Run and Benchmark Your First Photonic Quantum Circuit

Run a small photonic quantum circuit to see how optical modes and gates produce measurement outcomes, then compare those outcomes with an ideal simulation. You will need a quantum-photonics software package or hosted notebook; the steps below use PennyLane-style concepts, which apply to many circuit tools even when their syntax differs.

What You’ll Need

A computer with Python and a supported photonic quantum software library, or access to that library through a hosted notebook. Check the library’s current installation and device instructions before starting.
Basic familiarity with Python, circuits, and probabilities. You do not need a physical photonic processor: a simulator is the simplest first run.
A circuit target, such as two optical modes, a beam splitter, and photon-number measurements, plus a clear benchmark such as agreement with an analytic probability distribution.
Optional access to a photonic hardware service. Hardware may require an account, queue time, supported gate settings, and credits or usage limits; check these before submitting.

Step-by-Step

Choose a simulator and confirm its interface. Install a photonic simulator supported by your chosen framework, or open its maintained example notebook. Follow the current official setup guidance and verify that a minimal import or example runs. Photonic libraries differ in how they represent modes, states, gates, and measurements, so do not assume a snippet for one package works unchanged in another.
Define a small experiment before writing code. Use two modes, with one photon in the first and vacuum in the second: the input is often written as |1,0>. Apply a balanced beam splitter, then measure photon number in both output modes. This simple setup has a known ideal result: for an ideal lossless 50:50 splitter, one photon exits in either output with probability one-half. The exact output convention can depend on the beam-splitter definition.
Check the simulator’s conventions. Find how it specifies the input occupation, beam-splitter angle or reflectivity, and measurement result. Confirm whether its parameter describes an angle, an intensity fraction, or an amplitude. Also check mode ordering and whether measurements return occupation numbers, samples, or probabilities. These details are essential to interpreting the result.
Build the circuit in order. Create a two-mode device or circuit, prepare |1,0>, apply the balanced beam splitter, and request photon-number measurement on both modes. If the framework uses an explicit state-preparation operation, apply it before the gate. Keep the circuit short so that each operation is easy to inspect.
Run an exact or probability calculation first. If supported, ask the simulator for the output state or exact probabilities rather than drawing samples. Check that the probabilities are nonnegative and sum to approximately 1, allowing for small floating-point error. For the ideal one-photon experiment, the two outcomes should be (1,0) and (0,1), each near 0.5. If your convention gives a different labeling, verify that the same physical distribution is represented.
Run a finite-shot experiment. Set a documented number of repeated measurements, such as 10,000 shots, and collect the outcome counts. Convert each count to a frequency by dividing by the total number of valid shots. A typical result might be close to half in each output, but finite sampling means it will rarely be exactly 50:50.
Benchmark against the ideal prediction. Compare measured frequencies with the simulator’s exact probabilities. For this two-outcome test, report the absolute difference for each outcome, or use total variation distance: one-half the sum of the absolute probability differences. State the number of shots and the metric; a benchmark without these details is hard to reproduce.
Repeat with controlled changes. Run several independent batches or increase the shot count, keeping the input and circuit fixed. Sampling fluctuations generally shrink as shots increase, roughly in proportion to 1 divided by the square root of the shot count. Then change one setting at a time, such as the splitter ratio, and compare against the corresponding ideal prediction.
Try hardware only after the simulator is understood. Select a compatible photonic device and inspect its supported modes, gate parameters, input-state preparation, and measurement options. Submit the same experiment if supported. Save the device name, settings, timestamp, shot count, returned data, and any reported loss or calibration information. Compare hardware results with the ideal model, but do not treat deviations as proof of a software error: optical loss, imperfect operations, and detector behavior can matter.
Record a reproducible result. Save the source code or notebook, package versions, circuit description, random seed if available, requested and accepted shot counts, and raw counts. Keep ideal predictions and experimental results separate. This makes it possible to rerun the benchmark and diagnose changes later.

Common Mistakes

Mixing up amplitude and probability. A 50:50 intensity splitter is not necessarily entered as the number 0.5 in every API. Read the parameter definition and use the documented conversion.
Assuming modes are qubits. Photonic modes can contain zero, one, or multiple photons. A qubit-style bit-string interpretation may hide occupation-number details.
Comparing unlike quantities. Compare frequencies with probabilities, not raw counts with probabilities. Ensure both distributions use the same outcome ordering and include the same outcomes.
Expecting exact sample counts. Shot-based measurement is random. Small deviations from the ideal distribution are normal and should be interpreted in light of the sample size.
Ignoring lost or invalid events. Some hardware reports no-click events, discarded events, or postselected data. State which events were included and how the denominator was chosen.

Tips

Start with one photon and two modes; add complexity only after the baseline works.
Print the circuit or inspect its diagram before execution. Confirm preparation, gate order, and measurement locations.
Use an exact simulator result as the reference, and use a fixed seed where the simulator permits reproducible sampling.
Report the benchmark metric and shot count together. For more than two outcomes, total variation distance is a simple distribution-level comparison, but it does not identify the cause of an error.
Separate ideal simulation, noisy simulation, and hardware runs in your notes. They answer different questions.

Troubleshooting

Import or setup fails: Confirm the package name and installation instructions for your Python environment. Restart the notebook kernel after installation, and check that the notebook is using the same environment where the package was installed.

The circuit rejects a gate or state: Check the device’s number of modes and supported operations. Confirm that the input occupation is valid and that the gate parameter uses the expected units or range. If the target is hardware, an operation available in simulation may not be supported there.

Probabilities do not sum to one: Check whether the result includes only selected outcomes, whether postselection or loss is enabled, and whether values are amplitudes rather than probabilities. Inspect the full output-state or measurement documentation before renormalizing anything.

Results look reversed: Inspect mode ordering and outcome labels. A reported (0,1) may refer to a different mode order than expected; verify the convention rather than changing the physics.

Hardware differs substantially from the ideal prediction: First rerun the simulator and confirm the circuit and parameter interpretation. Then check device status, calibration information, loss, valid-shot count, and measurement settings. Repeat a small run if appropriate, and report the discrepancy instead of silently adjusting the data.

Frequently Asked Questions

Do I need a physical quantum computer?
No. A photonic simulator can execute the circuit and establish an ideal baseline. Hardware is optional and may have access or device constraints.

What does a balanced beam splitter do in this example?
Ideally, it distributes the single-photon detection probability equally between two output modes. The precise state phase and labels depend on the beam-splitter convention.

How many shots should I use?
Use enough to make sampling noise useful to observe; 10,000 is a reasonable illustrative starting point for a simple benchmark, not a universal requirement. Increase shots when you need tighter statistical precision.

What is a good first benchmark metric?
For two outcomes, compare each observed frequency with its ideal probability. Total variation distance is a compact summary when comparing complete distributions.

Why are hardware results not exactly 50:50?
Finite sampling causes variation, and real devices can also have loss, imperfect splitting, and detector limitations. Record these conditions before drawing conclusions.

Can I compare different photonic software packages?
Yes, if you implement equivalent input states, gate conventions, mode ordering, and measurement rules. Compare the resulting probability distributions, not just code or circuit labels.

Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.

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