# PQCA (Partitioned Quantum Cellular Automata)

A quantum cellular automaton iteratively applies some update circuit to some initial state.
A partitioned quantum cellular automaton (PQCA) derives its update circuit by partitioning
a lattice of qubits into cells, and then applying the same circuit to each cell.
The full update circuit is created by composing several such partitioned updates.
There is a review of Quantum Cellular Automata by Terry Farrelly, published in Quantum, and available at [doi:10.22331/q-2020-11-30-368](https://doi.org/10.22331/q-2020-11-30-368).

This python module allows for the easy creation and execution of partitioned quantum cellular automata.
To create an automaton you will need:
 - A starting state (list of 0s and 1s)
 - Update Frames (see `pqca.update_frame`)
 - A simulator / quantum computer (see `pqca.backend`)

An Update Frame combines a tessellation with a circuit to be applied
to each cell in that tessellation.
A tessellation just partitions a list of qubits into cells. For example
`pqca.tessellation.one_dimensional(10,2)`
partitions 10 qubits into 5 cells, each of size 2.
The Update Frame would then need to be a circuit on 2 qubits.
For more complicated tessellations you can use, e.g.
`pqca.tessellation.n_dimensional([4,2,4],[2,2,2])`
which partitions 32 qubits as though they were arranged in a lattice
of shape `4 x 2 x 4`, with each cell of size `2 x 2 x 2`.
The Update Frame would then need to be a circuit on 8 qubits.

One can then call `next(automaton)` which will advance the internal state of the automaton and return the new state.

## Installation

Install via `pip` from the command line with the command:
```
pip install pqca
```

## Example

Here is an example that creates two update frames,
both applying a simple CX gate, but with offset tessellations.
```python
# Create circuit
cx_circuit = qiskit.QuantumCircuit(2)
cx_circuit.cx(0, 1)

# Create tessellation
tes = pqca.tessellation.one_dimensional(10, 2)

# Create update frames
update_1 = pqca.UpdateFrame(tes, cx_circuit)
update_2 = pqca.UpdateFrame(tes.shifted_by(1), cx_circuit)


# Create initial state
initial_state = [1]*10

# Specify a backend; `pqca.backend.qiskit()` returns IBM's Aer simulator by default
# See backend.py for more details and instructions on coding your own backend
backend = pqca.backend.qiskit()

# Create the automaton
automaton = pqca.Automaton(initial_state, [update_1, update_2], backend)

# The automaton can be called like any other iterator
# The following line advances the internal state, and returns the new state
next(automaton)
```

## Documentation

Detailed documentation can be found at [readthedocs.io](https://partitioned-quantum-cellular-automata.readthedocs.io/en/latest/) as well as
in the docstrings of the python files themselves.

## Licensing

The source code is available under the MIT licence and can be found
on [Hector Miller-Bakewell's github](https://github.com/hmillerbakewell/partitioned-quantum-cellular-automata).

## Acknowledgements

This package was created as part of the [QuTune Project](https://iccmr-quantum.github.io/).