PyTheus, a highly-efficient discovery framework for quantum optics experiments

Digital Discovery of 100 diverse Quantum Experiments with PyTheus
Carlos Ruiz-Gonzalez, Sören Arlt, Jan Petermann, Sharareh Sayyad, Tareq Jaouni, Ebrahim Karimi, Nora Tischler, Xuemei Gu, Mario Krenn
Quantum 7, 1204 (2023).

Digital Discovery of a Scientific Concept at the Core of Experimental Quantum Optics
Sören Arlt, Carlos Ruiz-Gonzalez, Mario Krenn

The package can be installed with

pip install pytheusQ

NOTE: do not use pip install pytheus (it will install a different package)

To run one of the included examples, type e.g.

pytheus run --example ghz_346

Output of optimization is saved to a directory called output.

To list all examples, type

pytheus list

You can also run config json files by referring to them by their path.

pytheus run PATH_TO_YOUR_INPUT_FILE

Names of the subdirectories in output are specified by the name and content of the config file.

To plot the graph corresponding to one result saved as a json file, execute

pytheus plot PATH_TO_RESULT_FILE

To get help, add the --help option to any command. For instance

> pytheus run --help

Usage: pytheus run [OPTIONS] FILENAME

  Run an input file.

Options:
  --example  Load input file from examples directory.
  --help     Show this message and exit.

Our package allows for the discovery of quantum experiments for a range of experimental goals, constraints and resources. Experiments that can be produced include:

• state creation (heralded or post-selected)
• quantum gates (heralded or post-selected)
• measurements of quantum states
• entanglement swapping
• (covered elsewhere: mixed state creation)

Sources for photons in these experiments can be SPDC sources, deterministic single-photon sources or a mix of the two.

Detectors can be photon-number-resolving or not.

Each of these experiments can be described with a graph. The interpretation of nodes and edges varies with the kind of experiment.

With these varying interpretations (e.g. for single photon sources, input photons, entanglement swapping), different constraints apply on what kind of graph can correspond to an experiment (Topological Rules).

With the different ways of performing the experiments (heralded/post-selected & number-resolving/non-number-resolving), different events are selected out of all possibilities (post-selection rules).

All experiments that our package is applied to can be described by a graph. When describing state creation using SPDC each edge can be interpreted as a pair-creation. In this case all edges of the complete graph can be considered physically legitimate. When describing other experiments edges can be interpreted differently. Not every edge will be physically meaningful. Consequentially there are constraints on which connections of the complete graph are used in the optimization.

(A) Single Photon Sources and Input Photons

Deterministic single photon sources and input photons (such as in gates) are described as (input) vertices in a graph. An edge connecting an input vertex to a detector describes a path in which a photon can travel from the input into the detector. This interpretation stems from the Klyshko picture. From this a constraint on the graph follows. Two input vertices can not be connected by an edge. It could not be interpreted physically.

(B) Entanglement Swapping and Teleportation

In entanglement swapping, photons are entangled that have not interacted before. If we want to design an entanglement swapping experiment of two photons, the target is to discover a graph that produces an entangled state between the two photons. However any edge between the corresponding vertices would translate into a common source crystal. A constraint that ensures legitimate entanglement swapping is to remove any edge between the two parties

The rules for post-selecting coincidence events have been described in the Theseus paper. Here, post-selection projects the space of possibilities containing arbitrary combinations of crystals firing into the space of possibilities where only crystals fire for which all detectors at the end of the experiment click. In the graph picture these combinations correspond to the perfect matchings. A state is produced with fidelity one in post-selection if all possibilities of coincidence events contribute to that state.

Other experimental settings (such as heralding) and additional experimental resources (such as number-resolving detectors) perform a different kind of projection on the space of possibilities by selecting for different events. This different selection is reflected in the fidelity of the state. The products of the edge weights belonging to each possibility contribute to the norm of the fidelity.

