Coming soon
Quantum Computing
Program quantum computers, and know when they're worth it.
The complete course
- modules
- 66
- topics
- 703
- min lessons
- 15
What you'll be able to do.
Build and simulate quantum circuits
Stage 2 · Qubits, Gates & Circuits
Implement Grover, QFT and phase estimation
Stage 3 · Core Algorithms
Run VQE for chemistry, QAOA for optimization
Stage 4 · Simulation & Advanced Algorithms
Compile circuits for real hardware
Stage 5 · Hardware & Compilation
Estimate what fault tolerance will cost
Stage 6 · Error Correction & Fault Tolerance
Benchmark a quantum project against classical
Stage 7 · Laboratories & Project
Seven stages.One steady climb.
One qubit at the start. A compiled, error-aware program at the end.
66modules
in 7 stages
703topics
≈ 11 per module
≈176hours
of 15-minute lessons
≈23months
≈12months
≈6months
to finish the whole course
- 1
Math & Classical Foundations
The math qubits are written in
5 modules · 52 topics · ≈ 13 hr
- 2
Qubits, Gates & Circuits
How a qubit computes
11 modules · 117 topics · ≈ 29 hr
- 3
Core Algorithms
The algorithms that started it all
9 modules · 93 topics · ≈ 23 hr
- 4
Simulation & Advanced Algorithms
Molecules, optimization, learning
15 modules · 159 topics · ≈ 40 hr
- 5
Hardware & Compilation
From circuit to physical chip
10 modules · 107 topics · ≈ 27 hr
- 6
Error Correction & Fault Tolerance
Making noisy qubits reliable
12 modules · 132 topics · ≈ 33 hr
- 7
Laboratories & Project
Lab work, then a full project
4 modules · 43 topics · ≈ 11 hr
Months
04812160246801234
MonthsFinish · ≈ 23 months · ≈ 12 months · ≈ 6 months
Hours and months are estimates: one 15-minute lesson per topic, every day.
Every module.Every topic.
Stage 1
Math & Classical Foundations
The math qubits are written in
5 modules · 52 topics
1Foundations of Quantum Computing10 topics
- Quantum Computing as a Model of Computation
- Classical Bits, Quantum Bits, and Computational States
- Superposition, Interference, and Entanglement
- What a Quantum Computer Actually Produces
- Quantum Processors and Classical Host Computers
- Digital, Analog, and Hybrid Quantum Computation
- Physical Qubits and Logical Qubits
- Noisy Computation and Fault-Tolerant Computation
- Computational Advantage and Its Required Evidence
- The Quantum Computing Hardware and Software Stack
2Classical Computing Foundations for Quantum Algorithms10 topics
- Boolean Functions and Logic Circuits
- Deterministic and Randomized Algorithms
- Reversible and Irreversible Computation
- Time, Space, and Query Complexity
- Polynomial and Exponential Scaling
- Decision, Search, Sampling, and Estimation Problems
- Exact and Approximate Solutions
- Input Representation and Output Requirements
- Classical Preprocessing and Postprocessing
- Comparing Algorithms Under the Same Computational Assumptions
3Complex Numbers and Linear Algebra12 topics
- Complex Amplitudes and Phase
- Vectors, Inner Products, and Norms
- Orthonormal Bases and Basis Changes
- Matrices, Linear Maps, and Operator Composition
- Conjugate Transposes and Hermitian Operators
- Unitary Operators and Norm Preservation
- Eigenvalues, Eigenvectors, and Spectral Decomposition
- Projectors and Orthogonal Subspaces
- Trace, Positive Operators, and Matrix Functions
- Matrix Exponentials and Continuous Evolution
- Singular Value Decomposition and Operator Norms
- Dirac Notation for States and Operators
4Tensor Products and Composite Systems10 topics
- Tensor Products of State Spaces
- Product Bases and Computational Basis Ordering
- Tensor Products of Vectors and Matrices
- Operators Acting on Selected Subsystems
- Expanding Multiqubit States in Different Bases
- Register Size and Hilbert-Space Dimension
- Reordering Qubits and Permuting Subsystems
- Tensor-Product Structure and State Factorization
- Reshaping State Vectors into Bipartite Matrices
- Tracking Dimensions in Multiregister Calculations
5Probability, Sampling, and Statistical Estimation10 topics
- Probability Distributions and Conditional Probability
- Expectation Values and Variance
- Independent Trials and Repeated Circuit Executions
- Measurement Counts and Empirical Frequencies
- Estimating Probabilities from Finite Samples
- Confidence Intervals and Statistical Uncertainty
- Precision, Confidence, and Sample Requirements
- Bias, Variance, and Mean-Squared Error
- Comparing Distributions from Quantum Experiments
- Distinguishing Statistical Noise from Systematic Error
Stage 2
Qubits, Gates & Circuits
How a qubit computes
11 modules · 117 topics
6Qubit States and Quantum State Evolution10 topics
- Computational Basis States and State Normalization
- Pure States and Probability Amplitudes
- Global Phase and Relative Phase
- Superposition Relative to a Chosen Basis
- The Bloch Sphere and Its Coordinates
- Unitary Evolution of a Qubit
- Measurement Probabilities and State Update
- Repeated Preparation and Measurement
- Why Amplitudes Are Not Directly Readable Data
