry in PennyLane Reduce molecular simulation cost by selecting active orbitals in PennyLane. Combine active space selection with VQE for accurate molecular ground state energies.
- PennyLane Adaptive Variational Circuits with ADAPT-VQE in PennyLane Implement a simplified ADAPT-VQE algorithm in PennyLane. Build an operator pool, greedily select operators by gradient magnitude, grow the ansatz iteratively, and compare convergence against fixed UCCSD for the H2 molecule.
- tket Advanced Circuit Optimization with tket Master advanced tket compilation: custom PassManagers, PauliSimp, CliffordSimp, noise-aware routing with Architecture graphs, KAK decomposition, and backend-agnostic portability across IBM, IonQ, and Quantinuum.
- Qiskit Advanced Error Mitigation in Qiskit Runtime Use Qiskit Runtime's built-in error mitigation options: resilience levels, zero-noise extrapolation, and Probabilistic Error Cancellation in the Estimator primitive.
- Amazon Braket Analog Hamiltonian Simulation with QuEra Aquila Program QuEra's Aquila neutral-atom processor through Amazon Braket to run analog Hamiltonian simulations with Rydberg blockade physics.
- Qiskit Characterizing Real Quantum Hardware Noise with Qiskit Implement noise characterization using Qiskit Experiments: T1 inversion recovery, T2 Ramsey, single-qubit RB, two-qubit RB, and cross-resonance tomography on a fake backend.
- Cirq Circuit Routing and Optimization in Cirq Use Cirq's transformer framework to route circuits onto device topologies, optimize gate sequences, and reduce circuit depth.
- PennyLane Compiling Quantum Programs with PennyLane Catalyst Use PennyLane Catalyst to JIT-compile hybrid quantum-classical programs with JAX, enabling fast execution on both simulators and quantum hardware.
- Strawberry Fields Continuous-Variable Quantum Neural Networks with Strawberry Fields Build a continuous-variable quantum neural network using Strawberry Fields with differentiable backends, implementing the Killoran et al. CV-QNN architecture for function approximation.
- tket Custom Compilation Passes in TKET Build and compose custom compilation pass sequences in pytket. Learn how to rebase to hardware native gates, apply optimization passes, and profile circuit depth improvements.
- PennyLane Decomposing Arbitrary Gates into Clifford+T with PennyLane Understand why Clifford+T is the universal fault-tolerant gate set, the cost of T gates in magic state distillation, and how to analyze T-count with PennyLane.
- PennyLane Diagnosing and Avoiding Barren Plateaus in PennyLane Understand why barren plateaus occur in deep variational circuits, how to detect them in PennyLane, and practical strategies to avoid them including layerwise training and structured ansatze.
- Qiskit Error Suppression with Qiskit Runtime Use Qiskit Runtime's built-in error suppression techniques including dynamical decoupling, TREX readout error mitigation, and resilience levels to improve results on real hardware.
- Cirq Fast Clifford Simulation with Cirq Use Cirq's CliffordSimulator to efficiently simulate large stabilizer circuits, enabling 100+ qubit experiments on a laptop.
- Qiskit Fault-Tolerant Quantum Gates: Why T Gates Need Magic States Physical vs logical gates, transversal Cliffords on the surface code, the Eastin-Knill obstruction, and the 15-to-1 magic state protocol that makes T gates fault-tolerant.
- Strawberry Fields Gaussian Boson Sampling with Strawberry Fields Run a Gaussian boson sampling circuit in Strawberry Fields: squeezed states, beamsplitters, and the connection to molecular vibronic spectra and graph similarity.
- Qiskit Hamiltonian Simulation with Qiskit: Pauli Evolution and Trotterization Implement first-order and second-order Trotter decomposition for the transverse-field Ising model using Qiskit's PauliEvolutionGate and SuzukiTrotter, measure energy expectation value evolution, and analyze Trotter step error as a function of step size.
- Qiskit Hamiltonian Simulation with Trotterization in Qiskit Simulate quantum systems by decomposing time evolution into circuits using first and second-order Trotterization. Practical implementation with Qiskit's PauliEvolutionGate and LieTrotter.
- PennyLane High-Performance Simulation with PennyLane Lightning and GPU Explore PennyLane's Lightning family of high-performance simulation backends, learn how to use adjoint differentiation for efficient gradient computation, and understand when to deploy lightning.qubit, lightning.gpu, and lightning.kokkos.
- Qiskit Hybrid Quantum-Classical Optimization: A Deep Dive into VQE A comprehensive guide to the Variational Quantum Eigensolver: ansatz design, optimizer selection, barren plateaus, and a complete H2 ground state calculation using Qiskit's Estimator primitive.
