What are photonic qubits in quantum computing?

Influences the principles of quantum mechanics to perform tasks that are intractable for classical computers. At the heart of quantum computing lies the qubit, the quantum equivalent of the classical bit. Unlike a classical bit, which can exist in a definite state of 0 or 1, a qubit can exist in a superposition of both states simultaneously. This fundamental difference, along with other quantum phenomena like entanglement, allows quantum computers to achieve exponential speedups for computational problems.

The physical realization of a qubit is the photonic qubit, where information is encoded in the properties of photons, the fundamental particles of light. Photons, as quanta of the electromagnetic wave, possess several quantum mechanical properties that can be broken to represent and operate quantum information. Among these, polarization is a particularly well-suited property for encoding qubits.

Polarization Encoding

The polarization of a photon describes the orientation of its oscillating electric field as it propagates through space. There are two primary types of polarization: linear and circular. In linear polarization, the electric field oscillates along a fixed direction perpendicular to the direction of the photon’s propagation. For instance, a photon can be linearly polarized vertically or horizontally. These two orthogonal polarization states can be mapped to the two basis states of a qubit, typically denoted as |0⟩ and |1⟩. For example, a vertically polarized photon might represent |0⟩, while a horizontally polarized photon represents |1⟩, or vice versa. Similarly, other pairs of orthogonal linear polarizations, such as +45⁰ and -45⁰, can also serve as the computational basis.

A feature of quantum mechanics is that a qubit can exist in a superposition of its basis states. For a photonic qubit encoded in linear polarization, this means a single photon can be in a superposition of being both vertically and horizontally polarized simultaneously. Mathematically, the state of such a qubit can be represented as

 |ψ⟩ = α|0⟩ + β|1⟩,

where α and β are complex amplitudes such that α²+β² = 1.

These amplitudes fix the probability of measuring the qubit in the |0⟩ or |1⟩ state. For instance, if a photon is in the state 1/√2|0⟩+1/√2|1⟩, there is a 50% probability of measuring it as vertically polarized (|0⟩) and a 50% probability of measuring it as horizontally polarized (|1⟩).

While linear polarization is commonly used for conceptual simplicity, other polarization encodings, such as circular polarization (left and right circularly polarized light), can also be employed. Furthermore, other properties of photons, like their path, frequency, or arrival time (temporal modes), can also be used to encode qubits.

Generation of Photonic Qubits

Generating single photons with polarization states is vital for understanding photonic qubits. One of the greatest common methods for generating entangled photon pairs, which can then be used to produce single photons, is spontaneous parametric down-conversion (SPDC).

In this non-linear optical process, a pump laser beam is directed into a non-linear crystal, and infrequently, a pump photon splits into two lower-energy photons (signal and slouch photons) that are entangled with each other. These entangled photons can be engineered to have specific polarization states, which can then be used as a resource for various quantum information tasks, including generating single photonic qubits with desired superposition states.

 For example, by measuring one photon of an entangled pair, the other photon is projected into a specific quantum state, which can serve as a qubit.

Another non-linear optical process, second harmonic generation (SHG), can be used to generate photons with twice the frequency of the input photons. While not directly a source of qubits, SHG can be used in conjunction with other processes to operate the properties of photons for quantum information processing.

Creating a large number of high-quality, indistinguishable photonic qubits and controlling them remains a important challenge. Unwanted entanglements between qubits can also arise, making exact control more difficult.

Operation of Photonic Qubits

To perform quantum computations, it is necessary to operate the state of qubits using quantum gates. For photonic qubits encoded in polarization, these gates are implemented using optical elements that adjust the polarization state of the photons. For example, wave plates (such as half-wave plates and quarter-wave plates) can rotate the polarization of a photon by specific angles, realizing single-qubit rotation gates. Polarizing beam splitters can transmit photons with one polarization and reflect photons with the orthogonal polarization, which can be used in combination with other elements to implement more complex gates.

One of the fundamental two-qubit gates is the controlled-NOT (CNOT) gate. Implementing a CNOT gate between two photonic qubits has been challenging because photons typically do not interact strongly with each other. However, significant progress has been made using various techniques, including employing non-linear optical materials, measurement-based schemes, and interfacing photons with other quantum systems like atoms or superconducting circuits. Researchers have also developed integrated photonic quantum gates on chips, offering potential for scalability and stability. These integrated devices use waveguides and optical components made up of a single substrate to operate photonic qubits.

