Photonic Qubits

Introduction

So far, we’ve explored qubit implementations based on matter: superconducting circuits with engineered energy levels, and ions trapped by electric fields. In both cases, quantum information is stored and manipulated by specific energy levels governed by Hamiltonians.

But now, let’s look at something entirely different: light-photons. These are the most fundamental carriers of energy and information in physics. But how can a particle with no mass, no rest frame (i.e., photons are always moving), and no internal structure be used as a qubit?

In photonic quantum computing, we don’t rely on Hamiltonians do define or control our qubits. Instead, we use the inherent properties of light, like its polarization, spatial mode, or path, to define quantum states. In a way, we shift from “quantum matter” to “quantum optics”.

Qubit from Light

Photonic qubits are defined using degrees of freedom of a single photon. A degree of freedom is a physical property that can take on two or more distinguishable configurations. In the context of photons, it refers to polarization directions, propagation paths, or arrival times. When we choose two configurations—such as horizontal vs. vertical polarization—we can assign them to the states $\ket{0}$ and $\ket{1}$, forming a qubit.

The two most common and intuitive encodings are:

• Polarization encoding:
  • $\ket{0}$: horizontal polarization
  • $\ket{1}$: vertical polarization
• Dual-rail encoding:
  • $\ket{0}$: one photon in path A
  • $\ket{1}$: one photon in path B

Polarization encoding is simple and easy to visualize. It uses optical elements like wave plates that rotate the polarization of light.

Dual-rail encoding well-suited to integrated photonic circuits (chips that process light). These circuits can include beam splitters, phase shifters, and detectors all on a single chip, allowing for compact and stable quantum processors.

In both cases, we’re not dealing with bound energy levels of atoms or circuits, but with the external physical configuration of a light.

Manipulating Photonic Qubits

Unlike ions or superconducting qubits, photons naturally don’t interact with each other. This makes two-qubit gates extremely difficult. To work around this, most scalable photonic computing schemes use a different approach:

Measurement-based quantum computing (MBQC)

Instead of applying gates dynamically, MBQC works as follows:

1. Prepare a resource state

First, we prepare an entangled resource state known as a cluster state. This is a highly entangled arrangement of qubits, typically laid out in a line or lattice. Each qubit is first initialized in the state $\ket{+}=\frac{1}{\sqrt{2}}(\ket{0}+\ket{1})$ and entangled with its neighbors using controlled-$Z$ (CZ) gates.

In photonic systems, we can’t apply CZ gates directly because photons don’t interact. Instead, we use techniques from the KLM protocol, which simulate CZ gates probabilistically using beam splitters, ancilla photons, and photon detectors. While this process is non-deterministic, it can be repeated until it succeeds, and is central to building large photonic cluster states.

2. Perform measurements

Since the cluster state is entangled, measuring one qubit immediately affects the state of the others. To manipulate the remaining qubits, we measure qubits in a specific basis and in the correct order.

Most readers are familiar with measuring a qubit in the standard computational basis: $\braces{\ket{0}, \ket{1}}$. But in MBQC, we often need to measure in other bases–such as Hadamard basis $\braces{\ket{+}, \ket{-}}$.

Measuring in a different basis is like asking a different yes/no question about the qubit. Instead of asking “Is the qubit in $\ket{0}$ or $\ket{1}$?”, we’re asking “Is the qubit in $\ket{+}$ or $\ket{-}$?”.

This choice of measurement basis is crucial in MBQC, because it determines which quantum gates is effectively applied to the remaining part of the cluster. The computation unfolds through these measurements, step by step.

3. Classical feedforward

The remaining part of the cluster evolves based not only on the measurement basis, but also on the measurement outcomes. These outcomes—such as $+$ or $-$—introduce known variations (typically extra gates) into the state of the unmeasured qubits.

Since we know the measurement outcome once it’s observed, we can adapt the rest of the computation accordingly. This process of using known classical information to adjust future quantum operations is called classical feedforward.