- The No-Cloning Principle and Its Computational Consequences
7Single-Qubit Gates and Interference10 topics
- Pauli X, Y, and Z Gates
- The Hadamard Gate and Basis Conversion
- Phase Gates and Rotation Gates
- Rotation Axes and Rotation Angles
- Gate Composition and Noncommutativity
- Inverse Gates and Circuit Reversal
- Constructive and Destructive Interference
- Converting Relative Phase into Measurement Probabilities
- Decomposing General Single-Qubit Operations
- Recognizing Equivalent Circuits Up to Global Phase
8Multiqubit Gates and Elementary Circuits11 topics
- Controlled Operations and Control Conditions
- Controlled-NOT and Controlled-Z Gates
- Controlled Rotations and Controlled Unitaries
- SWAP and Qubit Permutations
- Toffoli and Multicontrolled Gates
- Computing the Action of a Multiqubit Circuit
- Entangling and Nonentangling Operations
- Phase Kickback from Controlled Operations
- Register Initialization and Measurement Mapping
- Circuit Identities and Simple Gate Cancellation
- Endianness and Bitstring Interpretation
9Entanglement and Computational Correlations10 topics
- Product States and Entangled States
- Preparing and Analyzing Bell States
- Correlations in Different Measurement Bases
- Schmidt Decomposition and Schmidt Rank
- Entanglement Entropy for Bipartite Pure States
- Local Operations and Entanglement Structure
- GHZ States and Multipartite Correlations
- Entanglement Witnesses as Diagnostic Tools
- Entanglement and the Difficulty of Classical Simulation
- Why Entanglement Alone Does Not Establish Quantum Speedup
10Observables and Quantum Measurement11 topics
- Hermitian Observables and Their Eigenvalues
- Projective Measurement and the Born Rule
- Measuring in Different Bases
- Expectation Values of Pauli Operators
- Joint Measurement of Commuting Observables
- Measurement Disturbance and Incompatible Observables
- Ancilla-Assisted Measurement
- Generalized Measurements and POVMs
- Conditional States and Postselection
- Measurement Outcomes as Classical Information
- The Resource Cost of Discarded Outcomes
11Density Matrices and Mixed States11 topics
- Density Operators for Pure and Mixed States
- Statistical Mixtures and Coherent Superpositions
- Positivity, Trace, and Physical State Conditions
- Unitary Evolution in Density-Matrix Form
- Partial Trace and Reduced States
- Classical Correlation and Quantum Entanglement in Mixed States
- Purity and the Bloch Ball
- Von Neumann Entropy
- Purification and Ancillary Systems
- Trace Distance and State Distinguishability
- Fidelity and State-Comparison Conventions
12Quantum Channels and Open-System Evolution11 topics
- Closed-System and Open-System Descriptions
- Completely Positive Trace-Preserving Maps
- Kraus Operators and Channel Representations
- Unitary Dilation and Environment Models
- Channel Composition and Tensor Products
- Bit-Flip, Phase-Flip, and Depolarizing Channels
- Amplitude Damping and Dephasing
- Coherent Errors and Stochastic Errors
- Quantum Instruments and Measurement Channels
- Choi Matrices and Channel Validity
- Markovian Models and Their Limitations
13The Circuit Model and Computational Universality10 topics
- Quantum Registers, Gates, Measurements, and Classical Wires
- Circuit Families and Input-Size Scaling
- Circuit Width, Size, and Depth
- Universal Gate Sets
- Clifford Gates and Non-Clifford Resources
- Exact and Approximate Gate Synthesis
- Deferred Measurement and Its Assumptions
- Classical Control Within a Quantum Computation
- Uniform Circuits and Algorithm Descriptions
- Relating Abstract Circuits to Physical Execution
14Reversible Logic, Ancillas, and Uncomputation11 topics
- Embedding Classical Functions into Reversible Operations
- Reversible Boolean Networks
- Clean Ancillas and Borrowed Ancillas
- Intermediate Results and Garbage Registers
- Compute-Use-Uncompute Patterns
- Removing Unwanted Entanglement with Workspace
- Ancilla Reuse and Space-Time Tradeoffs
- Reversible Comparisons and Conditional Logic
- Controlled Arithmetic and Reversible Subroutines
- Why Reset Is Not a General Replacement for Uncomputation
- Verifying Reversible Subroutines on All Basis Inputs
15Quantum Programming Workflow11 topics
- Translating an Algorithm into Registers and Subroutines
- Building Circuits with a Quantum Software Framework
- Parameterized Circuits and Parameter Binding
- Defining Reusable Gates and Composite Operations
- Selecting Statevector, Noisy, and Hardware Execution Targets
- Sampling Bitstrings and Estimating Observables
- Separating Circuit Construction from Execution
- Interpreting Results with Explicit Qubit Conventions
- Managing Random Seeds and Experiment Configuration
- Tracking Software Versions and Backend Assumptions
- Organizing Reproducible Quantum Programs
16Classical Simulation of Quantum Computation11 topics
- Statevector Simulation and Memory Scaling
- Density-Matrix Simulation and Noise Representation
- Quantum Trajectories and Stochastic Simulation