(A) Heralding

Heralding is a less strict form of selecting events. Instead of putting a detector in every path and selecting for coincidence, only a subset of the paths are detected heralding an output state in the unmeasured paths. This selection rule not only allows for possibilities where one photon is in every path (perfect matchings) but also for other possibilities (edge covers) as long as they cover the heralding detectors. This can lead to cross-terms that are not present when post-selecting for coincidence in all paths. Consequentially it is more difficult to find a graph with fidelity one, also requiring more experimental resources.

(B) Single Photon Sources and Input Photons

When describing heralded experiments (above) one has to consider edge covers instead of perfect matchings in the graph for possible events. These possibilities include one edge being included twice in an edge cover, corresponding to a crystal firing twice in an experiment. For single photon sources and other deterministic input photons such possibilities do not exist. Only edge covers that cover the input vertices exactly once are considered for the norm of the fidelity.

(C) Photon Number-Resolving Detectors

Photon number-resolving detectors are a valuable resource that can restrict the space of possibilities more than a regular detector. When one can be certain that exactly one photon, and not two, has entered a detector it reduces the number of events that could have led to this outcome, eliminating cross terms.

(D) States in Fock Basis

...

As explained above, the loss function depend largely on the different experimental conditions. Independent of these conditions they fall into two categories.

• Fidelity
• Count Rate

A Fidelity of one ensures that an experiment has no unwanted cross terms. Every possibility that is selected for contributes directly to the target outcome.

However, we have come to find that optimizing exclusively for fidelity in some cases can lead the optimization to scale down the weights of the entire graph to minimize the contributions of crossterms. While the fidelity will be very close to one in those cases the generally low edge weights would lead to very low count rates of successful events in actual experiments.

To find solutions with higher weights we have introduced the simplified count rate as a loss function.

This section gives examples for config files showcasing the features for different kinds of experiments that can searched for.

This is used when the in- and out-going states can be clearly defined by a state functions. For those, the loss functions cr and fid are used.

Below are some examples to give an idea of the scope.

For further details, refer to the definition of the function setup_for_target in main.py.

Here is an example for a config file optimizing for a graph that creates a three particle four-dimensional GHZ state.

{
  "description": "Finding a setup for the creation of the three-particle four-dimensional GHZ state. It can be realized with three ancillary particles",
  "foldername": "ghz_346",
  "target_state": [
    "000",
    "111",
    "222",
    "333"
  ],
  "num_anc": 3,
  "loss_func": "cr",
  "thresholds": [
    0.25,
    0.1
  ],
  "samples": 10,
  "optimizer": "L-BFGS-B",
  "ftol": 1e-06,
  "edges_tried": 20,
  "tries_per_edge": 5
}

General info is given by description. With foldername one can give a custom name for the subfolder where solutions are saved.

In the simple case of post-selected state creation with SPDC crystals, target_state, num_anc and loss_func are all that are needed to define the objective of the optimization.

thresholds is necessary to decide whether a topological optimization step has been successful. In this case, when 1-countrate < 0.25 and 1-fidelity < 0.1.

For an example how topological constraints on the starting graph of the optimization are dealt with, consider the example of a post-selected CNOT(2,3) quantum gate.

{
  "description": "Postselected CNOT between a qubit (control) and a qutrit (target). Two ancillary photons from SPDC.",
  "foldername": "cnot_23",
  "target_state": [
    "0000",
    "0101",
    "0202",
    "1011",
    "1112",
    "1210"
  ],
  "in_nodes": [
    0,
    1
  ],
  "out_nodes": [
    2,
    3
  ],
  "num_anc": 2,
  "loss_func": "cr",
  "thresholds": [
    0.3,
    0.1
  ],
  "samples": 10,
  "optimizer": "L-BFGS-B",
  "ftol": 1e-06,
  "edges_tried": 30,
  "tries_per_edge": 5
}

Here, target_state defines a logic table. It is defined through in_nodes and out_nodes, which entries belong to incoming photons and which belong to outgoing photons. These definitions suffice to automatically put constraints on the starting graph.