Quantum algorithms are applied as sequences of quantum gates arranged in a quantum circuit. By designing these circuits, quantum computers can perform complex calculations. Simulating molecular vibrations with photons and experimental realizations of Shor’s quantum factoring algorithm using photonic qubits validates the potential of photonic quantum computation.

Advantages of Photonic Qubits

Photonic qubits offer some advantages for quantum information processing and communication:

• Long coherence times: Photons interact weakly with their environment, leading to relatively long coherence times, which is crucial for performing complex quantum computations.
• High-speed transmission: Photons travel at the speed of light and can be transmitted over long distances through optical fibre with relatively low loss at certain wavelengths (e.g., 1.3µm). This makes them perfect for quantum communication and networking.
• Well-established technology: The field of optics is mature, with a vast array of well-developed tools and techniques for generating, operating, and detecting photons.
• Ease of operation: Single-qubit gates can be executed with high reliability using standard optical components.
• Interconnectivity: Photons can easily interact with other quantum systems, such as atoms and superconducting circuits, enabling hybrid quantum systems.

Challenges and Limitations of Photonic Qubits

Despite their advantages, photonic qubits also face several challenges:

• Weak interactions: The weak interaction between photons makes it difficult to implement two-qubit gates, which are essential for universal quantum computation. While progress has been made, achieving hi-fi two-qubit gates remains a challenge.
• Scalability: Creating and controlling a large number of indistinguishable photonic qubits is demanding. As the number of qubits increases, the complexity of the optical setups and the potential for errors also grow.
• Loss: While transmission through optical fiber is relatively good at certain wavelengths, losses still occur, especially over long distances. Amplifying quantum signals is not possible due to the no-cloning theorem, which states that an unknown quantum state cannot be perfectly copied. Quantum repeaters are being explored as a potential solution to extend the reach of quantum communication.
• Detection efficiency: Achieving near-perfect detection efficiency for single photons can still be challenging in some scenarios.

Applications of Photonic Qubits

Photonic qubits are at the forefront of several quantum technologies:

• Quantum Cryptography: Photonic qubits are widely used in quantum key distribution (QKD) protocols. QKD controls the principles of quantum mechanics to establish secure communication channels by encoding cryptographic keys in the states of photons. Any attempt by an eavesdropper to intercept the photons will inevitably disturb their quantum state, which can be detected by the real communicating parties, ensuring the security of the key exchange. Various QKD protocols, such as BB84 and Ekert91, rely on the transmission and measurement of polarized single photons. Satellite-relayed intercontinental quantum networks using photons have also been established.
• Quantum Teleportation: Quantum teleportation, the transfer of the quantum state of a qubit from one location to another using entanglement and classical communication, has been successfully established using photonic qubits.
• Quantum Computing and Simulation: Photonic qubits are a platform for building fault-tolerant quantum computers. Researchers are actively working on developing scalable photonic quantum computing architectures using integrated photonics, linear optics, and measurement-based quantum computation. Photonic systems are also well-suited for quantum simulation, where quantum systems are used to study other complex quantum systems.
• Quantum Networks: The ability to transmit photonic qubits over long distances makes them a natural choice for building quantum networks. These networks will enable secure communication, circulated quantum computing, and access to remote quantum resources.

What is the concept of quantum photonics?

Quantum photonics is a field that controls the principles of quantum mechanics using photons, the fundamental particles of light, for various quantum technologies. It involves the generation, manipulation, transmission, and detection of photons to encode and process quantum information. Photonic qubits, where quantum information is encoded in properties of photons like polarization, are a key element of quantum photonics.

Quantum photonics has important applications in quantum communication, enabling secure quantum key distribution (QKD) over long distances due to photons’ ability to travel at the speed of light through optical fiber with low loss. It also plays a critical role in quantum computing and simulation, with researchers developing integrated photonic circuits and systems for implementing quantum algorithms and simulating complex quantum systems. Other applications include quantum teleportation and the development of quantum networks. The field benefits from well-established optical technologies and the relatively long coherence times of photons.

What is the difference between a photonic qubit and a superconducting qubit?