- Stabilizer Simulation of Clifford Circuits
- The Gottesman-Knill Theorem and Its Scope
- Tensor Networks and Circuit Contraction
- Matrix Product States and Entanglement Growth
- Approximate Simulation and Truncation Error
- Choosing a Simulator for a Circuit Family
- Recognizing Classically Tractable Special Cases
- Using Classical Simulation as a Validation Tool
Stage 3
Core Algorithms
The algorithms that started it all
9 modules · 93 topics
17State Preparation and Data Encoding11 topics
- Preparing Computational Basis and Product States
- Preparing Structured Superposition States
- Basis, Angle, and Amplitude Encoding
- Normalization and Information Representation
- General State Preparation and Circuit Cost
- Loading Classical Data into Quantum Registers
- Quantum Data Access and QRAM Assumptions
- Preparing States with Known Symmetries
- Approximate State Preparation and Error Budgets
- Input-Preparation Costs in Claimed Speedups
- Matching the Encoding to the Required Output
18Oracle Construction and Quantum Arithmetic11 topics
- Bit Oracles and Phase Oracles
- Implementing Predicates as Reversible Circuits
- Controlled Addition and Subtraction
- Integer Multiplication and Modular Arithmetic
- Reversible Comparators and Range Tests
- Fixed-Point Representations and Numerical Precision
- Table Lookup and Quantum Read-Only Memory Circuits
- Modular Exponentiation as a Quantum Subroutine
- Ancilla Cleanup in Arithmetic Circuits
- Counting Oracle Gates Instead of Treating Queries as Free
- Testing Arithmetic and Oracle Correctness
19Introductory Quantum Query Algorithms10 topics
- The Oracle Model and Promise Problems
- Deutsch's Algorithm
- The Deutsch-Jozsa Algorithm
- The Bernstein-Vazirani Algorithm
- Simon's Problem and Hidden Structure
- Interference Patterns in Query Algorithms
- Classical Postprocessing of Quantum Samples
- Query Complexity and Total Implementation Cost
- Exact and Bounded-Error Query Algorithms
- What Toy Algorithms Demonstrate About Quantum Computation
20The Quantum Fourier Transform10 topics
- The Discrete Fourier Transform and Quantum State Amplitudes
- Fourier Basis States and Phase Structure
- Deriving the Quantum Fourier Transform Circuit
- Controlled Phase Rotations and Bit Reversal
- The Inverse Quantum Fourier Transform
- Approximate Fourier Transforms
- Semiclassical Fourier Transform Circuits
- Periodic States and Fourier Sampling
- Gate Complexity and Rotation Precision
- Why the QFT Does Not Directly Output a Classical Fourier Spectrum
21Quantum Phase Estimation11 topics
- Eigenstates, Eigenvalues, and Eigenphases
- Controlled Powers of a Unitary
- Phase Kickback into an Estimation Register
- Standard Phase Estimation with the Inverse QFT
- Resolution, Success Probability, and Repetitions
- Inputs That Are Superpositions of Eigenstates
- Iterative and Adaptive Phase Estimation
- Approximate Evolution and Phase-Estimation Error
- Extracting Energy Estimates from Unitary Evolution
- Trading Circuit Depth, Ancillas, and Measurement Cost
- Validating Phase Estimates on Small Known Systems
22Shor's Algorithm and Number-Theoretic Computation11 topics
- Integer Factoring and Classical Number-Theoretic Preprocessing
- Reducing Factoring to Order Finding
- Modular Exponentiation in Superposition
- Period Information from Quantum Phase Estimation
- Continued Fractions and Candidate Orders
- Verifying Orders and Recovering Factors
- Failure Cases and Repetition Requirements
- Arithmetic Precision and Reversible Resource Costs
- Quantum Algorithms for Discrete Logarithms
- Hidden Subgroup Structure in Number-Theoretic Algorithms
- Distinguishing Small Demonstrations from Scalable Implementations
23Grover Search and Amplitude Amplification11 topics
- Unstructured Search and Marked States
- Building a Search Oracle from a Predicate
- Reflection About the Initial State
- Grover Iterations as Rotations in a Subspace
- Choosing the Number of Iterations
- Multiple Solutions and Unknown Solution Counts
- General Amplitude Amplification
- Fixed-Point Amplification Strategies
- Quantum Search Lower Bounds
- Oracle Construction and End-to-End Search Cost
- Verifying Candidate Solutions Classically
24Quantum Amplitude Estimation9 topics
- Encoding a Quantity as a Success Probability
- Amplitude Estimation Through Phase Estimation
- Query Scaling and Precision Requirements
- Iterative and Maximum-Likelihood Approaches
- Circuit Depth and Repeated Sampling Tradeoffs
- State-Preparation and Controlled-Operation Costs
- Estimating Means and Monte Carlo Quantities
- Confidence Guarantees and Estimation Bias
- Comparing Quantum and Classical Estimation Under Equal Access Models
25Quantum Walk Algorithms9 topics
- Classical Random Walks and Quantum Walks
- Discrete-Time Coined Quantum Walks
- Continuous-Time Quantum Walks
- Graph Structure, Adjacency, and Transition Operators
- Interference and Spreading Behavior
- Quantum Walk Search
- Spectral Gaps and Algorithmic Performance
