A quantum computing simulator.

## What Is PyQCS?

PyQCS is a Quantum Computing Simulator built for physics. It currently features two simulator backends for different purposes, and a way to construct circuits in a relatively readable manner.

By default PyQCS employs a relatively slow simulator backend using dense state vectors stored in NumPy arrays. The gates are implemented as NumPy ufuncs. Because the states are implemented as NumPy arrays there is a significant overhead compared to other simulators. Note that any implementation using dense state vectors shows exponential growth in the number of qbits. Therefore this simulator backend is limited to qbit numbers below 30 for reasonable performance. For simulations requiring more qbits we recommend a high performance framework, such as GPT’s QIS module.

The second backend uses a graphical state representation (see for instance arXiv:quant-ph/0504117) which allows for the simulation of stabilizer states and -circuits. The graphical simulator is considerably faster, in particular it does not exhibit exponential growth in the number of qbits. The graphical states are available as pyqcs.graph.state.GraphState.

Unlike other simulators PyQCS focuses on the state: Users start from a state, modify the state (using circuits) and then either look at the state or sample from the state. This direct access to the state is useful when debugging circuits or when considering physical problems. However, it slows down compuations.

## Using PyQCS

To do some computation one has to build a quantum circuit and apply it to a state. States are created using pyqcs.State.new_zero_state(<number of qbits>).

Circuits are built from the fundamental gates (see Built-in Gates) by joining them together using the | operator:

```from pyqcs import H, CX, X

circuit = H(0) | CX(1, 0) | X(1)
```

The usage of the | is in analogy to the UNIX pipe: gates are applied from left to right. This is in agreement with the Feynman quantum circuit diagrams.

Note: the circuit above would have the following matrix representation:

```X(1) CZ(1,0) H(0)
```

Applying a circuit to a state is done using multiplication:

```from pyqcs import State

state = State.new_zero_state(2)
resulting_state = circuit * state
```

New in v2.2.0 is the circuitpng function that allows displaying circuits as PNGs (using a pdflatex implementation and imagemagick):

```from pyqcs import H, CX, circuitpng
circuit = (H(1) | H(2)) | CX(2, 1) | (H(1) | H(2))
circuitpng(circuit)
```

## Built-in Gates

PyQCS currently has the following gates built-in:

X
Pauli-X or NOT gate. Flips the respective qbit.
H
C = CX
CNOT (controlled NOT) gate. Flips the act-qbit, if the control-qbit is set.
R
R, Rz or R_phi, the rotation gate. Rotates the respective qbit around a given angle.
M
Measurement gate: this gate measures the respective gate, collapsing the wave function and storing the result in the classical part of the state.
Z
Pauli-Z gate.
B = CZ
Controlled Z gate.

## TODOs

• Add a subclass of pyqcs.state.state.BasicState that has an improved __str__ method.
• Write lot’s of documentation.
• Add a NoisyGateListExecutor that allows to implement a noise model.
• Allow graphical states to be multiplied with each other to compute the overlap.
• Add a way to use graphical states as basis states for compression.
• Add a fast dense state vector simulator.
• Add a way to export circuits to GPT’s QIS module.
 [1] Real quantum computers have an intrinsic time evolution. This is omitted in PyQCS and reintroduced for error simulation. PyQCS therefore operates on a discrete quasi-time with every time-site being before or after a gate application.