# The Qiskit Elements¶

## Terra¶

Terra, the ‘earth’ element, is the foundation on which the rest of Qiskit lies. Terra provides a bedrock for composing quantum programs at the level of circuits and pulses, to optimize them for the constraints of a particular device, and to manage the execution of batches of experiments on remote-access devices. Terra defines the interfaces for a desirable end-user experience, as well as the efficient handling of layers of optimization, pulse scheduling and backend communication.

Qiskit Terra is organized in six main modules:

1. Circuit A quantum circuit is a model for quantum computing in which a computation is done by performing a sequence of quantum operations (usually gates) on a register of qubits. A quantum circuit usually starts with the qubits in the $$|0,…,0>$$ state and these gates evolve the qubits to states that cannot be efficiently represented on a classical computer. To extract information on the state a quantum circuit must have a measurement which maps the outcomes (possible random due to the fundamental nature of quantum systems) to classical registers which can be efficiently represented.

2. Pulse A pulse schedule is set of pulses which are sent to a quantum experiment that are applied to a channel (experimental input line). This is a lower level than circuits and requires each gate in the circuit to be represented as a set of pulses. At this level the experiments can be designed to reduce errors (dynamical decoupling, error mitigation, and optimal pulse shapes).

3. Transpiler A major part of research on quantum computing is working out how to run a quantum circuits on real devices. In these devices, experimental errors and decoherence introduce errors during computation. Thus, to obtain a robust implementation it is essential to reduce the number of gates and the overall running time of the quantum circuit. The transpiler introduces the concept of a pass manager to allow users to explore optimization and find better quantum circuits for their given algorithm. We call it a transpiler as the end result is still a circuit.

4. Providers Once the user has made the circuits to run on the backend they need to have a convenient way of working with it. In Terra we do this using four parts:

1. A Provider is an entity that provides access to a group of different backends (for example, backends available through the IBM Quantum Experience). It interacts with those backends to, for example, find out which ones are available, or retrieve an instance of a particular backend.

2. Backend represent either a simulator or a real quantum computer and are responsible for running quantum circuits and returning results. They have a run method which takes in a qobj as input and returns a BaseJob object. This object allows asynchronous running of jobs for retrieving results from a backend when the job is completed.

3. Job instances can be thought of as the “ticket” for a submitted job. They find out the execution’s state at a given point in time (for example, if the job is queued, running, or has failed) and also allow control over the job.

4. Result. Once the job has finished Terra allows the results to be obtained from the remote backends using result = job.result(). This result object holds the quantum data and the most common way of interacting with it is by using result.get_counts(circuit). This method allows the user to get the raw counts from the quantum circuit and use them for more analysis with quantum information tools provided by Terra.

5. Quantum Information To perform more advanced algorithms and analysis of the circuits run on the quantum computer, it is important to have tools to implement simple quantum information tasks. These include methods to both estimate metrics and generate quantum states, operations, and channels.

6. Visualization In Terra we have many tools to visualize a quantum circuit. This allows a quick inspection of the quantum circuit to make sure it is what the user wanted to implement. There is a text, python and latex version. Once the circuit has run it is important to be able to view the output. There is a simple function (plot_histogram) to plot the results from a quantum circuit including an interactive version. There is also a function plot_state and plot_bloch_vector that allow the plotting of a quantum state. These functions are usually only used when using the statevector_simulator backend but can also be used on real data after running state tomography experiments (Ignis).

## Aer¶

Aer, the ‘air’ element, permeates all Qiskit elements. To really speed up development of quantum computers we need better simulators, emulators and debuggers. Aer helps us understand the limits of classical processors by demonstrating to what extent they can mimic quantum computation. Furthermore, we can use Aer to verify that current and near-future quantum computers function correctly. This can be done by stretching the limits of simulation, and by simulating the effects of realistic noise on the computation.

Aer provides a high performance simulator framework for quantum circuits using the Qiskit software stack. It contains optimized C++ simulator backends for executing circuits compiled in Terra. Aer also provides tools for constructing highly configurable noise models for performing realistic noisy simulations of the errors that occur during execution on real devices.

Qiskit Aer includes three high performance simulator backends:

Qasm Simulator

Allows ideal and noisy multi-shot execution of qiskit circuits and returns counts or memory. There are multiple methods that can be used that simulate different cirucits more efficiently. These inlude:

1. statevector - Uses a dense statevector simulation.

2. stabilizer - Uses a Clifford stabilizer state simulator that is only valid for Clifford circuits and noise models.

3. extended_stabilizer - Uses an approximate simulator that decomposes circuits into stabilizer state terms, the number of which grows with the number of non-Clifford gates.

4. matrix_product_state - Uses a Matrix Product State (MPS) simulator.

Statevector Simulator

Allows ideal single-shot execution of qiskit circuits and returns the final statevector of the simulator after application.

Unitary Simulator

Allows ideal single-shot execution of qiskit circuits and returns the final unitary matrix of the circuit itself. Note that the circuit cannot contain measure or reset operations for this backend.

## Ignis¶

Ignis, the ‘fire’ element, is dedicated to fighting noise and errors and to forging a new path. This includes better characterization of errors, improving gates, and computing in the presence of noise. Ignis is meant for those who want to design quantum error correction codes, or who wish to study ways to characterize errors through methods such as tomography, or even to find a better way for using gates by exploring dynamical decoupling and optimal control.

Ignis provides code for users to easily generate circuits for specific experiments given a minimal set of user input parameters. Ignis code contains three fundamental building blocks:

Circuits

The circuits module provides the code to generate the list of circuits for a particular Ignis experiment based on a minimal set of user parameters. These are then run on Terra or Aer.

Fitters

The results of an Ignis experiment are passed to the Fitters module where they are analyzed and fit according to the physics model describing the experiment. Fitters can plot the data plus fit and output a list of parameters.

Filters

For certain Ignis experiments, the fitters can output a Filter object. Filters can be used to mitigate errors in other experiments using the calibration results of an Ignis experiment.

Qiskit Ignis is organized into three types of experiments that can be performed:

Characterization

Characterization experiments are designed to measure parameters in the system such as noise parameters (T1, T2-star, T2), Hamiltonian parameters such as the ZZ interaction rate and control errors in the gates.

Verification

Verification experiments are designed to verify gate and small circuit performance. Verification includes state and process tomography, quantum volume and randomized benchmarking (RB). These experiments provide the information to determine performance metrics such as the gate fidelity.

Mitigation

Mitigation experiments run calibration circuits that are analyzed to generate mitigation routines that can be applied to arbitrary sets of results run on the same backend. Ignis code will generate a list of circuits that run calibration measurements. The results of these measurements will be processed by a Fitter and will output a Filter than can be used to apply mitigation to other results.

## Aqua¶

Aqua, the ‘water’ element, is the element of life. To make quantum computing live up to its expectations, we need to find real-world applications. Aqua is where algorithms for quantum computers are built. These algorithms can be used to build applications for quantum computing. Aqua is accessible to domain experts in chemistry, optimization, finance and AI, who want to explore the benefits of using quantum computers as accelerators for specific computational tasks.

Problems that may benefit from the power of quantum computing have been identified in numerous domains, such as Chemistry, Artificial Intelligence (AI), Optimization and Finance. Quantum computing, however, requires very specialized skills. To address the needs of the vast population of practitioners who want to use and contribute to quantum computing at various levels of the software stack, we have created Qiskit Aqua.