- PennyLane Lithium Hydride VQE with PennyLane: From Molecule to Energy Full VQE for LiH using PennyLane's qchem module: molecular Hamiltonian, Hartree-Fock initial state, UCCSD ansatz, optimization, and potential energy surface scan.
- Qiskit Measuring Quantum Volume with Qiskit Implement the quantum volume protocol in Qiskit to compare hardware quality across devices. Understand how QV relates to circuit depth, qubit count, and gate fidelity.
- OpenFermion Molecular Simulation with OpenFermion and Qiskit Build a complete quantum chemistry pipeline: encode the H2 Hamiltonian with OpenFermion, transform it to qubits via Jordan-Wigner, then find the ground state energy using VQE on Qiskit's statevector simulator.
- Qiskit Molecular Simulation with Qiskit Nature Set up and run a molecular ground state energy calculation in Qiskit Nature: driver setup, active space selection, Jordan-Wigner mapping, and VQE optimization.
- Cirq Noise Characterization in Cirq Characterize noise in Cirq circuits using cross-entropy benchmarking and depolarizing error models. Validate against Google Quantum AI hardware specifications.
- tket Noise Mitigation Techniques in tket How to use tket's compiler passes and error mitigation tools to improve results from noisy quantum hardware.
- PennyLane Noise-Aware Training for Variational Quantum Circuits Train variational quantum circuits directly on realistic noise models using PennyLane. Compare circuits trained with and without noise, insert depolarizing and amplitude damping channels, and apply noise injection techniques to improve real hardware performance.
- OpenQASM OpenQASM 3 Advanced Features: Gates, Timing, and Classical Control A deep dive into OpenQASM 3's most powerful new capabilities: parameterized gate definitions, precise timing control with delay and stretch, mid-circuit measurement, classical feedforward, and a complete quantum teleportation program.
- Mitiq Probabilistic Error Cancellation with Mitiq Learn how probabilistic error cancellation (PEC) works as a powerful generalization of zero-noise extrapolation, and how to implement it with Mitiq to extract near-ideal expectation values from noisy quantum hardware.
- Amazon Braket Pulse-Level Quantum Control with Amazon Braket Program quantum hardware at the pulse level using Amazon Braket's OpenPulse interface. Define custom gate sequences and explore native hardware calibrations.
- Qiskit Qiskit Pulse: Low-Level Quantum Hardware Control Go below the circuit level with Qiskit Pulse: build custom microwave pulse schedules, define your own single-qubit gates via pulse calibration, measure qubit coherence times T1 and T2, and review the legacy workflow for IBM Quantum backends.
- Qiskit Qiskit State Tomography: Reconstruct an Unknown Qubit State Reconstruct an unknown 1- or 2-qubit state with Qiskit's state tomography protocol. Covers measurement basis selection, SPAM correction, and how many shots you actually need.
- Mitiq Qiskit vs Mitiq for Zero-Noise Extrapolation: Which to Use Side-by-side Qiskit Runtime and Mitiq for zero-noise extrapolation: which library handles gate folding better, when Richardson extrapolation outperforms linear fits, and which to pick.
- Concepts Quantum Channels and Kraus Operators: The Language of Quantum Noise The formal framework for describing any quantum operation: CPTP maps, Kraus operators, the Choi matrix, and how common noise channels (depolarising, amplitude damping, phase damping) are expressed mathematically.
- PennyLane Quantum Chemistry in PennyLane: H2 Ground State via VQE Walk through a real VQE simulation in PennyLane: build the H2 Hamiltonian, construct a UCCSD ansatz, and converge to the ground state energy in under 50 iterations.
- Q# Quantum Chemistry Simulation with Q# Use Q# and the Microsoft.Quantum.Chemistry library to simulate molecular ground state energies, covering Jordan-Wigner encoding, Broombridge data, and phase estimation.
- Concepts Quantum Error Mitigation: ZNE vs PEC vs Clifford Data Regression A practical comparison of the three main quantum error mitigation strategies (zero-noise extrapolation, probabilistic error cancellation, and Clifford data regression) with working Mitiq code and guidance on when to use each.
- PennyLane Quantum GANs with PennyLane Build a quantum generative adversarial network in PennyLane with a quantum generator and classical discriminator.
- PennyLane Quantum Generative Adversarial Networks with PennyLane Implement a patch quantum GAN in PennyLane with a parametric quantum generator and classical neural network discriminator. Covers adversarial training, mode collapse, and how entanglement contributes to output diversity.
