Quantum Fredkin And Toffoli Gates On A Versatile Programmable Silicon Photonic Chip
Leda Billock
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quantum fredkin and toffoli gates on a versatile programmable silicon photonic chip
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Quantum logic gates are backbones of quantum information processing (QIP), wherein the typical three-qubit Fredkin and Toffoli gates are essential in quantum computation and communication. So far, the quantum Fredkin gate has only been demonstrated with pre-entangled input states in free-space optics, which limits its usage for independent input photons. Here, we put forward an exquisite scheme and experimentally perform a proof-of-principle demonstration of three-qubit Fredkin and Toffoli gates on a programmable quantum photonic chip. Our scheme can also be used to realize a series of other two-qubit quantum gates. Our work sheds light on the merits of quantum photonic chip in implementing quantum logic gates, and paves the way for advanced quantum chip processors.
Quantum computation1 is one of the great challenges in quantum information processing, while it enables the exponential speedup of computations and solves numerous NP-hard problems which cannot be effectively tackled by the classical computing2,3. Recently, extensive attention has been raised in realizing large-scale universal quantum computing with instinctive systems including superconducting qubits4, linear optics5, atoms6 and NMR qubits7. Quantum logic gates acting as key components of quantum circuits are essential for quantum computation. However, the efficient realization of more qubits quantum logic gates still remains a significant challenge due to the difficulty in chaining various gates together in a circuit, e.g., the three-qubit Toffoli gate requires six CNOT gates8, while the Fredkin gate corresponds to a more difficult decomposition. Some ingenious methods of realizing three-qubit Toffoli and Fredkin gates have been experimentally demonstrated with large-scale bulk optics systems9,10. By expanding the qubit space to a higher dimensional Hilbert space, Lanyon et al. exhibited the realization of Toffoli gate with a photonic system9. A quantum Fredkin gate acting on photons is experimentally demonstrated with the pre-entangled input states, which cannot act as an independent gate device10. The inherent limited programmability, less scalability and instability of bulky optical gates restrict their wide deployment.
where \(1/\gamma _1^6\) is the experimental success probability of the three-qubit quantum gate. For the calculated matrices show in Fig. 1 for Fredkin gate and Toffoli gate, we obtained a success probability of 0.056 for the Fredkin gate and 0.017 for the Toffoli gate. The success probability of the Toffoli gate is higher than 1/72 (0.014) achieved in the previous experiment9.
Besides the three-qubit Toffoli and Fredkin gates, our scheme can also be potentially used to implement quantum gates with more qubits such as the n-qubit Toffoli gates (n>3) (see Supplementary Note 3). An even more interesting point is that our scheme can also be used to realize a heralded Toffoli gate with ancillary photons (see Supplementary Note 4 for details). Using the multiplexing approach23, the success probability of such heralded Toffoli gate can be boosted to near-deterministic level, thus making it potentially promising for future applications in scalable optical quantum circuits.
Y.L. and A.Q.L. jointly conceived the idea. Y.L. performed the numerical simulations and theoretical analysis. Y.L., L.W., H.H.Z. and H.Z. did the fabrication and experiments. Y.L., L.W., Y.S., X.Z. and L.C.K. involved in the discussion and data analysis. Y.L., Y.S., A.Q.L. X.Z. and L.K.C. wrote the manuscript. L.C.K. and A.Q.L. supervised and coordinated all the work. All authors commented on the manuscript.
The Fredkin gate (also controlled-SWAP gate and conservative logic gate) is a computational circuit suitable for reversible computing, invented by Edward Fredkin. It is universal, which means that any logical or arithmetic operation can be constructed entirely of Fredkin gates. The Fredkin gate is a circuit or device with three inputs and three outputs that transmits the first bit unchanged and swaps the last two bits if, and only if, the first bit is 1.
The Fredkin gate,[1] conceptualized by Edward Fredkin and Tommaso Toffoli at the MIT Laboratory for Computer Science, represents a pivotal advancement in the field of reversible computing and conservative logic. Developed within the framework of conservative logic, this 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.
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. By embodying principles of reversible computing, the Fredkin gate offers a practical solution to reducing the energy costs associated with digital computations, marking a significant shift towards more sustainable computing technologies.
Inputs on the left, including two constants, go through three gates to quickly determine the parity. The 0 and 1 bits swap places for each input bit that is set, resulting in parity bit on the 4th row and inverse of parity on 5th row.
Then the carry row and the inverse parity row swap if the parity bit is set and swap again if one of the p or q input bits are set (it doesn't matter which is used) and the resulting carry output appears on the 3rd row.
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. This approach allows for integrating Fredkin gates into large-scale quantum processors, paving the way for future quantum computing advancements.[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 (GHZ) 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. The availability of quantum Fredkin gates may facilitate the construction of quantum computers.[5][6]
Quantum computing can be applied to work toward vaccines and therapies as well as epidemiology, supply distribution, hospital logistics, and diagnostics. By harnessing the properties of quantum physics, quantum computers have the potential to sort through a vast number of possibilities nearly instantaneously and come up with a probable solution. How? Read the article.
Quantum theory is one of the most successful theories that have influenced the course of scientific progress during the twentieth century. It has presented a new line of scientific thought, predicted entirely inconceivable situations and influenced several domains of modern technologies. After more than 50 years from its inception, quantum theory married with computer science, another great intellectual triumph of the 20th century and the new subject of quantum computation was born. Quantum computing merges two great scientific revolutions of the 20th century: quantum physics and computer science.
The first wave of technology was about steam power, the second was electricity, the third is high tech and the fourth wave we are now entering is physics at the molecular level, such as AI, nano and bio technology; then we will see the fifth wave of technology which will be dominated by physics at atomic and sub-atomic level i.e. electron spin and photon polarization used to process information. Some mainframes will be replaced by quantum computers in future, but mobile phones & laptops will not be replaced due to the need for a cooling infrastructure for the qubits.
The theory of computation has traditionally been studied almost entirely in the abstract, as a topic in pure mathematics. This is to miss the point of it. Computers are physical objects, and computations are physical processes. What computers can or cannot compute is determined by the laws of physics alone, and not by pure mathematics.
Linear algebra is about linear combinations. That is, using arithmetic on columns of numbers called vectors and arrays of numbers called matrices, to create new columns and arrays of numbers. Linear algebra is the study of lines and planes, vector spaces and mappings that are required for linear transforms.
It is a relatively young field of study, having initially been formalized in the 1800s in order to find unknowns in systems of linear equations. A linear equation is just a series of terms and mathematical operations where some terms are unknown; for example:
Equations like this are linear in that they describe a line on a two-dimensional graph. The line comes from plugging in different values into the unknown x to find out what the equation or model does to the value of y.
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