Whitepaper Tutorials¶ Circuits and Gates Overview Setup Basic Circuits and Outputs Built-in Gates Specifying the Input State and Composing Circuits Circuit Transformation and Visualization Gradient and Variational Optimization Overview Setup PQC Grad and JIT Optimization via ML Backend Optimization via Scipy Interface Density Matrix and Mixed State Evolution Overview Setup Density Matrix Simulation with tc.DMCircuit AD and JIT Compatibility Monte Carlo Noise Simulation with tc.Circuit Externalizing the Randomness Different Types of Measurement API Overview Setup Conditional Measurements Post Selection Plain Measurements Evaluation on Pauli String Sum Overview Setup Parameterized Quantum Circuits Main Optimization Loop 1. Pauli-string Operators Sum 2. Vmap the Pauli-string Operators Sum 3. Sparse Matrix 4. Dense Matrix 5. MPO Utilizing vmap in Quantum Circuit Simulations Overview Setup vmap the Input States Minimal Example vmap the Circuit Weights Minimal Example vmap the Quantum Noise Minimal Example vmap the Circuit Structure Minimal Example vmap the Circuit Measurements Minimal Example QuOperator in TensorCircuit Overview Setup Introduction to QuOperator/QuVector QuVector as the Input State for the Circuit QuVector as the Output State of the Circuit QuOperator as Operator to be Evaluated on the Circuit QuOperator as the Quantum Gate Applied on the Circuit Customized Contraction Overview Setup Advanced Automatic Differentiation Overview Setup Forward AD Jacobian Quantum Fisher Information Hessian \(\langle \psi \vert H \vert \partial \psi \rangle\)