- PennyLane Quantum Natural Gradient in PennyLane Implement quantum natural gradient descent in PennyLane using the quantum Fisher information matrix. Compare convergence against standard gradient descent on a VQE benchmark.
- Stim Quantum Phase Estimation: Deep Dive and Applications A thorough treatment of quantum phase estimation covering circuit construction, precision trade-offs, the Hadamard test variant, iterative QPE, and applications in eigenvalue estimation, the HHL algorithm, and quantum simulation.
- Qiskit Quantum Process Tomography with Qiskit Characterize quantum gates and channels using process tomography in Qiskit. Understand how to reconstruct the process matrix and interpret fidelity results.
- Stim Quantum Resource Estimation: How Many Qubits Do You Actually Need? How to estimate the physical qubit count, T-gates, and runtime needed for fault-tolerant quantum algorithms. Use Azure Quantum Resource Estimator and manual calculations for Shor's algorithm and quantum chemistry.
- Qiskit Quantum State Tomography with Qiskit Reconstruct an unknown quantum state from measurement data using Qiskit's StateTomography workflow. Understand when tomography is useful and when it is not.
- PennyLane Quantum Transfer Learning with PennyLane Combine a classical pre-trained CNN with a parameterized quantum circuit for image classification using PennyLane's quantum transfer learning technique.
- Qiskit Randomized Benchmarking with Qiskit Run randomized benchmarking protocols in Qiskit to measure average gate fidelity and diagnose systematic errors on real quantum hardware.
- Qiskit Run Bigger Circuits with Qiskit Circuit Cutting (Wire + Gate) Split a large quantum circuit across smaller QPUs using Qiskit's circuit cutting addon. Covers both wire cuts and gate cuts, plus when the classical overhead becomes prohibitive.
- Cirq Simulating Google Sycamore Circuits with Cirq Build and simulate random quantum circuits on the Google Sycamore topology using Cirq. Implement FSimGate with Sycamore parameters, realistic noise models, and cross-entropy benchmarking (XEB) to measure circuit fidelity.
- Cirq Simulating Superconducting Qubit Physics in Cirq Use Cirq's tools for simulating Google-style superconducting circuits: fSim gates, GridQubits, device topology, and the cross-entropy benchmarking protocol.
- Stim Surface Code Simulation: Stim + PyMatching Tutorial Simulate a distance-3 surface code using Stim and decode syndromes with PyMatching. Measure logical error rates and compute the code threshold from simulation data.
- Qiskit SWAP Networks and Qubit Routing in Qiskit Learn how Qiskit's transpiler inserts SWAP gates to route circuits onto device connectivity graphs. Understand routing heuristics and how to minimize SWAP overhead.
- Concepts The HHL Algorithm: Quantum Linear Systems A conceptual and mathematical introduction to the HHL algorithm for solving linear systems Ax=b, including its assumptions, exponential speedup claim, and important caveats.
- Concepts The Surface Code: Quantum Error Correction at Scale How the surface code works: the 2D lattice geometry, X and Z stabilizer measurements, logical operators, and why it's the leading candidate for fault-tolerant quantum computing.
- Concepts Topological Quantum Computing: Anyons, Braids, and Inherently Fault-Tolerant Qubits Understand how 2D anyons with non-Abelian statistics enable quantum gates through braiding, why topological qubits are inherently protected from local errors, and where Microsoft's topological qubit program stands after the 2025 announcement.
- D-Wave Ocean Understanding Minor-Embedding in D-Wave Problems Learn how logical problem variables map to physical qubits through minor-embedding, and how to diagnose and fix chain breaks on D-Wave hardware.
- Amazon Braket Verbatim Compilation with Amazon Braket Run circuits on Amazon Braket without compiler modifications using verbatim compilation. Understand native gate sets and topology requirements.
- PyQuil VQE Implementation in PyQuil Implement the Variational Quantum Eigensolver (VQE) in PyQuil to find the ground state energy of molecular hydrogen. Build the Hamiltonian, parameterized ansatz, and classical optimization loop.
- Cirq VQE with Cirq and OpenFermion Build a complete VQE implementation for H2 using Cirq's parametric gates, OpenFermion for the qubit Hamiltonian, scipy for classical optimization, and the parameter shift rule for exact gradients.
- Qiskit Water Molecule Simulation with Qiskit Nature and VQE A complete end-to-end VQE simulation of the water molecule using Qiskit Nature: PySCFDriver setup, active space reduction from 10 electrons in 7 orbitals to 4 electrons in 4 orbitals, Jordan-Wigner mapping, UCCSD ansatz, and comparison with Hartree-Fock and CCSD references.