- Constructing Walk Operators as Circuits
- Graph Access, State Preparation, and Implementation Overhead
Stage 4
Simulation & Advanced Algorithms
Molecules, optimization, learning
15 modules · 159 topics
26Hamiltonians and Computational Representations10 topics
- Hamiltonians as Generators of Quantum Evolution
- Local Terms and Many-Body Interactions
- Pauli Strings and Operator Expansions
- Sparse and Structured Hamiltonians
- Spin Models and Computational Basis Choices
- Symmetries and Conserved Quantities
- Commutators and Noncommuting Terms
- Energy Scales, Norms, and Simulation Time
- Truncating Infinite-Dimensional Models
- Converting a Physical Model into a Computational Problem
27Digital Hamiltonian Simulation11 topics
- Approximating Time Evolution with Quantum Circuits
- Product Formulas and Trotter-Suzuki Decompositions
- Choosing Term Order and Time-Step Size
- Commutator Structure and Simulation Error
- Exponentiating Pauli Strings
- Higher-Order and Randomized Product Formulas
- Sparse-Hamiltonian Simulation Models
- Time-Dependent Hamiltonians
- Controlled Time Evolution for Other Algorithms
- Dividing Error Between Modeling, Simulation, and Gate Synthesis
- Comparing Simulation Methods for a Specific Hamiltonian
28Block Encodings and Linear Combinations of Unitaries10 topics
- Embedding a Matrix into a Larger Unitary
- Block-Encoding Normalization and Ancilla Registers
- Constructing Encodings from Available Data Access
- Linear Combinations of Unitaries
- PREPARE and SELECT Operations
- Postselection Probabilities and Success Amplification
- Oblivious Amplitude Amplification
- Combining and Multiplying Block Encodings
- Qubitization and Signal Operators
- Accounting for Encoding Cost in Algorithm Complexity
29Quantum Signal Processing and Singular Value Transformation10 topics
- Polynomial Transformations of Quantum Signals
- Alternating Signal Operations and Phase Rotations
- Polynomial Degree, Parity, and Boundedness Conditions
- Quantum Singular Value Transformation
- Transforming Singular Values of Encoded Matrices
- Polynomial Approximations to Useful Functions
- Hamiltonian Simulation Through Polynomial Transformations
- Matrix Inversion and Spectral Filtering Applications
- Approximation Precision and Circuit Resource Tradeoffs
- Recognizing the Access Assumptions Behind QSVT Algorithms
30Quantum Linear Algebra Algorithms11 topics
- Encoding Vectors and Linear Operators
- The Quantum Linear Systems Problem
- The HHL Algorithm and Its Computational Structure
- Condition Numbers and Solution Accuracy
- Sparsity and Data-Access Requirements
- Linear-System Solving Through Singular Value Transformation
- Preparing and Interpreting a Quantum Solution State
- Extracting Selected Properties of a Solution
- Why Reading the Entire Solution Can Remove an Advantage
- Preconditioning and Problem Structure
- Comparisons with Classical and Quantum-Inspired Methods
31Ground-State and Thermal-State Algorithms10 topics
- Ground-State Energy and Ground-State Preparation
- Initial-State Overlap and Success Probability
- Spectral Gaps and Preparation Difficulty
- Phase-Estimation-Based Energy Filtering
- Adiabatic Ground-State Preparation
- Imaginary-Time-Inspired Quantum Methods
- Gibbs States and Thermal Observables
- Purification-Based Thermal-State Representations
- Symmetry Sectors and Excited-State Access
- Assessing State Quality Through Measurable Quantities
32Quantum Simulation for Chemistry and Materials12 topics
- Electronic Structure as a Quantum Computing Problem
- Basis Sets, Active Spaces, and Model Reduction
- Fermionic Creation and Annihilation Operators
- Jordan-Wigner and Bravyi-Kitaev Mappings
- Particle Number and Other Physical Symmetries
- Qubit Reduction Through Known Symmetries
- Reference States and Physically Motivated State Preparation
- Energy Differences and Required Numerical Precision
- Molecular Dynamics Observables and Time Correlations
- Lattice Models and Materials Simulation Tasks
- Comparing Against Appropriate Classical Simulation Methods
- Connecting Scientific Accuracy to Quantum Resource Requirements
33Encoding Optimization Problems10 topics
- Binary Variables and Objective Functions
- Quadratic Unconstrained Binary Optimization
- Mapping QUBO Problems to Ising Hamiltonians
- Constraints and Penalty Terms
- Penalty Strength and Energy-Scale Tradeoffs
- Higher-Order Terms and Auxiliary Variables
- Feasible Subspaces and Constraint-Preserving Encodings
- Graph Structure and Hardware Connectivity
- Recovering and Verifying Candidate Solutions
- Comparing Encodings by Qubits, Depth, and Solution Quality
34Variational and Hybrid Quantum Algorithms12 topics
- Parameterized Quantum Circuits and Ansatz Families
- Quantum Measurements Inside a Classical Optimization Loop
- Defining Cost Functions and Training Objectives
- Parameter-Shift Gradient Estimation
- Finite Differences and Stochastic Gradient Methods
- Shot Noise in Objective and Gradient Estimates
