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arXiv:1303.4008 · Physical Review A

Enhancing the W -state quantum-network-fusion process with a single Fredkin gate

Sinan Bugu, Can Yesilyurt, Fatih Özaydin

Published Mar 25, 2013• 90 citations
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Abstract

Integrating a single Fredkin (controlled swap) gate to the previously introduced $W$ state fusion mechanism [Ozdemir et al., New J. Phys. 13, 103003 (2011)] and using an ancillary photon, we increase the size of the fused $W$ states and essentially, we improve the success probability of the fusion process in a promising way for a possible deterministic $W$-state fusion mechanism. Besides fusing arbitrary size $W$ states, our setup can also fuse Bell states to create $W$ states with a success probability $3/4$ which is much higher than the previous works. Therefore using only this setup, it is now possible to start with Bell pairs to create and expand arbitrary size $W$ states. Since a higher probability of success implies a lower cost of resource in terms of the number of the states spent to achieve a target size, our setup gives rise to more cost-efficient scenarios.

DOI
10.1103/physreva.87.032331

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A quantum Fredkin gate (Conference Presentation)

Raj B. Patel, Joseph Ho, Franck Ferreyrol +2 more

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.

•Dec 7, 2016•0 citations
Integrating a single Fredkin (controlled swap) gate to the previously introduced WWW state fusion mechanism [Ozdemir et al., New J. Phys. 13, 103003 (2011)] and using an ancillary photon, we increase the size of the fused WWW states and essentially, we improve the success probability of the fusion process in a promising way for a possible deterministic WWW-state fusion mechanism. Besides fusing arbitrary size WWW states, our setup can also fuse Bell states to create WWW states with a success probability 3/43/43/4 which is much higher than the previous works. Therefore using only this setup, it is now possible to start with Bell pairs to create and expand arbitrary size WWW states. Since a higher probability of success implies a lower cost of resource in terms of the number of the states spent to achieve a target size, our setup gives rise to more cost-efficient scenarios.
We propose an optical scheme to prepare large-scale entangled networks of WWW states. The scheme works by simultaneously fusing three polarization-encoded WWW states of arbitrary size via accessing only one qubit of each WWW state. It is composed of a Fredkin gate (controlled-swap gate), two fusion gates [as proposed in S. K. Ozdemir et al., New J. Phys. 13, 103003 (2011)], and an HHH-polarized ancilla photon. Starting with three nnn-qubit WWW states, the scheme prepares a new WWW state with $3(n\ensuremath{-}1)$ qubits after postselection if both fusion gates operate successfully, i.e., a fourfold coincidence at the detectors. The proposed scheme reduces the cost of creating arbitrarily large WWW states considerably when compared to previously reported schemes.
Creation of large-scale W state quantum networks is a key step for realization of various quantum information tasks.Regarding the photonics technology, a simple optical setup was proposed for the fusion of two W states.Recently it was shown that via a single Fredkin gate, this basic so-called fusion setup can be enhanced.However the main problem was that the probability of success of realization of Fredkin gate with linear optics is too low.In this work, we show that the same enhancement can be made possible via one Tooli and one CNOT gate, instead of a Fredkin gate.Not only the probability of success of the combination of these two gates is much higher, than that of a single Fredkin gate via linear optics, but also there is another method for implementing our setup with current photonics technology, almost with a unity success probability: A hybrid circuit consisting of a Tooli gate which can be implemented via one-way quantum computation on a weighted graph state of 8 qubits with a unity success probability and a linear optical CNOT gate which has a success probability close to unity.Therefore the preparation of polarization based encoded multi particle entangled W states of arbitrary sizes becomes considerably more ecient.
Fusion measurements are a key primitive for linear-optical quantum computing and quantum networks. Type-I and type-II fusion gates are widely used to combine small entangled resource states into larger photonic states, but without ancillary resources their success probability is limited to 1/21/21/2. Existing 3/43/43/4-efficient type-I schemes rely on entangled Bell-pair ancillary states, whose preparation is itself probabilistic and resource-intensive. Here we propose a boosted type-I fusion gate using only four ancillary single photons and standard linear-optical primitives. For multiqubit GHZ and graph states, the gate succeeds directly with probability 5/85/85/8, while a distillation protocol converts partially entangled outcomes into additional successful events, raising the total success probability to 11/1611/1611/16 after one stage and asymptotically to 3/43/43/4. We quantify the practical advantage of this scheme by estimating the photonic resources required for generating representative large entangled photonic states and show that the proposed gate significantly reduces the required overhead compared with existing schemes. These results expand the set of resource-efficient linear-optical primitives and enable a substantial reduction in the resource requirements for scalable photonic quantum computing and quantum communication.
Fusion gates enable the creation of large entangled photonic states for linear-optical quantum computing and communication protocols. However, their success probability is limited to 1/21/21/2 without additional photonic resources. Previous schemes for boosting type-I fusion have used four ancillary single photons or a two-qubit Bell state, whose preparation is probabilistic and resource intensive. Here we propose a boosted type-I fusion gate using only two independent ancillary single photons and no entangled ancillary input. It achieves a direct success probability of 5/85/85/8, matching that of the previous four-single-photon proposal while using half as many ancillary photons. The circuit is predominantly passive, with a single active element that applies a phase shift or swaps two modes according to intermediate photodetection outcomes. Unlike the previous schemes, successful outputs occupy fixed modes and require no further conditional output routing. In particular, we show that the gate is more robust to heralded ancillary-photon loss than previously proposed boosted gates and reduces the average number of single photons required to generate a six-qubit ring graph state by more than 4.6%4.6\%4.6% compared with other type-I schemes. It therefore offers a resource-efficient primitive for scalable fusion-based photonic quantum information processing.
Abstract We introduce a nonunitary partial-swap gate for fusing arbitrary small-sized photonic W-states into a large-scale entangled network of W-state efficiently without ancillary photons. A partial-swap gate is designed in an optical architecture based on linear optics elements. By introducing auxiliary degree of freedom, this gate provides a higher success probability with less cost. Our implementation can create a larger target state with a simpler set-up than previous proposals for W-state fusion. Also all ‘garbage’ states are recyclable, i.e., there is no complete failure output in our scheme in principle.
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.