htlogicalgates 0.6.2

Find circuit implementations for logical gates of QECCs.

Hardware-Tailored Logical Gates

This package can be used to compile circuit implementations for logical Clifford gates of quantum error-correcting codes. The main features are:

• works for every stabilizer code (runtime increases with code size),
• works for every logical Clifford gate, and
• by providing a connectivity map of qubits, hardware-tailored circuits can be obtained.

During circuit compilation, the number of two-qubit gates is minimized. By constructing hardware-tailored circuits, further qubit permutations are avoided altogether.

Requirements

A list of Python package dependencies is included in pyproject.toml and are automatically installed together with the package.

Furthermore, a valid Gurobi license is neccesary for the circuit compilation. There exists a wide-range of licences, including one for academic use that is free of charge. You can find further information on the Gurobi downloads page.

Installation

This Python package is available on PyPI and can be installed using pip via

pip install htlogicalgates

Alternatively, you can clone this repository and include it in your project.

License

This package is distributed under the MIT License.

If you want to support work like this, please cite: our paper (tba)

Tutorials

The following sections of this readme, along with more examples and guiding information, can be found as Jupyter notebook tutorials:

• Basic Tutorial
• Advanced Tutorial

How to tailor logical circuits

The main workflow for tailoring a circuit starts with creating three central objects:

import htlogicalgates as htlg

stab_code = htlg.StabilizerCode("4_2_2")
connectivity = htlg.Connectivity("circular", num_qubits=4)
logical_gate = htlg.Circuit(2)
logical_gate.h(0)

After importing the package, we create three objects:

• First, we create a StabilizerCode for which we wish to find a logical circuit. In this example, we pass "4_2_2", which selects the $⟦4,2,2⟧$ color code. Some common codes are predefined (see below), but custom codes can also be specified through a set of stabilizer generators.

• Next, we create a Connectivity that stores connections between qubits on the target hardware. Two-qubit gates will only be allowed between connected qubits. For this example, we use a "circular" connectivity on num_qubits=4 qubits. Other predefined connectivities can be queried via htlg.available_connectivities(). Moreover, a custom connectivity can be created from an adjacency matrix.

• Finally, we initialize a Circuit with the number of logical qubits and add a Hadamard gate on the first qubit (note that we count qubits starting at 0). In the following we will tailor a circuit that implements the action of this circuit on the logical level of the stabilizer code.

Note that we created a Connectivity for $n=4$ qubits and a logical Circuit for $k=2$ qubits since we are using the $⟦n=4,k=2,2⟧$-code.

Now we can pass these objects to the function tailor_logical_gate:

circ, status = htlg.tailor_logical_gate(stab_code, connectivity, logical_gate, num_cz_layers=2)

The parameter num_cz_layers determines the number of CZ gate layers in the ansatz circuit. Generally speaking, more CZ layers make the ansatz more expressive and can lead to circuits with less two-qubit gates in total, while increasing runtime. If you can not find a specific gate, try to increase the number of CZ gate layers.

The return value status indicates the state of the optimization:

• "Optimal" : The returned circuit is optimal in terms of two-qubit gates.
• "Bound {n}" : The returned circuit is not optimal in terms of two-qubit games but there is no circuit with less than $n$ two-qubit gates.
• "Infeasible" : There is no physical circuit for the given stabilizer code, connectivity, logical circuit, and number of CZ gate layer.
• "Time out" : A physical circuit was not found in the given time limit.

If the status message is "Optimal" or "Bound {n}", then circ contains the physical circuit implementation. Otherwise, it is None.