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arXiv:quant-ph/0408118 · Physical Review Letters

Nearly Deterministic Linear Optical Controlled-NOT Gate

Kae Nemoto, William J. Munro

Published Dec 15, 2004• 659 citations
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Abstract

We show how to construct a near deterministic CNOT gate using several single photons sources, linear optics, photon number resolving quantum nondemolition detectors, and feed forward. This gate does not require the use of massively entangled states common to other implementations and is very efficient on resources with only one ancilla photon required. The key element of this gate is nondemolition detectors that use a weak cross-Kerr nonlinearity effect to conditionally generate a phase shift on a coherent probe if a photon is present in the signal mode. These potential phase shifts can then be measured using highly efficient homodyne detection.

DOI
10.1103/physrevlett.93.250502

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We show how to construct a near deterministic CNOT gate using several single photons sources, linear optics, photon number resolving quantum nondemolition detectors, and feed forward. This gate does not require the use of massively entangled states common to other implementations and is very efficient on resources with only one ancilla photon required. The key element of this gate is nondemolition detectors that use a weak cross-Kerr nonlinearity effect to conditionally generate a phase shift on a coherent probe if a photon is present in the signal mode. These potential phase shifts can then be measured using highly efficient homodyne detection.
On the basis of the probe coherent state and weak cross-Kerr nonlinearities, we present a scheme of a nearly deterministic Controlled-NOT gate. In this construction, feed-forward methods, quantum nondemolition detectors and several optical elements are applied. It is a potentially practical quantum gate with certain features. First, the lack of auxiliary photons is allowable, which decreases consumption of resources. Secondly, employment of the signal photon from either of target output ports and three quantum nondemolition detectors enable the success probability to approach unit and judge whether the signal photons lose or not. Thirdly, the displacement measurement is adopted, and thus the Controlled-NOT gate works against photon loss of the probe coherent state. Finally, in order to circumvent the effect of dephasing, the monochromatic signal photons are exploited.
Quantum information offers the promise of being able to perform certain communication and computation tasks that cannot be done with conventional information technology (IT). Optical quantum information processing (QIP) holds particular appeal, since it offers the prospect of communicating and computing with the same type of qubit. Linear optical techniques have been shown to be scalable, but the corresponding quantum computing circuits need many auxiliary resources. Here we present an alternative approach to optical QIP, based on the use of weak cross-Kerr nonlinearities and homodyne measurements. We show how this approach provides the fundamental building blocks for highly efficient non-absorbing single photon number resolving detectors, two qubit parity detectors, Bell state measurements and finally near deterministic control-not (CNOT) gates. These are essential QIP devices.
Abstract. Quantum information offers the promise of being able to perform certain communication and computation tasks that cannot be done with conventional information technology (IT). Optical Quantum Information Processing (QIP) holds particular appeal, since it offers the prospect of communicating and computing with the same type of qubit. Linear optical techniques have been shown to be scalable, but the corresponding quantum computing circuits need many auxiliary resources. Here we present an alternative approach to optical QIP, based on the use of weak cross-Kerr nonlinearities and homodyne measurements. We show how this approach provides the fundamental building blocks for highly efficient non-absorbing single photon number resolving detectors, two qubit parity detectors, Bell state measurements and finally near deterministic control-not (CNOT) gates. These are essential QIP devices.
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 (ddd-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 ddd 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.
Processing information quantum mechanically is known to enable new communication and computational scenarios that cannot be accessed with conventional information technology (IT). It is known that such quantum processing can be performed with linear optical techniques, measurement and feed-forward. However, here the gates are intrinsically probabilistic and so scaling up such an approach requires considerable qubit resources. Here we present an alternative approach to optical QIP, based on the use of weak cross-Kerr non-linearities and highly efficient homodyne measurements. This approach enables a parity gate between optical qubits, mediated by an additional optical probe mode, enabling near-deterministic Bell state measurement and entangling gates. Our approach is therefore the basis for very efficient, scalable optical QIP, and provides a natural method for distributing such processing, combining it with quantum communication.
Abstract By harnessing weak cross‐Kerr nonlinearities, it proposes two deterministic hyperparallel quantum control gates, including the hyperparallel controlled‐NOT (hyper‐CNOT) gate and hyperparallel Fredkin (hyper‐Fredkin) gate for photonic systems in the polarization and spatial degrees of freedom (DoFs), which are composed of two procedures for the implementations of the first polarized control (CNOT and Fredkin) gates and the second spatial control (CNOT and Fredkin) ones in turn. Moreover, compared with the two two‐photon CNOT gates (three‐photon Fredkin gates) in one DoF, the hyper‐CNOT (hyper‐Fredkin) gate is provided with more straightforward quantum circuits, lower computational costs of resource overhead (without the assistance of single photons or entangled states), less cross‐Kerr nonlinear interactions between three photons and the coherent states, and reduces the effect caused by photon‐loss noise. The success probabilities of two quantum control gates are approximated unit by performing the corresponding classical feed‐forward operations based on the different measuring outcomes of the X‐homodyne detectors to be aimed at the coherent states, and they are robust against the photon loss as well, which are feasible with the current technology and convenient in practical applications.