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

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Experimental demonstration of a Hadamard gate for coherent state qubits

Anders Tipsmark, Ruifang Dong, Amine Laghout, Miroslav Ježek, Ulrik L. Andersen

Published May 1, 2011• 1 citation
Publisher

Abstract

In recent years coherent state qubits, |α〉 ± | - α〉 have gained much interest. The main reason is the promise to realize a universal set of coherent state quantum gates with a relative low overhead using, only linear optics and photon counters. A universal set of gates consists of a single mode and a two mode phase gate and a Hadamard gate. The Hadamard is the gate that transforms one set of basis states into the conjugate basis, e.g | ± α〉 - | - α〉. Here we present an experimental demonstration of a Hadamard gate for coherent state qubits. The implementation is based on the scheme proposed by Marek and Fiurasek (2010).

DOI
10.1109/cleoe.2011.5943446

Related papers

Experimental demonstration of a Hadamard gate for coherent state qubits

Anders Tipsmark, Ruifang Dong, Amine Laghaout +3 more

We discuss and make an experimental test of a probabilistic Hadamard gate for coherent state qubits. The scheme is based on linear optical components, nonclassical resources, and the joint projective action of a photon counter and a homodyne detector. We experimentally characterize the gate for the coherent states of the computational basis by full tomographic reconstruction of the transformed output states. Based on the parameters of the experiment, we simulate the fidelity for all coherent state qubits on the Bloch sphere.

arXiv:1107.0822•Physical Review A•Nov 8, 2011•77 citations

High-dimensional quantum gates using full-field spatial modes of photons

Florian Brandt, Markus Hiekkamäki, Frédéric Bouchard +2 more

Unitary transformations are the fundamental building blocks of gates and operations in quantum information processing, allowing the complete manipulation of quantum systems in a coherent manner. In the case of photons, optical elements that can perform unitary transformations are readily available only for some degrees of freedom, e.g., wave plates for polarization. However, for high-dimensional states encoded in the transverse spatial modes of light, performing arbitrary unitary transformations remains a challenging task for both theoretical proposals and actual implementations. Following the idea of multi-plane light conversion, we show that it is possible to perform a broad variety of unitary operations at high quality by using only a few phase modulation planes. More importantly, we experimentally implement several high-dimensional quantum gates for up to five-dimensional states encoded in the full-field mode structure of photons. In particular, we realize cyclic and quantum Fourier transformations, known as Pauli X ^ -gates and Hadamard H ^ -gates, respectively, with an average visibility of more than 90%. In addition, we demonstrate near-perfect “unitarity” by means of quantum process tomography, unveiling a process purity of 99%. Last, we demonstrate the benefit of the two independent spatial degrees of freedom, i.e., azimuthal and radial, and implement a two-qubit controlled-NOT quantum operation on a single photon. Thus, our demonstrations open up new paths to implement high-dimensional quantum operations, which can be applied to various tasks in quantum communication, computation, and sensing schemes.

arXiv:1907.13002•Optica•Dec 23, 2019•177 citations

Deterministic Hadamard gate for microwave cat-state qubits in circuit QED

Simon E. Nigg

We propose the implementation of a deterministic Hadamard gate for logical photonic qubits encoded in superpositions of coherent states of a harmonic oscillator. The proposed scheme builds on a recently introduced set of conditional operations in the strong dispersive regime of circuit QED [Z. Leghtas et al., Phys. Rev. A 87, 042315 (2013)]. We further propose an architecture for coupling two such logical qubits and provide a universal set of deterministic quantum gates. Based on parameter values taken from the current state of the art, we give estimates for the achievable gate fidelities accounting for fundamental gate imperfections and finite coherence time due to photon loss.

