Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0308134 · Physical Review Letters

Experimental Nonlinear Sign Shift for Linear Optics Quantum Computation

Kaoru Sanaka, Thomas D. Jennewein, Jian-Wei Pan, Kevin J. Resch, Anton Zeilinger

Published Jan 9, 2004• 81 citations
arXivHTMLPDF

Abstract

We have realized the nonlinear sign shift operation for photonic qubits. This operation shifts the phase of two photons reflected by a beam splitter using an extra single photon and measurement. We show that the conditional phase shift is (1.05+/-0.06)pi in clear agreement with theory. Our results show that, by using an ancilla photon and conditional detection, nonlinear optical effects can be implemented using only linear optical elements. This experiment represents an essential step for linear optical implementations of scalable quantum computation.

DOI
10.1103/physrevlett.92.017902

Related papers

Quantum Computing: Linear Optics Implementations

Pål Sundsøy, Egil Fjeldberg

One of the main problems that optical quantum computing has to overcome is the efficient construction of two-photon gates. Theoretically these gates can be realized using Kerr-nonlinearities, but the techniques involved are experimentally very difficult. We therefore employ linear optics with projective measurements to generate these non-linearities. The downside is that the measurement-induced nonlinearities achieved with linear optics are less versatile and the success rate can be quite low. This project is mainly the result of a literature study but also a theoretical work on the physics behind quantum optical multiports which is essential for realizing two-photon gates. By applying different postcorrection techniques we increase the probability of success in a modifed non-linear sign shift gate which is foundational for the two photon controlled-NOT gate. We prove that it's not possible to correct the states by only using a single beam splitter. We show that it might be possible to increase the probability of success using a more complex setup with at least two error-correcting beam splitters.

arXiv:1607.03935•Jul 13, 2016•2 citations

On Photonic Implementation of Quantum Computers

Svetomir Simonović

The first section of the work investigates light modes as a means of implementing optical qubits and qudits. The modes considered are polarization mode, path mode, transverse spatial mode, frequency mode, temporal bin-mode and temporal mode. Subsequently, mathematical model of linear optical elements like beam splitters (BS) and phase shifters are deduced and their capability of representing any single qubit optical gate is exposed. Finally Knill, Laflamme and Milburn (KLM) method of using linear optical elements to promote nonlinear operations based on nonlinear (nondeterministic) sign-flip gate (NS) is explained, and designs of two qubits conditional sign flip gate (c-z1/16) and CNOT gate, both based on KLM method, are demonstrated. So, universal set of quantum gates based on linear optics is possible.

Advanced Technologies & Materials•Dec 2, 2023•0 citations

Bounds on the probability of success of postselected nonlinear sign shifts implemented with linear optics

Emanuel H. Knill

The fundamental gates of linear optics quantum computation are realized by using single photons sources, linear optics, and photon counters. Success of these gates is conditioned on the pattern of photons detected without using feedback. Here it is shown that the maximum probability of success of these gates is typically strictly less than 1. For the one-mode nonlinear sign shift, the probability of success is bounded by 1/2. For the conditional sign shift of two modes, this probability is bounded by 3/4. These bounds are still substantially larger than the highest probabilities shown to be achievable so far, which are 1/4 and 2/27, respectively.

arXiv:quant-ph/0307015•Physical Review A•Dec 18, 2003•58 citations

Quantum logic operations using linear optical elements

J. D. Franson, B. C. Jacobs, T. B. Pittman

Knill, Laflamme, and Milburn [1] have shown that probabilistic quantum logic operations can be implemented using linear optical elements, such as beam splitters and phase shifters, additional photons (ancilla) and post-selection based on the results of measurements on the ancilla. This may seem somewhat surprising, since logic operations are inherently nonlinear. Here the nonlinearity is produced by the quantum measurement process used in the post-selection. Nonlinearities of this kind are inherently quantum-mechanical and have no classical analogy.

Nonlinear Optics•Jan 1, 2002•1 citation

Quantum gates using linear optics and postselection

E. Knill

Recently it was realized that linear optics and photodetectors with feedback can be used for theoretically efficient quantum information processing. The first of three steps toward efficient linear optics quantum computation is to design a simple postselected gate that implements a nonlinear phase shift on one mode. Here a computational strategy is given for finding postselected gates for bosonic qubits with helper photons. A more efficient conditional sign flip gate is obtained. What is the maximum efficiency for such gates? This question is posed and it is shown that the probability of success cannot be 1.

arXiv:quant-ph/0110144•Physical Review A•Nov 14, 2002•113 citations

Spatiotemporal few-photon optical nonlinearities through linear optics and measurement

Kevin J. Resch

It is well known that optical nonlinearities are extremely weak at the quantum, or single-photon, level. This has been one of the major difficulties for optical implementations of universal, scalable quantum computation. Knill, Laflamme, and Milburn [Nature (London) 409, 46 (2001)] showed, among other things, that one could perform the elusive two-qubit logic gates with only linear-optical elements if one also uses extra single photons and measurement. In this work, we apply linear-optics techniques to produce effects in few-photon beams that are more familiar to strong-field nonlinear optics. Specifically, we show that these methods are sufficient to change the spatial (or temporal) properties of a light beam with strong dependence on its constituent number of photons; such phenomena cannot occur via linear optics alone.