- Expressibility, Entanglement, and Trainability
- Barren Plateaus and Uninformative Gradients
- Initialization and Problem-Informed Circuit Structure
- Optimizer Stopping Criteria and Repeated Runs
- Separating Optimization Error from Hardware and Sampling Error
- Accounting for Total Hybrid Execution Cost
35The Variational Quantum Eigensolver10 topics
- The Variational Principle and Energy Minimization
- Hamiltonian Decomposition into Measurable Terms
- Hardware-Efficient and Problem-Inspired Ansatze
- Unitary Coupled-Cluster Concepts
- Adaptive Ansatz Construction
- Symmetry Preservation and Physical Constraints
- Measurement Grouping and Energy-Estimation Cost
- Convergence Diagnostics and Local Minima
- Excited-State Extensions
- Validating VQE Against Exact Small-System Results
36The Quantum Approximate Optimization Algorithm11 topics
- Cost Hamiltonians and Mixing Hamiltonians
- Alternating Unitary Layers
- QAOA Depth and Parameter Structure
- Choosing Initial States and Mixers
- Constraint-Preserving Mixer Design
- Parameter Optimization and Transfer Strategies
- Sampling Solutions from an Optimized Circuit
- Approximation Quality and Success Probability
- Circuit Connectivity and Compilation Overhead
- Comparisons with Classical Heuristics and Exact Solvers
- Limits of Small-Instance Performance Extrapolation
37Quantum Machine Learning11 topics
- Learning from Classical Data and Quantum Data
- Quantum Feature Maps and Encoded Data Geometry
- Quantum Kernels and Kernel Estimation
- Variational Quantum Models
- Training Objectives and Measurement-Based Predictions
- Data Reuploading and Circuit Structure
- Generalization, Overfitting, and Trainability
- Data-Loading and Repeated-Measurement Costs
- Classical Simulability of Proposed Learning Models
- Strong Classical Baselines and Fair Comparisons
- Conditions Required for a Meaningful Learning Advantage
38Adiabatic Computing and Analog Quantum Simulation10 topics
- Adiabatic Evolution and the Adiabatic Theorem
- Initial and Problem Hamiltonians
- Spectral Gaps and Evolution Schedules
- Quantum Annealing and Thermal Effects
- Mapping Problems to Restricted Interaction Graphs
- Embedding Overhead and Parameter Precision
- Analog Simulation of Target Hamiltonians
- Programmability and Accessible Observables
- Digital, Analog, and Digital-Analog Tradeoffs
- Validation and Classical Comparison for Analog Experiments
39Measurement-Based Quantum Computing9 topics
- Resource States and Computation Through Measurements
- Graph States and Cluster States
- Preparing Entangled Resource States
- Measurement Bases as Computational Instructions
- Adaptive Measurements and Classical Feedforward
- Byproduct Operators and Pauli Frames
- Implementing Logical Circuit Operations by Measurement
- Universality and Non-Clifford Measurement Resources
- Comparing Resource Requirements with Circuit-Based Computation
40Quantum Complexity and Computational Limits12 topics
- P, BPP, BQP, and Their Definitions
- Promise Problems and Bounded-Error Computation
- Known Containments and Unresolved Class Relationships
- NP Problems and Unsupported Speedup Assumptions
- QMA and Quantum Verification
- The Local Hamiltonian Problem
- Query Lower Bounds and the Polynomial Method
- Worst-Case, Average-Case, and Practical Difficulty
- Sampling Problems and Classical Simulation Barriers
- Oracle Separations and Their Interpretation
- Approximation, Precision, and Input-Access Caveats
- Why Quantum Computing Does Not Make Every Problem Efficient
Stage 5
Hardware & Compilation
From circuit to physical chip
10 modules · 107 topics
41Computational Requirements for Quantum Hardware10 topics
- Defining a Physical Qubit
- Initialization, Gate Operations, and Measurement
- Coherence and Operation-Time Requirements
- Entangling Operations and Interaction Connectivity
- Native Gate Sets and Available Control
- Reset, Reuse, and Mid-Circuit Measurement
- Leakage Beyond the Computational Subspace
- Parallel Operations and Crosstalk Constraints
- Physical Resources Needed for Logical Qubits
- Matching Hardware Capabilities to Algorithm Requirements
42Physical Qubit Platforms11 topics
- Superconducting Qubits as Computing Elements
- Trapped-Ion Qubits and Shared Motional Resources
- Neutral-Atom Qubits and Rydberg Interactions
- Semiconductor Spin Qubits
- Photonic Qubits and Measurement-Driven Operations
- Oscillator Modes and Bosonic Encodings
- Proposed Topological Qubits and Their Physical Assumptions
- Comparing Connectivity, Gate Times, and Error Mechanisms
- Comparing Initialization, Measurement, and Qubit Movement
- Platform Tradeoffs for Error-Corrected Computation
- Separating Physical Demonstrations from System-Level Capability
43Quantum Processor Architecture and Execution10 topics
- Quantum Processing Units and Classical Control Systems
- Qubit Arrays, Couplers, and Interaction Zones
- Local, Long-Range, and Reconfigurable Connectivity