arXiv:1401.6884•Physical Review A•Feb 27, 2014•36 citations

Demonstration of an all-optical quantum controlled-NOT gate

Jeremy L. O’Brien, Geoff J. Pryde, Andrew G. White +2 more

The promise of tremendous computational power, coupled with the development of robust error-correcting schemes, has fuelled extensive efforts to build a quantum computer. The requirements for realizing such a device are confounding: scalable quantum bits (two-level quantum systems, or qubits) that can be well isolated from the environment, but also initialized, measured and made to undergo controllable interactions to implement a universal set of quantum logic gates. The usual set consists of single qubit rotations and a controlled-NOT (CNOT) gate, which flips the state of a target qubit conditional on the control qubit being in the state 1. Here we report an unambiguous experimental demonstration and comprehensive characterization of quantum CNOT operation in an optical system. We produce all four entangled Bell states as a function of only the input qubits' logical values, for a single operating condition of the gate. The gate is probabilistic (the qubits are destroyed upon failure), but with the addition of linear optical quantum non-demolition measurements, it is equivalent to the CNOT gate required for scalable all-optical quantum computation.

arXiv:quant-ph/0403062•APS•Mar 8, 2004•61 citations

An approach to realize a quantum Hadamard gate through optical implementation

Shihan Sajeed, Anis Ahmed, S. M. Ullah +1 more

Transverse modes of optical fields are proposed to be used as qubits for the implementation of quantum Hadamard gate. Mach-Zehnder Interferometer (MZI), phase shifter, y-junction beam splitters and other optical devices are utilized to realize a quantum Hadamard gate. The possibility of this encoding scheme was designed, simulated and verified through rigorous numerical analyses using the Beam propagation method. The proposed gate has the potential of being more compact and easily realizable than some other optical implementation proposals since it is based on planar light wave circuit technology and can be constructed very easily by using a Mach-Zehnder Interferometer. The Results proved that the design is able to perform the required Hadamard transformation and the conclusion was reached that the model was a successful implementation of a quantum Hadamard gate.

IEEE International Conference on Electro Information Technology•May 1, 2010•2 citations

Coherent-state linear optical quantum computing gates using simplified diagonal superposition resource states

Austin P. Lund, Timothy C. Ralph

In this paper we explore the possibility of fundamental tests for coherent-state optical quantum computing gates [T. C. Ralph et al., Phys. Rev. A 68, 042319 (2003)] using sophisticated but not unrealistic quantum states. The major resource required in these gates is a state diagonal to the basis states. We use the recent observation that a squeezed single-photon state $[S(r)\ensuremath{\mid}1⟩]$ approximates well an odd superposition of coherent states $(\ensuremath{\mid}\ensuremath{\alpha}⟩\ensuremath{-}\ensuremath{\mid}\ensuremath{-}\ensuremath{\alpha}⟩)$ to address the diagonal resource problem. The approximation only holds for relatively small $\ensuremath{\alpha}$, and hence these gates cannot be used in a scalable scheme. We explore the effects on fidelities and probabilities in teleportation and a rotated Hadamard gate.