Physical Review A•Nov 24, 2004•8 citations
We have realized the nonlinear sign shift operation for photonic qubits. This operation shifts the phase of two photons reflected by a beam splitter using an extra single photon and measurement. We show that the conditional phase shift is (1.05+/-0.06)pi in clear agreement with theory. Our results show that, by using an ancilla photon and conditional detection, nonlinear optical effects can be implemented using only linear optical elements. This experiment represents an essential step for linear optical implementations of scalable quantum computation.
One of the main problems that optical quantum computing has to overcome is the efficient construction of two-photon gates. Theoretically these gates can be realized using Kerr-nonlinearities, but the techniques involved are experimentally very difficult. We therefore employ linear optics with projective measurements to generate these non-linearities. The downside is that the measurement-induced nonlinearities achieved with linear optics are less versatile and the success rate can be quite low. This project is mainly the result of a literature study but also a theoretical work on the physics behind quantum optical multiports which is essential for realizing two-photon gates. By applying different postcorrection techniques we increase the probability of success in a modifed non-linear sign shift gate which is foundational for the two photon controlled-NOT gate. We prove that it's not possible to correct the states by only using a single beam splitter. We show that it might be possible to increase the probability of success using a more complex setup with at least two error-correcting beam splitters.
The first section of the work investigates light modes as a means of implementing optical qubits and qudits. The modes considered are polarization mode, path mode, transverse spatial mode, frequency mode, temporal bin-mode and temporal mode. Subsequently, mathematical model of linear optical elements like beam splitters (BS) and phase shifters are deduced and their capability of representing any single qubit optical gate is exposed. Finally Knill, Laflamme and Milburn (KLM) method of using linear optical elements to promote nonlinear operations based on nonlinear (nondeterministic) sign-flip gate (NS) is explained, and designs of two qubits conditional sign flip gate (c-z1/16) and CNOT gate, both based on KLM method, are demonstrated. So, universal set of quantum gates based on linear optics is possible.
The fundamental gates of linear optics quantum computation are realized by using single photons sources, linear optics, and photon counters. Success of these gates is conditioned on the pattern of photons detected without using feedback. Here it is shown that the maximum probability of success of these gates is typically strictly less than 1. For the one-mode nonlinear sign shift, the probability of success is bounded by 1/2. For the conditional sign shift of two modes, this probability is bounded by 3/4. These bounds are still substantially larger than the highest probabilities shown to be achievable so far, which are 1/4 and 2/27, respectively.
Knill, Laflamme, and Milburn [1] have shown that probabilistic quantum logic operations can be implemented using linear optical elements, such as beam splitters and phase shifters, additional photons (ancilla) and post-selection based on the results of measurements on the ancilla. This may seem somewhat surprising, since logic operations are inherently nonlinear. Here the nonlinearity is produced by the quantum measurement process used in the post-selection. Nonlinearities of this kind are inherently quantum-mechanical and have no classical analogy.
Recently it was realized that linear optics and photodetectors with feedback can be used for theoretically efficient quantum information processing. The first of three steps toward efficient linear optics quantum computation is to design a simple postselected gate that implements a nonlinear phase shift on one mode. Here a computational strategy is given for finding postselected gates for bosonic qubits with helper photons. A more efficient conditional sign flip gate is obtained. What is the maximum efficiency for such gates? This question is posed and it is shown that the probability of success cannot be 1.
It is well known that optical nonlinearities are extremely weak at the quantum, or single-photon, level. This has been one of the major difficulties for optical implementations of universal, scalable quantum computation. Knill, Laflamme, and Milburn [Nature (London) 409, 46 (2001)] showed, among other things, that one could perform the elusive two-qubit logic gates with only linear-optical elements if one also uses extra single photons and measurement. In this work, we apply linear-optics techniques to produce effects in few-photon beams that are more familiar to strong-field nonlinear optics. Specifically, we show that these methods are sufficient to change the spatial (or temporal) properties of a light beam with strong dependence on its constituent number of photons; such phenomena cannot occur via linear optics alone.