Instead of physically correcting the state, we adjust the basis of future measurements or reinterpret the outcome to account for the effect. This allows the computation to continue along the correct logical path, even though individual measurement outcomes are random.

We’ll see how this works in the next section with the Hadamard gate example.

Example: Hadamard Gate via MBQC

Let’s walk through how to apply a Hadamard gate using MBQC.

Suppose we start with an input qubit $\ket{\psi}$, and we want to apply a Hadamard gate to it. In MBQC, we do this by preparing a simple 2-qubit cluster state:

\[\ket{\psi} \otimes \ket{+} \xrightarrow{\text{apply CZ}} \ket{\text{cluster}}\]

This entangles the input qubit with and ancilla qubit in the $\ket{+}$ state using a controlled-$Z$ gate.

Now, we measure the first qubit (the input) in the Hadamard basis, which consists of the states $\ket{+}$ and $\ket{-}$. This measurement collapses the cluster into a new state where the quantum information of the input is effectively teleported to the second qubit (the ancilla), with a Hadamard gate applied to it.

The measurement outcome will be either $+$ or $-$. The Hadamard basis is also called X basis because $\ket{+}$ and $\ket{-}$ are eigenstates of the $X$ operator (feel free to verify this). As a result, the output qubit—which was originally the ancilla—ends up in the state:

• $H\ket{\psi}$ if the outcome is $+$.
• $XH\ket{\psi}$ if the outcome is $-$.

You can see that if the measurement outcome is $-$, the output qubit ends up with an extra $X$ gate applied. This $X$ gate didn’t appear out of nowhere; it’s a direct consequence of measuring the input qubit in the $X$ basis.

At first, it might seem like we should apply another $X$ gate to correct the output qubit when the outcome is $-$. But in practice, we don’t do that—because this kind of byproduct error happens every time we perform a measurement-based gate. If we tried to fix it physically each time, the process would be inefficient and error-prone.

Instead, we take advantage of the fact that we know the measurement outcome. Since the output qubit is in either $XH\ket{\psi}$ or $H\ket{\psi}$, we can use this classically. For example, if the outcome was $-$, and we now want to apply another gate $U$, we simply apply $UX$ instead of $U$. This effectively cancels out the unwanted $X$ gate. This approach is called classical feedforward, and it’s a central part of how MBQC works.

Why MBQC?

Photons are hard to store, but easy to measure. Once you entangle them into a cluster, you can run the entire computation using only single-photon measurements-no real-time gates required.

Pros, Cons, and Current Status

Pros

• No decoherence: Photons are naturally immune to decoherence, as they don’t interact with the environment.
• Fast transmission: Speed of light.
• Room-temperature operation: Photonic systems can operate at room temperature, unlike superconducting qubits that require dilution refrigerators.
• Naturally mobile: Photons can be easily transmitted over long distances without loss of information.

Cons

• No direct interaction: Photons don’t interact with each other, making entanglement challenging.
• Resource overhead: KLM protocol requires many ancilla photons and probabilistic gates, leading to resource overhead.
• Difficult to store: Photons are hard to delay or buffer without loss.
• Detector and source inefficiencies: Single-photon detectors and sources still have technical limitations, leading to inefficiencies.

Current Status

While photonic quantum computers are still in the early stages of development, recent process shows that the field is advancing quickly. Several companies like Xanadu and PsiQuantum are working on photonic quantum computing. Xanadu has developed a photonic quantum computer called Aurora, a 12-qubit photonic quantum computer. It comprises 35 photonic chips interconnected by 13 kilometers of fiber optic cables, all operating at room temperature.

Photonic quantum computing is fundamentally an optics-driven challenge: its success depends on breakthroughs in laser stability, photon source efficiency, low-loss optical integration, high-performance detectors, and error correction codes suited for photonic systems.

As these optical technologies continue to improve, photonics may become the most scalable, network-friendly, and energy-efficient platform for quantum computing—especially in the long term.