arXiv:quant-ph/0410204•Physical Review A•Mar 8, 2005•9 citations
In recent years coherent state qubits, |α〉 ± | - α〉 have gained much interest. The main reason is the promise to realize a universal set of coherent state quantum gates with a relative low overhead using, only linear optics and photon counters. A universal set of gates consists of a single mode and a two mode phase gate and a Hadamard gate. The Hadamard is the gate that transforms one set of basis states into the conjugate basis, e.g | ± α〉 - | - α〉. Here we present an experimental demonstration of a Hadamard gate for coherent state qubits. The implementation is based on the scheme proposed by Marek and Fiurasek (2010).
We discuss and make an experimental test of a probabilistic Hadamard gate for coherent state qubits. The scheme is based on linear optical components, nonclassical resources, and the joint projective action of a photon counter and a homodyne detector. We experimentally characterize the gate for the coherent states of the computational basis by full tomographic reconstruction of the transformed output states. Based on the parameters of the experiment, we simulate the fidelity for all coherent state qubits on the Bloch sphere.
Unitary transformations are the fundamental building blocks of gates and operations in quantum information processing, allowing the complete manipulation of quantum systems in a coherent manner. In the case of photons, optical elements that can perform unitary transformations are readily available only for some degrees of freedom, e.g., wave plates for polarization. However, for high-dimensional states encoded in the transverse spatial modes of light, performing arbitrary unitary transformations remains a challenging task for both theoretical proposals and actual implementations. Following the idea of multi-plane light conversion, we show that it is possible to perform a broad variety of unitary operations at high quality by using only a few phase modulation planes. More importantly, we experimentally implement several high-dimensional quantum gates for up to five-dimensional states encoded in the full-field mode structure of photons. In particular, we realize cyclic and quantum Fourier transformations, known as Pauli X ^ -gates and Hadamard H ^ -gates, respectively, with an average visibility of more than 90%. In addition, we demonstrate near-perfect “unitarity” by means of quantum process tomography, unveiling a process purity of 99%. Last, we demonstrate the benefit of the two independent spatial degrees of freedom, i.e., azimuthal and radial, and implement a two-qubit controlled-NOT quantum operation on a single photon. Thus, our demonstrations open up new paths to implement high-dimensional quantum operations, which can be applied to various tasks in quantum communication, computation, and sensing schemes.
We propose the implementation of a deterministic Hadamard gate for logical photonic qubits encoded in superpositions of coherent states of a harmonic oscillator. The proposed scheme builds on a recently introduced set of conditional operations in the strong dispersive regime of circuit QED [Z. Leghtas et al., Phys. Rev. A 87, 042315 (2013)]. We further propose an architecture for coupling two such logical qubits and provide a universal set of deterministic quantum gates. Based on parameter values taken from the current state of the art, we give estimates for the achievable gate fidelities accounting for fundamental gate imperfections and finite coherence time due to photon loss.
The promise of tremendous computational power, coupled with the development of robust error-correcting schemes, has fuelled extensive efforts to build a quantum computer. The requirements for realizing such a device are confounding: scalable quantum bits (two-level quantum systems, or qubits) that can be well isolated from the environment, but also initialized, measured and made to undergo controllable interactions to implement a universal set of quantum logic gates. The usual set consists of single qubit rotations and a controlled-NOT (CNOT) gate, which flips the state of a target qubit conditional on the control qubit being in the state 1. Here we report an unambiguous experimental demonstration and comprehensive characterization of quantum CNOT operation in an optical system. We produce all four entangled Bell states as a function of only the input qubits' logical values, for a single operating condition of the gate. The gate is probabilistic (the qubits are destroyed upon failure), but with the addition of linear optical quantum non-demolition measurements, it is equivalent to the CNOT gate required for scalable all-optical quantum computation.
Transverse modes of optical fields are proposed to be used as qubits for the implementation of quantum Hadamard gate. Mach-Zehnder Interferometer (MZI), phase shifter, y-junction beam splitters and other optical devices are utilized to realize a quantum Hadamard gate. The possibility of this encoding scheme was designed, simulated and verified through rigorous numerical analyses using the Beam propagation method. The proposed gate has the potential of being more compact and easily realizable than some other optical implementation proposals since it is based on planar light wave circuit technology and can be constructed very easily by using a Mach-Zehnder Interferometer. The Results proved that the design is able to perform the required Hadamard transformation and the conclusion was reached that the model was a successful implementation of a quantum Hadamard gate.
In this paper we explore the possibility of fundamental tests for coherent-state optical quantum computing gates [T. C. Ralph et al., Phys. Rev. A 68, 042319 (2003)] using sophisticated but not unrealistic quantum states. The major resource required in these gates is a state diagonal to the basis states. We use the recent observation that a squeezed single-photon state $[S(r)\ensuremath{\mid}1⟩]$ approximates well an odd superposition of coherent states $(\ensuremath{\mid}\ensuremath{\alpha}⟩\ensuremath{-}\ensuremath{\mid}\ensuremath{-}\ensuremath{\alpha}⟩)$ to address the diagonal resource problem. The approximation only holds for relatively small $\ensuremath{\alpha}$, and hence these gates cannot be used in a scalable scheme. We explore the effects on fidelities and probabilities in teleportation and a rotated Hadamard gate.