- Moving Quantum States and Moving Physical Qubits
- Control, Readout, and Feedback Latency
- Shared Resources and Restrictions on Parallel Execution
- Calibration Data as an Input to Computation
- Execution Windows and Device Drift
- Modular Processors and Intermodule Operations
- Hardware Abstraction and Backend Capability Descriptions
44Quantum Compilation and Gate Synthesis11 topics
- Compilation from Algorithms to Native Instructions
- Intermediate Circuit Representations
- Decomposing Composite and Multicontrolled Operations
- Single-Qubit Rotation Synthesis
- Two-Qubit Gate Decomposition
- Clifford and Non-Clifford Gate Accounting
- Approximate Synthesis and Precision Allocation
- Gate Cancellation, Commutation, and Circuit Rewriting
- Ancilla-Assisted Compilation Tradeoffs
- Preserving Circuit Semantics During Optimization
- Comparing Compiled Circuits with Hardware-Relevant Metrics
45Qubit Mapping, Routing, and Scheduling10 topics
- Logical Circuit Wires and Physical Qubit Assignments
- Initial Layout Selection
- Connectivity Constraints and Routing Requirements
- SWAP Insertion and Alternative Routing Strategies
- Gate Direction and Native Interaction Constraints
- Error-Aware Layout and Routing
- Scheduling Gates with Unequal Durations
- Idle Time, Parallelism, and Crosstalk
- Mapping Measurements Back to Logical Registers
- Comparing Layouts Across Multiple Compilation Runs
46Dynamic Circuits and Hybrid Runtime Systems10 topics
- Mid-Circuit Measurement and Conditional Execution
- Measurement-Based Reset and Qubit Reuse
- Classical Branching Inside a Quantum Program
- Real-Time Feedforward and Its Latency
- Repeat-Until-Success Subroutines
- Adaptive Algorithms and Experiment Updates
- Circuit-Level Feedback and Host-Level Optimization
- Batching Circuits and Parameter Sets
- Result Dependencies and Execution Ordering
- Estimating Runtime Beyond Quantum Gate Time
47Physical Noise and Device Error Models11 topics
- Relaxation and T1 Processes
- Dephasing, T2, and Inhomogeneous Broadening
- Gate Overrotation and Calibration Error
- Stochastic Pauli Errors and Model Approximation
- State-Preparation and Measurement Errors
- Leakage, Loss, and Erasure Events
- Spatially and Temporally Correlated Errors
- Crosstalk and Spectator-Qubit Effects
- Idle Errors and Scheduling Dependence
- Device Drift and Nonstationary Noise
- Choosing a Noise Model Appropriate to an Experiment
48Device Characterization and Benchmarking11 topics
- Readout Calibration and Assignment Matrices
- Quantum State Tomography
- Quantum Process Tomography
- Gate-Set Tomography Concepts
- Randomized Benchmarking and Average Error Estimates
- Interleaved and Cycle Benchmarking
- Coherence, Leakage, and Crosstalk Characterization
- Separating Gate Error from State-Preparation and Measurement Error
- Circuit-Level and Application-Level Benchmarks
- Logical Performance and Physical Performance Metrics
- Benchmark Assumptions and Interpretation Limits
49Quantum Error Mitigation12 topics
- Estimating Ideal Quantities from Noisy Computation
- Readout Error Mitigation
- Zero-Noise Extrapolation
- Probabilistic Error Cancellation
- Symmetry Verification and Postselection
- Virtual Distillation and Multiple-Copy Methods
- Learning Corrections from Classically Tractable Circuits
- Randomized Compiling and Noise Tailoring
- Dynamical Decoupling as Error Suppression
- Sampling Overhead and Uncertainty Amplification
- Distinguishing Mitigation, Suppression, and Error Correction
- Validating Mitigated Results Against Independent Evidence
50Efficient Measurement and Observable Estimation11 topics
- Decomposing Objectives into Observable Terms
- Grouping Compatible Measurements
- Basis Changes for Multiqubit Pauli Measurements
- Allocating Shots Across Unequal Variances
- Covariance Between Estimated Terms
- Overlap Estimation and Hadamard Tests
- Classical Shadows and Randomized Measurement Schemes
- Estimating Many Observables from Shared Data
- Adaptive Measurement Allocation
- Measurement Cost in Complete Algorithm Resource Estimates
- Reporting Observable Estimates with Uncertainty
Stage 6
Error Correction & Fault Tolerance
Making noisy qubits reliable
12 modules · 132 topics
51Principles of Quantum Error Correction11 topics
- Protecting Quantum Information Without Copying It
- Encoding Logical States into Larger Hilbert Spaces
- Bit-Flip and Phase-Flip Repetition Codes
- Detecting Errors Without Measuring Logical Information
- Error Syndromes and Recovery Operations
- Correctable Error Sets and the Knill-Laflamme Conditions
- Code Distance and Error-Correction Capability
- Degenerate Codes and Equivalent Errors
- Error Detection, Correction, and Erasure Recovery
- Physical Error Rates and Logical Failure Rates
- Repeated Correction in the Presence of Noisy Operations
52Stabilizer and CSS Codes11 topics
- The Pauli Group and Commutation Relations
- Stabilizer Generators and Code Spaces
- Logical Operators and Their Equivalence Classes
