Fredkin gate
It is universal, which means that any logical or arithmetic operation can be constructed entirely of Fredkin gates.
The Fredkin gate,[1] conceptualized by Edward Fredkin and Tommaso Toffoli at the MIT Laboratory for Computer Science, was a pivotal advancement in the field of reversible computing and conservative logic.
Developed within the framework of conservative logic, the gate is designed to align computing processes with fundamental physical principles such as the reversibility of dynamical laws and the conservation of energy.
The technical rationale behind the Fredkin gate is rooted in addressing the inefficiencies of traditional computing, where irreversible operations typically result in significant energy dissipation.
In contrast to conventional logic gates, which often erase information and thus dissipate heat as per Landauer's principle,[2] the Fredkin gate maintains reversibility — a property that ensures no information is lost during the computation process.
This characteristic is particularly crucial as the demand for computational power grows, making energy efficiency a key consideration.
The invention of the Fredkin gate was motivated by the quest to minimize the energy footprint of computational operations.
It allows for the construction of computing systems that are not only efficient in terms of processing speed and power consumption but also environmentally sustainable.
It is easy to see that this circuit is reversible, i.e., "undoes" itself when run backwards.
The Fredkin gate can be defined using truth functions with AND, OR, XOR, and NOT, as follows: where S = (I1 XOR I2) AND C. Alternatively: One way to see that the Fredkin gate is universal is to observe that it can be used to implement AND, NOT and OR: We can encode the truth table in a hardware description language such as Verilog: Three-bit full adder (add with carry) using five Fredkin gates.
Inputs on the left, including two constants, go through three gates to quickly determine the parity.
The p and q inputs are only used as gate controls so they appear unchanged in the output.
Recent research has demonstrated the Fredkin gate on programmable silicon photonic chips.
These chips use a network of Mach-Zehnder interferometers to route photons efficiently, creating a versatile and scalable platform that can handle multiple quantum gates.
[4] In a photonic setup, the Fredkin gate serves as an effective controlled-SWAP mechanism, enabling the conditional swap of target qubits.
This is particularly valuable in generating high-fidelity Greenberger-Horne-Zeilinger states, which are crucial for quantum communication and other protocols.
The gate thus provides a powerful tool for quantum protocols that require efficient conditional operations.
[5] The Fredkin gate's controlled operations allow for estimating the overlap between quantum states without requiring resource-intensive quantum state tomography.
This makes it particularly useful for quantum communication, measurement, and cryptography, where efficiency and accuracy are paramount.
[5] On March 25, 2016, researchers from Griffith University and the University of Queensland announced they had built a quantum Fredkin gate that uses the quantum entanglement of particles of light to swap qubits.
