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A quantum Fredkin gate (Conference Presentation)

Raj B. Patel, Joseph Ho, Franck Ferreyrol, Timothy C. Ralph, Geoff J. Pryde

Published Dec 7, 2016• 0 citations
Publisher

Abstract

One of the greatest challenges in modern science is the realisation of quantum computers which, as their scale increases, will allow enhanced performance of tasks across many areas of quantum information processing. Quantum logic gates play a vital role in realising these applications by carrying out the elementary operations on the qubits; a key aim is minimising the resources needed to build these gates into useful circuits. While the salient features of a quantum computer have been shown in proof-of-principle experiments, e.g., single- and two-qubit gates, difficulties in scaling quantum systems to encode and manipulate multiple qubits has hindered demonstrations of more complex operations. This is exemplified by the classical Fredkin (or controlled-SWAP) gate [1] for which, despite many theoretical proposals [2,3] relying on concatenating multiple two-qubit gates, a quantum analogue has yet to be realised. Here, by directly adding control to a two-qubit SWAP unitary [4], we use photonic qubit logic to report the first experimental demonstration of a quantum Fredkin gate [5]. Our scheme uses linear optics and improves on the overall probability of success by an order of magnitude over previous proposals [2,3]. This optical approach allows us to add control an arbitrary black-box unitary which is otherwise forbidden in the standard circuit model [6]. Additionally, the action of our gate exhibits quantum coherence allowing the generation of the highest fidelity three-photon GHZ states to date. The quantum Fredkin gate has many applications in quantum computing, quantum measurements [7] and cryptography [8,9]. Using our scheme, we apply the Fredkin gate to the task of direct measurements of the purity and state overlap of a quantum system [7] without recourse to quantum state tomography.

