Quantum Computation Through Photons

 What is Photon?

A photon is a discrete unit of electromagnetic radiation, also known as a quantum of light. It has no mass or electric charge, and travels at the speed of light. Photons are considered to be the force carriers of the electromagnetic force.

Properties of photons

• Mass: Photons are massless particles.
• Charge: Photons have no electric charge.
• Spin: Photons have a spin of 1, which means they behave like tiny rotating particles.
• Energy: The energy of a photon is directly proportional to its frequency.
• Velocity: In a vacuum, photons always travel at the speed of light, which is approximately 299,792,458 meters per second.

How are photons created?

Photons are created when electrons transition from higher energy states to lower energy states within atoms or molecules. This phenomenon, known as photoelectric emission, results in the release of photons with an energy equal to the difference between the two energy states.

How do photons interact with matter?

Photons can interact with matter in two main ways:

1. Absorption

When photons are absorbed by matter, they are entirely consumed, and their energy is transferred to the material. This energy can excite electrons or generate heat.

2. scattering:

In this case, photons change direction upon interaction with matter, while their energy remains conserved.

Applications of photons

Photons have a wide range of applications, including:

• Vision: Photons constitute the electromagnetic radiation that is visible to our eyes.
• Photography: Photons are instrumental in exposing photographic film and digital sensors.
• Solar cells: Photons from the sun are employed in generating electricity through solar cells.
• Medical imaging: Photons are utilized in medical imaging techniques such as X-rays and MRI scans to produce body images.
• Quantum computing: Research is underway to explore the potential of photons in the development of quantum computers.

Conclusion

Photons are fundamental particles that play a crucial role in our understanding of the universe. Functioning as force carriers for the electromagnetic force, photons have a diverse array of applications. As our comprehension of photons advances, we can anticipate the emergence of even more remarkable applications for these extraordinary particles in the future.

Quantum Computation Through Photons

Photons as Qubits

Photons are discrete units of electromagnetic radiation, also known as quanta of light. They have no mass or electric charge, and travel at the speed of light. Due to their properties, photons can be used to construct qubits with nearly maximum coherence and to transmit quantum information over long distances.

Photons can be manipulated in a number of ways, including:

• Guiding: Photons can be guided by utilizing optical fibers.
• Delaying: Photons can be delayed by using phase shifters.
• Combining: Photons can be combined using beamsplitters.

Since a photon is an electromagnetic wave, it can have a polarization that describes the oscillation of an electric or magnetic field. The polarization of the photon can be perpendicular to its direction of motion, and can be represented on an orthogonal two-dimensional basis, where "x" represents the vertical axis and "y" represents the horizontal axis. This two-dimensional polarization property of photons can be used to construct qubits.

Fig. Polarization of light as a qubit. Horizontal polarization corresponds to qubit state, |x>, while vertical polarization corresponds to qubit state, |y>.

Polarization of Photons

Calcite crystals and Polaroid films can measure the polarization of photons based on their orientation. A photon with a vertical polarization (y-polarized) can be absorbed by a Polaroid film that is oriented vertically, while a photon with a horizontal polarization (x-polarized) can be transmitted by the same film.

A photon in a superposition state can be represented by the following equation:

|φ⟩ = α|x⟩ + β|y⟩

where α and β are complex numbers that represent the probability amplitudes of the photon being in the x-polarized and y-polarized states, respectively.

If the photon is passed through a second Polaroid film that is oriented in the same direction as the first film, then the probability of the photon being transmitted is |α|². However, if the second film is oriented at a right angle to the first film, then the photon will be absorbed.

This is because the polarization of the photon is perpendicular to the direction of its motion, and the two Polaroid films can only transmit photons that are polarized in the same direction as their own orientation.

In photon polarization qubits, quantum information can be encoded in the direction of polarization of the photon. The |0⟩ state is considered as vertical polarization, and the |1⟩ state is considered as horizontal polarization.

However, there are two main problems with using photon polarization qubits:

• Birefringence: This is the phenomenon where a crystal splits a light ray into two components polarized at right angles to each other, and these components propagate at different speeds. This can cause errors in the transmission of quantum information.
• Absorption: Some materials can only absorb one polarization of light. This can also cause errors in the transmission of quantum information.

Despite these problems, photon polarization qubits are a promising approach to quantum computing. They are relatively easy to create and manipulate, and they can be transmitted over long distances with relatively low error rates.

Dual-rail Encoding

In dual-rail encoding, a qubit is encoded in two spatial orthogonal modes, corresponding to cavities with zero or one photons. The empty cavity is in the state |0⟩, while the cavity with one photon is in the state |1⟩. Therefore, the two possible states of a dual-rail qubit are |01⟩ and |10⟩, with a total energy of ħω.

Fig. Manipulation of detection of dual-rail Q-bits.

Spatial dual-rail qubit

An arbitrary single qubit can evolve on a spatial dual-rail qubit with the help of a phase shifter and a beam splitter. The phase shifter is used to change the transmission phase, and the beam splitter is a partially reflecting mirror that is used to combine two optical modes coherently. The intensity reflectivity of the beam splitter is denoted by η. The computational basis is achieved by detecting and measuring the spatial mode that accommodates the photon.

Polarization dual-rail qubit

Arbitrary single qubit evolution on a polarization dual-rail qubit is obtained by the combination of half- and quarter-wave plates oriented at specific angles. Detection in the computational basis is achieved via a polarizing beam splitter (PBS) and photon counting.

The dual-rail encoded qubit is represented by the presence of a single photon in one or the other of the two spatial optical modes. Formally, the qubit of polarization encoding is equivalent to dual-rail encoding due to the basis of holding two orthogonal polarization modes. For example, we can define the following:

|0> = |10> = |H>  and   |1> = |0>|1> = |V>

where |H⟩ corresponds to a horizontally polarized photon and |V⟩ corresponds to a vertically polarized photon state.

Single-track encoded qubit

A single-track encoded qubit is represented by a single photon with no or fixed polarization in an optical mode.

Fig. Encoding of optical Q-bits.