Two additional features are heralding and single photon sources. A simple example is a CNOT gate between two qubits heralding on two ancillary detectors.

{
  "description": "Heralded CNOT gate between two qubits with two single photon sources. Similar has been done: https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.126.140501 could this have a better success probability?",
  "foldername": "cnot22sp",
  "target_state": [
    "0000",
    "0101",
    "1011",
    "1110"
  ],
  "num_anc": 2,
  "in_nodes": [
    0,
    1
  ],
  "out_nodes": [
    2,
    3
  ],
  "single_emitters": [
    4,
    5
  ],
  "heralding_out": true,
  "loss_func": "cr",
  "thresholds": [
    1,
    0.1
  ],
  "samples": 10,
  "optimizer": "L-BFGS-B",
  "ftol": 1e-06,
  "edges_tried": 30,
  "tries_per_edge": 5
}

Here, the two single photon sources given by single_emitters introduce further topological constraints on the starting graph. As they have the role of ancillary photons in this case, we need to set num_anc accordingly. The graph corresponding to this optimization will have a total of eight nodes. Two for incoming, two for outgoing, two for single photon sources and two for ancillary detectors.

If num_anc is larger than the sum of lengths of in_nodes and single_emitters, the necessary amount of particles is created through SPDC.

Additionaly heralding_out is set to true here. The photons corresponding to out_nodes will not be detected.

{
  "description": "Measurement for three particle W state",
  "foldername": "W_measurement",
  "target_state": [
    "001",
    "010",
    "100"
  ],
  "in_nodes": [
    0,
    1,
    2
  ],
  "num_anc": 0,
  "loss_func": "cr",
  "samples": 10,
  "optimizer": "L-BFGS-B",
  "ftol": 1e-06,
  "thresholds": [
    0.3,
    0.1
  ],
  "tries_per_edge": 5,
  "edges_tried": 30
}

When loss_func is set to "ent", no target state is set. Instead the optimizer maximizes the entanglement that can be achieved by a graph with the local dimensions given by dim.

{
  "description": "Maximizing entanglement in k=2 bi-partitions for four qubits.",
  "K": 2,
  "dim": 2222,
  "ftol": 1e-07,
  "loss_func": "ent",
  "min_edge": 4,
  "num_pre": 5,
  "optimizer": "SLSQP",
  "imaginary": false,
  "samples": 10,
  "thresholds": [
    0.000001
  ],
  "tries_per_edge": 3,
  "var_factor": 0
}

There is also the option to define an arbitrary loss function, which should be defined or imported in lossfunctions.py .

Here is an example for optimizing the assembly index of the graph.

{
  "foldername": "assembly",
  "loss_func": "lff",
  "lff_name": "top_n_assembly",
  "dimensions": [
    2,
    2,
    2,
    2
  ],
  "num_vertices": 4,
  "num_cols": 2,
  "size_of_graph": 8,
  "optimizer": "L-BFGS-B",
  "ftol": 1e-06,
  "samples": 1,
  "thresholds": [
    99999
  ],
  "topopt": false,
  "edges_tried": 30,
  "tries_per_edge": 5,
  "unicolor": false,
  "imaginary": false,
  "num_pre": 1,
  "save_history": true
}

To use a custom defined loss function loss_func should be set to "lff" (loss from function).

The name of the loss function is given as a string to lff_name. This function should be defined or imported in lossfunctions.py. It should take a Graph object and a cnfg dictionary as arguments and return a real number.

git clone https://github.com/artificial-scientist-lab/PyTheus.git

From the project root directory, submit

python -m venv venv

This will create a subfolder with your virtual environment.

To activate, type

. venv/bin/activate

Note the leading point!

Submit

python setup.py develop

from the project root directory (where setup.py is located). Any changes in the code will now automatically be reflected in your local package installation.