DOI
10.1117/12.2240833

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One of the greatest challenges in modern science is the realisation of quantum computers which, as their scale increases, will allow enhanced performance of tasks across many areas of quantum information processing. Quantum logic gates play a vital role in realising these applications by carrying out the elementary operations on the qubits; a key aim is minimising the resources needed to build these gates into useful circuits. While the salient features of a quantum computer have been shown in proof-of-principle experiments, e.g., single- and two-qubit gates, difficulties in scaling quantum systems to encode and manipulate multiple qubits has hindered demonstrations of more complex operations. This is exemplified by the classical Fredkin (or controlled-SWAP) gate [1] for which, despite many theoretical proposals [2,3] relying on concatenating multiple two-qubit gates, a quantum analogue has yet to be realised. Here, by directly adding control to a two-qubit SWAP unitary [4], we use photonic qubit logic to report the first experimental demonstration of a quantum Fredkin gate [5]. Our scheme uses linear optics and improves on the overall probability of success by an order of magnitude over previous proposals [2,3]. This optical approach allows us to add control an arbitrary black-box unitary which is otherwise forbidden in the standard circuit model [6]. Additionally, the action of our gate exhibits quantum coherence allowing the generation of the highest fidelity three-photon GHZ states to date. The quantum Fredkin gate has many applications in quantum computing, quantum measurements [7] and cryptography [8,9]. Using our scheme, we apply the Fredkin gate to the task of direct measurements of the purity and state overlap of a quantum system [7] without recourse to quantum state tomography.
Minimizing the resources required to build logic gates into useful processing circuits is key to realizing quantum computers. Although the salient features of a quantum computer have been shown in proof-of-principle experiments, difficulties in scaling quantum systems have made more complex operations intractable. This is exemplified in the classical Fredkin (controlled-SWAP) gate for which, despite theoretical proposals, no quantum analog has been realized. By adding control to the SWAP unitary, we use photonic qubit logic to demonstrate the first quantum Fredkin gate, which promises many applications in quantum information and measurement. We implement example algorithms and generate the highest-fidelity three-photon Greenberger-Horne-Zeilinger states to date. The technique we use allows one to add a control operation to a black-box unitary, something that is impossible in the standard circuit model. Our experiment represents the first use of this technique to control a two-qubit operation and paves the way for larger controlled circuits to be realized efficiently.
Quantum information science addresses how the storage, processing, and transmission of information are affected by uniquely quantum mechanical phenomena, such as superposition and entanglement. New technologies that harness these quantum effects are beginning to be realized in the areas of communication, information processing and precision measurement. For the realization of a universal gate set, by which, in principle, any quantum information task can be realized, two-qubit gates have been demonstrated and have been used to realize small-scale quantum circuits. However, scalability is becoming a critical problem. It may therefore be helpful to consider the use of three-qubit gates, which can simplify the structure of quantum circuits dramatically. Although both the controlled-SWAP (CSWAP) gate (also called Fredkin gate) and the controlled-controlled-NOT gate (also called Toffoli gate) are representative three-qubit gates, the Fredkin gates can be directly applied to many important quantum information protocols, e.g., error correction, fingerprinting, optimal cloning, and controlled entanglement filtering. Here we report a realization of the Fredkin gate using a photonic quantum circuit, following the theoretical proposal by Fiurasek. We achieve a fidelity of 0.85 for the classical truth table of CSWAP operation and an output state fidelity of 0.81 for a generated 3-photon Greenberger-Horne-Zeilinger (GHZ) state. We also confirmed that the gate is capable of genuine tripartite entanglement with a quantum coherence corresponding to a visibility of 0.69 for three-photon interferences. From these results, we estimate a process fidelity of 0.77, which indicates that our Fredkin gate can be applied to various quantum tasks.
Quantum information science addresses how the processing and transmission of information are affected by uniquely quantum mechanical phenomena. Combination of two-qubit gates has been used to realize quantum circuits, however, scalability is becoming a critical problem. The use of three-qubit gates may simplify the structure of quantum circuits dramatically. Among them, the controlled-SWAP (Fredkin) gates are essential since they can be directly applied to important protocols, e.g., error correction, fingerprinting, and optimal cloning. Here we report a realization of the Fredkin gate for photonic qubits. We achieve a fidelity of 0.85 in the computational basis and an output state fidelity of 0.81 for a 3-photon Greenberger-Horne-Zeilinger state. The estimated process fidelity of 0.77 indicates that our Fredkin gate can be applied to various quantum tasks.
Abstract Optimizing the physical realization of quantum gates is important to build a quantum computer. The controlled-SWAP gate, also named Fredkin gate, can be widely applicable in various quantum information processing schemes. In the present research, we propose and experimentally implement quantum Fredkin gate in a single-photon hybrid-degrees-of-freedom system. Polarization is used as the control qubit, and SWAP operation is achieved in a four-dimensional Hilbert space spanned by photonic orbital angular momentum. The effective conversion rate P of the quantum Fredkin gate in our experiment is (95.4 ± 2.6)%. Besides, we find that a kind of Greenberger–Horne–Zeilinger-like states can be prepared by using our quantum Fredkin gate, and these nonseparale states can show its quantum contextual characteristic by the violation of Mermin inequality. Our experimental design and coding method are useful for quantum computing and quantum fundamental study in high-dimensional and hybrid coding quantum systems.
In a recent remarkable experiment [Sci. Adv. 2, e1501531 (2016)], a 3-qubit quantum Fredkin (i.e., controlled-SWAP) gate was demonstrated by using linear optics. Here we propose a simple experimental scheme by utilizing the dispersive interaction in superconducting quantum circuit to implement a hybrid Fredkin gate with a superconducting flux qubit as the control qubit and two separated quantum memories as the target qudits. The quantum memories considered here are prepared by the superconducting coplanar waveguide resonators or nitrogen-vacancy center ensembles. In particular, it is shown that this Fredkin gate can be realized using a single-step operation and more importantly, each target qudit can be in an arbitrary state with arbitrary degrees of freedom. Furthermore, we show that this experimental scheme has many potential applications in quantum computation and quantum information processing such as generating arbitrary entangled states (discrete-variable states or continuous-variable states) of the two memories, measuring the fidelity and the entanglement between the two memories. With state-of-the-art circuit QED technology, the numerical simulation is performed to demonstrate that two-memory NOON states, entangled coherent states, and entangled cat states can be efficiently synthesized.