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Acta Physica Polonica A

Enhancing the W State Fusion Process With a Toffoli Gate and a CNOT Gate via One-Way Quantum Computation and Linear Optics

Fırat Diker, Fatih Özaydin, Md Sadik Hassan Arik

Published Apr 1, 2015• 15 citations

Abstract

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.

DOI: 10.12693/aphyspola.127.1189

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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.

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.

We propose an optical scheme to prepare large-scale entangled networks of

W

states. The scheme works by simultaneously fusing three polarization-encoded

W

states of arbitrary size via accessing only one qubit of each

W

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

H

-polarized ancilla photon. Starting with three

n

-qubit

W

states, the scheme prepares a new

W

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

W

states considerably when compared to previously reported schemes.

Implementation of quantum logic gates with linear optical elements plays a prominent role in quantum computing due to the relatively easier manipulation and realization. We present efficient schemes to implement controlled-NOT (CNOT) gate and controlled-swap (Fredkin) gate by solely using linear optics. We encode the control qubits and target qudits in photonic polarization (two-level) and spatial degrees of freedom (

d

-level), respectively. Based on the hybrid encoding, CNOT and Fredkin gates are constructed in a deterministic way without any borrowed ancillary photons or measurement-induced nonlinearities. Remarkably, the number of linear optics required to implement a CNOT gate has been reduced to one polarization beam splitter (PBS), while only

d

PBSs are necessary to implement a generalized Fredkin gate. The optical depths of all schemes are reduced to one and dimension-independent. Besides, the fidelity of our three-qubit Fredkin gate is higher than 99.7\% under realistic conditions, which is higher than the previous schemes.

We design linear-optics multiqubit quantum logic gates. We assume the traditional encoding of a qubit onto the state of a single photon in two modes (e.g., spatial or polarization). We suggest schemes allowing direct probabilistic realization of the fundamental Toffoli and Fredkin gates without resorting to a sequence of single- and two-qubit gates. This yields more compact schemes and potentially reduces the number of ancilla photons. The proposed setups involve passive linear optics, sources of auxiliary single photons or maximally entangled pairs of photons, and single-photon detectors. In particular, we propose an interferometric implementation of the Toffoli gate in the coincidence basis, which does not require any ancilla photons and is experimentally feasible with current technology.

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

1/2

. Existing

3/4

-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

5/8

, while a distillation protocol converts partially entangled outcomes into additional successful events, raising the total success probability to

11/16

after one stage and asymptotically to

3/4

. 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.