Tutorials

The algorithms in this category focus on quantum circuits whose output distributions encode solutions to structured problems with verifiable output. Verifiability means that you can check the consistency between measured data, either through evaluating the chosen bitstring or by knowing that false positives do not occur.

The tutorials highlight techniques where repeated sampling enables estimation of problem-specific quantities (for example, cost function values or spectral weights). These methods are particularly relevant for optimization and simulation tasks with symmetries.

• Sample-based quantum diagonalization of a chemistry Hamiltonian

• Compute dissociation curves for strong coupling systems with QunaSys QSCI

• Quantum approximate optimization algorithm

• Advanced techniques for QAOA

• Pauli Correlation Encoding to reduce Maxcut requirements

• Higher-order binary optimization with Q-CTRL's Optimization Solver

These tutorials focus on estimating physically meaningful quantities, such as energy or correlation values, by preparing quantum states and measuring observables. Techniques include both variational and Trotterized circuit approaches that balance circuit expressiveness with circuit-depth efficiency. Emphasis is placed on workflows that reduce quantum resource demands while maintaining accuracy, and enabling practical estimation of observables in chemical and physical systems.

• Krylov quantum diagonalization of lattice Hamiltonians

• Nishimori phase transition

• Dissociation PES curves with Qunova HiVQE

• Variational quantum eigensolver

• Ground state energy estimation of the Heisenberg chain with VQE

• Quantum kernel training

• CHSH inequality

This section features algorithms with well-defined theoretical guarantees that are designed to run on future error-corrected quantum hardware. The circuits or sampling overhead for these algorithms scale in a manner that is not depth-efficient and are thereby are more likely to demonstrate quantum advantage when fault-tolerant quantum computers exist. These tutorials illustrate how the methods operate in idealized settings and demonstrate small scale examples.

• Grover's algorithm

Workload optimization focuses on either efficient orchestration of classical and quantum resources or tailored methods for improving quantum circuit manipulation.

• Qiskit AI-powered transpiler service introduction

• Transpilation optimizations with SABRE

• Compare transpiler settings

• Long-range entanglement with dynamic circuits

Addons enable advanced circuit manipulation, such as cutting, backpropagating observables, or approximating circuits, that allow users to sidestep hardware limitations at the cost of increased classical compute overhead.

• Approximate quantum compilation for time evolution circuits

• Operator backpropagation (OBP) for estimation of expectation values

• Wire cutting for expectation values estimation

• Circuit cutting for periodic boundary conditions

• Circuit cutting for depth reduction

Error mitigation addresses the challenge of noise without full fault tolerance by recovering accurate expectation values through controlled circuit manipulation and post-processing.

• Utility-scale error mitigation with probabilistic error amplification

• Combine error mitigation options with the estimator primitive

• Error mitigation with the IBM Circuit function

• Real-time benchmarking for qubit selection

Error detection identifies faulty operations to return noise-free results shot-by-shot by post-processing.

• Repeat until success

• Repetition codes