## 📄️ Quantum gates and circuits

Quantum gates and circuits are essential when working on quantum computing. Here we describe basic treatment of them in QURI Parts.

## 📄️ Sampler

Unlike statevector simulation, sampling measurements are necessary in order to estimate expectation value of operators on a quantum computer. In sampling measurements, execution of a quantum circuit and a subsequent measurement of qubits are repeated multiple times. Estimation of expectation value of operators is then performed using statistics of the repeated measurements.

## 📄️ Quantum states

Quantum states are essential when working on quantum computing. Here we describe basic treatment of them in QURI Parts.

## 📄️ Operators

In this tutorial, we introduce 2 objects, Operator and PauliLabel, that represents operators in quantum mechanics. You may construct various physical observables with them. In QURI Parts, we mainly work with operators consists of Pauli strings.

## 📄️ Estimators

In this tutorial, we introduce how to compute expectation values of operators $O$ for a given state $|\psi \rangle$:

## 📄️ Fermion-qubit mappings

In order to simulate the dynamics of physical systems with a quantum computer, it is necessary to map the Hamiltonian of an electron to the qubit counterpart. Hamiltonians for fermionic systems, as typically used in quantum chemistry, are often expressed using anti-commuting creation and annihilation operators: $ci^{\dagger}$, $ci$ under second quantization. If we can rewrite the creation and annihilation operators as Pauli operators that can act on qubits, we can represent them on a quantum computer.

## 📄️ Sampling estimation

In order to estimate expectation value of operators on a quantum computer, sampling measurements are necessary. In sampling measurements, execution of a quantum circuit and a subsequent measurement of qubits are repeated multiple times. Estimation of expectation value of operators is then performed using statistics of the repeated measurements.

## 🗃️ Real devices

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## 📄️ Circuit transpiler

For various reasons, we may want to convert a quantum circuit to another quantum circuit that is semantically equivalent.

## 📄️ Noisy simulation

Quantum circuits running on real machines are affected by a variety of stochastic noises. In QURI Parts, noise models can be defined to represent these noises and reproduce them on simulators. (Qulacs is used in this tutorial.)

## 🗃️ Error Mitigation

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## 📄️ Data recording

Sometimes it is useful to store the snapshots of data during the calculation for some tasks such as debugging. QURI Parts provides the smart way to do it with @recordable decorator.