- Counting Encoded Qubits
- Binary Symplectic Representations
- Syndrome Computation in the Stabilizer Formalism
- The Five-Qubit Code
- Shor and Steane Codes
- CSS Construction from Classical Codes
- Encoding Circuits and Stabilizer Measurement
- Simulating Stabilizer Error-Correction Experiments
53Surface Codes and Topological Quantum Memories11 topics
- Data Qubits and Syndrome Qubits
- Local Stabilizers on a Two-Dimensional Lattice
- Planar and Rotated Surface-Code Layouts
- Boundaries, Logical Operators, and Code Distance
- Repeated Syndrome Measurement Cycles
- Error Chains and Detection Events
- Logical Memory Experiments
- Circuit-Level Noise and Correlated Faults
- Thresholds, Pseudothresholds, and Finite-Size Effects
- Physical-Qubit Overhead for a Target Logical Error Rate
- Connectivity and Scheduling Requirements of Surface Codes
54Syndrome Extraction and Decoding11 topics
- Ancilla Circuits for Parity Measurements
- Fault Propagation During Syndrome Extraction
- Measurement Errors and Syndrome History
- Constructing Decoding Problems from Detection Events
- Minimum-Weight Matching Decoders
- Union-Find and Belief-Propagation Approaches
- Degeneracy and Correlated-Error Information
- Decoding Erasures and Biased Noise
- Decoder Accuracy, Throughput, and Latency
- Pauli-Frame Updates and Deferred Physical Corrections
- Evaluating Decoders Under Matched Noise Assumptions
55Quantum LDPC and Other Qubit Code Families11 topics
- Code Rate, Distance, and Check Weight
- Quantum Low-Density Parity-Check Codes
- Hypergraph-Product Code Construction
- Product and Bicycle Code Families
- Geometric Locality and Long-Range Connectivity Tradeoffs
- Subsystem Codes and Gauge Operators
- Bacon-Shor and Color-Code Concepts
- Concatenated Code Architectures
- Measurement Schedules as Part of Code Design
- Comparing Memory Overhead with Logical-Operation Overhead
- Matching a Code Family to Hardware Constraints
56Bosonic Quantum Error Correction10 topics
- Encoding a Qubit in an Oscillator Mode
- Fock States and Phase-Space Descriptions
- Photon Loss, Dephasing, and Displacement Errors
- Cat-Code Encodings
- Binomial Codes
- Gottesman-Kitaev-Preskill Codes
- Finite-Energy States and Approximate Encodings
- Syndrome Extraction with Ancillary Systems
- Combining Bosonic and Qubit-Level Codes
- Resource and Noise Assumptions of Bosonic Protection
57Fault-Tolerant Quantum Computation10 topics
- Fault-Tolerant Gadgets and Error Propagation
- Fault-Tolerant State Preparation
- Fault-Tolerant Syndrome Measurement
- Fault-Tolerant Logical Measurement
- Transversal Operations and Their Restrictions
- Threshold Theorems and Their Assumptions
- Error Budgets Across a Complete Computation
- Leakage Handling and Correlated Faults
- Decoder and Classical-Control Requirements
- Demonstrating Logical Improvement as Code Size Increases
58Logical Gates and Magic-State Resources11 topics
- Logical Clifford Operations
- Code Deformation and Logical Qubit Movement
- Lattice Surgery and Joint Logical Measurements
- Gate Teleportation Within a Quantum Processor
- State Injection and Non-Clifford Operations
- Magic-State Distillation
- T States, Toffoli Resources, and Alternative Resource States
- Factory Throughput and Logical-Gate Demand
- Scheduling Computation Around Resource-State Availability
- Logical Rotation Synthesis and Precision Requirements
- Comparing Fault-Tolerant Gate Implementations
59Quantum Resource Estimation12 topics
- Defining Problem Size and Required Output Accuracy
- Logical Qubit, Gate, and Depth Estimates
- T Count, T Depth, and Toffoli Count
- State Preparation and Reversible Workspace
- Allocating Failure Probability Across Algorithm Components
- Selecting Code Distance from a Noise Model
- Data-Qubit, Syndrome-Qubit, and Factory Overhead
- Logical Cycle Time and Classical Feedback Latency
- Measurement Repetitions and Total Wall-Clock Time
- Space-Time Tradeoffs and Hardware Assumptions
- Sensitivity Analysis for Uncertain Device Parameters
- Comparing Resource Estimates on Consistent Terms
60Quantum Program Verification and Validation11 topics
- Specifications for Quantum Subroutines and Outputs
- Basis-State Tests and Phase-Sensitive Tests
- Comparing Statevectors Up to Global Phase
- Checking Controlled Operations and Relative-Phase Behavior
- Unitarity, Normalization, and Channel-Validity Checks
- Testing Ancilla Cleanup and Register Independence
- Comparing Equivalent Circuit Implementations
- Verifying Compiled Circuits Against Their Source
- Small-Instance Classical Reference Calculations
- Statistical Tests for Sampled Outputs
- Limits of Validation When Classical Simulation Becomes Infeasible
61Quantum Experiment Design and Reproducibility11 topics
- Defining the Question and Success Criteria
- Selecting Representative Problem Instances
- Recording Circuits, Parameters, and Compilation Settings
- Recording Backend Properties and Calibration Context
