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Quantum Computing
Programmiere Quantencomputer — und weißt, wann sie sich lohnen.
Der komplette Kurs
- Module
- 66
- Themen
- 703
- Min. pro Lektion
- 15
Was du danach kannst.
Quantenschaltkreise bauen und simulieren
Etappe 2 · Qubits, Gates & Circuits
Grover, QFT und Phasenschätzung implementieren
Etappe 3 · Core Algorithms
VQE für Chemie, QAOA für Optimierung fahren
Etappe 4 · Simulation & Advanced Algorithms
Schaltkreise für echte Hardware kompilieren
Etappe 5 · Hardware & Compilation
Abschätzen, was Fehlertoleranz kosten wird
Etappe 6 · Error Correction & Fault Tolerance
Ein Quantenprojekt gegen klassisch benchmarken
Etappe 7 · Laboratories & Project
Sieben Etappen.Ein stetiger Aufstieg.
Ein Qubit am Anfang. Ein kompiliertes, fehlerbewusstes Programm am Ende.
66Module
in 7 Etappen
703Themen
≈ 11 pro Modul
≈176Stunden
in Lektionen à 15 Minuten
≈23Monate
≈12Monate
≈6Monate
bis zum Ende des Kurses
- 1
Math & Classical Foundations
Die Mathematik, in der Qubits geschrieben sind
5 Module · 52 Themen · ≈ 13 Std.
- 2
Qubits, Gates & Circuits
Wie ein Qubit rechnet
11 Module · 117 Themen · ≈ 29 Std.
- 3
Core Algorithms
Die Algorithmen, die alles begannen
9 Module · 93 Themen · ≈ 23 Std.
- 4
Simulation & Advanced Algorithms
Moleküle, Optimierung, Lernen
15 Module · 159 Themen · ≈ 40 Std.
- 5
Hardware & Compilation
Vom Schaltkreis zum physischen Chip
10 Module · 107 Themen · ≈ 27 Std.
- 6
Error Correction & Fault Tolerance
Verrauschte Qubits verlässlich machen
12 Module · 132 Themen · ≈ 33 Std.
- 7
Laboratories & Project
Laborarbeit, dann ein ganzes Projekt
4 Module · 43 Themen · ≈ 11 Std.
Monate
04812160246801234
MonateZiel · ≈ 23 Monate · ≈ 12 Monate · ≈ 6 Monate
Stunden und Monate sind Schätzungen: eine 15-Minuten-Lektion pro Thema, jeden Tag.
Jedes Modul.Jedes Thema.
Modul- und Themen-Titel bleiben Englisch — die Sprache, in der das Fach arbeitet.
Etappe 1
Math & Classical Foundations
Die Mathematik, in der Qubits geschrieben sind
5 Module · 52 Themen
1Foundations of Quantum Computing10 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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
Etappe 2
Qubits, Gates & Circuits
Wie ein Qubit rechnet
11 Module · 117 Themen
6Qubit States and Quantum State Evolution10 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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
Etappe 3
Core Algorithms
Die Algorithmen, die alles begannen
9 Module · 93 Themen
17State Preparation and Data Encoding11 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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
Etappe 4
Simulation & Advanced Algorithms
Moleküle, Optimierung, Lernen
15 Module · 159 Themen
26Hamiltonians and Computational Representations10 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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
Etappe 5
Hardware & Compilation
Vom Schaltkreis zum physischen Chip
10 Module · 107 Themen
41Computational Requirements for Quantum Hardware10 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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
Etappe 6
Error Correction & Fault Tolerance
Verrauschte Qubits verlässlich machen
12 Module · 132 Themen
51Principles of Quantum Error Correction11 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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
Etappe 7
Laboratories & Project
Laborarbeit, dann ein ganzes Projekt
4 Module · 43 Themen
63Foundational Quantum Programming Laboratories10 Themen
- 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 Themen
- 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 Themen
- 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 Themen
- 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
Fünfzehn Minuten.Jeden Tag.
- 1
Eine Lektion passt in die Mittagspause
Eine Idee nach der anderen, auf kurzen Folien. Eine ganze Lektion dauert etwa fünfzehn Minuten.
- 2
Übung mit sofortigem Feedback
Die Fragen stecken in der Lektion. Antworte und sieh sofort, ob es sitzt.
- 3
Eine Serie, die dich zurückholt
Eine Lektion am Tag hält die Serie am Leben. Kleine, stetige Schritte tragen dich durch.
- 1
Eine Lektion passt in die Mittagspause
Eine Idee nach der anderen, auf kurzen Folien. Eine ganze Lektion dauert etwa fünfzehn Minuten.
- 2
Übung mit sofortigem Feedback
Die Fragen stecken in der Lektion. Antworte und sieh sofort, ob es sitzt.
- 3
Eine Serie, die dich zurückholt
Eine Lektion am Tag hält die Serie am Leben. Kleine, stetige Schritte tragen dich durch.
Für die ersten Quantum-Hires.
Devs beim ersten Schaltkreis
Physik-Absolventen auf dem Weg in die Industrie
R&D-Teams, die Quanten-Use-Cases testen
Wo du am meisten wächst
Ein Quantenprojekt gegen klassisch benchmarken
Etappe 7 · Laboratories & Project
Wohin dieser Kurs führt.
Der Job, um den dieser Kurs gebaut ist, und wie Menschen hineinkommen.
Im Job
- Ein Problem als Quantenschaltkreis ausdrücken
- Ihn auf einem Simulator und auf echter Hardware ausführen
- Die Fehler reduzieren, die Rauschen zum Ergebnis hinzufügt
So kommt man hinein
Ein junges Feld: Die meisten Rollen verlangen ein Studium in Physik, Informatik oder Mathematik, oft mit Master oder Promotion.
Sei von Anfang an dabei.
Frühzugriff für Einzelpersonen, Piloten für Teams. Sag uns, wer lernt.
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