- Separating Training, Tuning, and Evaluation Instances
- Randomizing Execution Order to Reduce Drift Bias
- Choosing Shot Budgets and Repetition Plans
- Comparing Ideal, Noisy, and Hardware Results
- Tracking Queue Time, Execution Time, and Classical Overhead
- Preserving Raw Counts and Processing Decisions
- Reporting Negative Results and Reproducibility Limits
62Evaluating Quantum Advantage and Application Fit12 topics
- Theoretical Speedup and Practical Computational Advantage
- Exact, Approximate, and Heuristic Comparisons
- Choosing Strong Classical Baselines
- Matching Input Access and Output Requirements
- Including Data Preparation and Result Extraction
- Accounting for Error Correction or Mitigation Costs
- Benchmark Selection and Favorable-Instance Bias
- Scaling Studies and Finite-Size Effects
- Independent Verification of Application-Relevant Results
- Distinguishing Demonstrated Results from Resource Projections
- Identifying Problems with Unfavorable Quantum Overheads
- Writing a Qualified Technical Feasibility Assessment
Stage 7
Laboratories & Project
Lab work, then a full project
4 modules · 43 topics
63Foundational Quantum Programming Laboratories10 topics
- Simulating Single-Qubit States and Basis Changes
- Building Interference Circuits and Predicting Outcomes
- Preparing Bell and GHZ States
- Comparing Pure States with Classical Mixtures
- Implementing Quantum Channels in a Simulator
- Building a Reversible Function with Ancilla Cleanup
- Comparing Statevector and Stabilizer Simulation
- Implementing Small Quantum Query Algorithms
- Testing Qubit Ordering and Measurement Interpretation
- Measuring Sampling Error Across Repeated Experiments
64Quantum Algorithm and Simulation Laboratories11 topics
- Implementing the QFT and Its Approximate Form
- Estimating Eigenphases of Known Unitaries
- Building a Small Order-Finding Demonstration
- Comparing Grover Search with Explicit Oracle Costs
- Estimating an Amplitude Under Different Shot Budgets
- Simulating a Small Spin Hamiltonian
- Comparing Product-Formula Accuracy and Circuit Depth
- Solving a Small Chemistry Problem with VQE
- Evaluating QAOA Against Classical Optimization Baselines
- Testing a Quantum Kernel with Matched Classical Comparisons
- Producing a Resource Estimate for a Chosen Algorithm
65Noise, Error-Correction, and Systems Laboratories10 topics
- Comparing Compiled Circuits on Different Connectivity Graphs
- Executing a Circuit with Mid-Circuit Measurement and Feedforward
- Reconstructing a Small Quantum State from Measurements
- Evaluating Error Mitigation with Full Uncertainty Accounting
- Simulating Repetition, Stabilizer, and Surface-Code Memories
- Building a Syndrome-Extraction Circuit
- Comparing Decoder Behavior Under Different Error Models
- Tracking Logical Error as Physical Noise and Code Size Change
- Estimating Magic-State Factory Demand
- Comparing Hardware Results with Validated Noisy Simulations
66Integrated Quantum Computing Project12 topics
- Defining a Computational Problem and Classical Baseline
- Specifying Input Access, Output, Accuracy, and Confidence
- Selecting an Algorithm and Computational Model
- Building Reusable Quantum and Classical Components
- Validating Small Instances and Numerical Assumptions
- Compiling for a Chosen Hardware Architecture
- Evaluating Noise, Sampling, and Approximation Errors
- Selecting a Mitigation or Fault-Tolerance Strategy
- Estimating Physical Resources and Total Runtime
- Comparing Results Against the Original Success Criteria
- Documenting Reproducible Experiments and Remaining Limitations
- Presenting an Evidence-Based Assessment of Application Feasibility
Fifteen minutes.Every day.
- 1
A lesson fits a lunch break
One idea at a time, in short slides. A whole lesson takes about fifteen minutes.
- 2
Practice with instant feedback
Questions sit inside the lesson. Answer one and see right away whether you got it.
- 3
A streak that brings you back
A lesson a day keeps the streak alive. Small, steady sessions carry you through.
- 1
A lesson fits a lunch break
One idea at a time, in short slides. A whole lesson takes about fifteen minutes.
- 2
Practice with instant feedback
Questions sit inside the lesson. Answer one and see right away whether you got it.
- 3
A streak that brings you back
A lesson a day keeps the streak alive. Small, steady sessions carry you through.
For the first quantum hires.
Developers writing their first circuit
Physics grads bound for industry
R&D teams testing quantum use cases
Where this course leads.
The job this course is built around, and how people get into it.
On the job
- Express a problem as a quantum circuit
- Run it on a simulator and on real hardware
- Reduce the errors noise adds to the result
How people get in
A young field: most roles ask for a degree in physics, computer science or maths, often a graduate one.
Be first in line.
Early access for individuals, pilots for teams. Tell us who's learning.
enterprise@astratrainer.com