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

Quantum Electronics and Laser Science Conference

Quantum computation with continuous variables: requirement of nonlinearity for photon counting

Stephen D. Bartlett, Barry C. Sanders

Published Jun 25, 2003• 0 citations
Publisher

Abstract

Summary form only given. We show that universal continuous-variable (CV) quantum computation can be obtained using linear optics (phase-space displacements and squeezing), homodyne measurement with classical feed-forward, and a realization of the photon counting projective value measurements (PVM). We describe the PVM for current (ideal) photodetectors, and demonstrate that such detectors cannot be used to implement the photon counting PVM with linear optics alone. Specifically, proposals to implement photon counting using arrays of beamsplitters to distribute the photons across several modes is insufficient for universal CV quantum computation. The photon counting PVM carries with it an implicit nonlinearity, and we discuss how it can be implemented in a CV system using a Kerr interaction (or another nonlinear Hamiltonian) and homodyne measurement. The resource requirements of this measurement scheme compared with using linear optics and current photodetectors are outlined.

DOI
10.1109/qels.2002.1031342

Related papers

Universal continuous-variable quantum computation: Requirement of optical nonlinearity for photon counting

Stephen D. Bartlett, Barry C. Sanders

Although universal continuous-variable quantum computation cannot be achieved via linear optics (including squeezing), homodyne detection, and feed-forward, inclusion of ideal photon-counting measurements overcomes this obstacle. These measurements are sometimes described by arrays of beam splitters to distribute the photons across several modes. We show that such a scheme cannot be used to implement ideal photon counting and that such measurements necessarily involve nonlinear evolution. However, this requirement of nonlinearity can be moved ``off-line,'' thereby permitting universal continuous-variable quantum computation with linear optics.

arXiv:quant-ph/0110039•Physical Review A•Mar 18, 2002•165 citations

Universal Quantum Computation with Continuous-Variable Cluster States

Nicolas C. Menicucci, Peter van Loock, Mile Gu +3 more

We describe a generalization of the cluster-state model of quantum computation to continuous-variable systems, along with a proposal for an optical implementation using squeezed-light sources, linear optics, and homodyne detection. For universal quantum computation, a nonlinear element is required. This can be satisfied by adding to the toolbox any single-mode non-Gaussian measurement, while the initial cluster state itself remains Gaussian. Homodyne detection alone suffices to perform an arbitrary multimode Gaussian transformation via the cluster state. We also propose an experiment to demonstrate cluster-based error reduction when implementing Gaussian operations.

arXiv:quant-ph/0605198•Physical Review Letters•Sep 13, 2006•884 citations

Measurement-induced continuous-variable quantum interactions

Radim Filip, Petr Marek, Ulrik L. Andersen

We propose feasible implementations of basic continuous-variable (CV) interactions (squeezer, parametric amplifier, and quantum nondemolition interaction) between light modes without the requirement for in-line nonlinear couplings in a strongly pumped optical medium. The method is based entirely on linear optics, homodyne detection, and off-line squeezed ancillary states and therefore represents the CV analog of the measurement-induced nonlinearity approach, previously used in single-photon qubit experiments to probabilistically implement a controlled-NOT gate.

Physical Review A•Apr 4, 2005•151 citations

Quantum computation using linear optics

Gerard J Milburn

Summary form only given. Quantum computers are expected to increase the efficiency of solving problems such as factoring large integers. However an experimental implementation of even relatively simple quantum information processing with a few to a dozen qubits presents an enormous technological challenge. One of the earliest proposals for quantum computation is based on implementing a quantum bit with two optical modes containing one photon. The proposal is appealing due to the ease with which photon interference can be observed. However these early proposals required huge single photon optical nonlinearities. Unfortunately currently available optical nonlinearities are too weak and too noisy to be useful. Recently however we have discovered that efficient quantum computation is possible using only beam splitters, phase shifters, single photon sources and photodetectors. Our methods exploit feed forward from photo-detectors and are robust against errors from photon loss and detector inefficiency. In this tutorial I will outline this scheme, highlighting the technical challenges required to implement it. The tutorial will be relatively self contained with a brief introduction to quantum optics and quantum computation.

Quantum Electronics and Laser Science Conference•Jun 25, 2003•0 citations

Efficient measurement-based quantum computing with continuous-variable systems

Matthias Ohliger, Jens Eisert

We present strictly efficient schemes for scalable measurement-based quantum computing using continuous-variable systems: These schemes are based on suitable non-Gaussian resource states, ones that can be prepared using interactions of light with matter systems or even purely optically. Merely Gaussian measurements such as optical homodyning as well as photon counting measurements are required, on individual sites. These schemes overcome limitations posed by Gaussian cluster states, which are known not to be universal for quantum computations of unbounded length, unless one is willing to scale the degree of squeezing with the total system size. We establish a framework derived from tensor networks and matrix product states with infinite physical dimension and finite auxiliary dimension general enough to provide a framework for such schemes. Since in the discussed schemes the logical encoding is finite dimensional, tools of error correction are applicable. We also identify some further limitations for any continuous-variable computing scheme from which one can argue that no substantially easier ways of continuous-variable measurement-based computing than the presented one can exist.

arXiv:1112.2641•Physical Review A•Jun 21, 2012•38 citations

Quantum computing with continuous-variable clusters

Mile Gu, Christian Weedbrook, Nicolas C. Menicucci +2 more

Continuous-variable cluster states offer a potentially promising method of implementing a quantum computer. This paper extends and further refines theoretical foundations and protocols for experimental implementation. We give a cluster-state implementation of the cubic phase gate through photon detection, which, together with homodyne detection, facilitates universal quantum computation. In addition, we characterize the offline squeezed resources required to generate an arbitrary graph state through passive linear optics. Most significantly, we prove that there are universal states for which the offline squeezing per mode does not increase with the size of the cluster. Simple representations of continuous-variable graph states are introduced to analyze graph state transformations under measurement and the existence of universal continuous-variable resource states.

arXiv:0903.3233•Physical Review A•Jun 17, 2009•354 citations
Summary form only given. We show that universal continuous-variable (CV) quantum computation can be obtained using linear optics (phase-space displacements and squeezing), homodyne measurement with classical feed-forward, and a realization of the photon counting projective value measurements (PVM). We describe the PVM for current (ideal) photodetectors, and demonstrate that such detectors cannot be used to implement the photon counting PVM with linear optics alone. Specifically, proposals to implement photon counting using arrays of beamsplitters to distribute the photons across several modes is insufficient for universal CV quantum computation. The photon counting PVM carries with it an implicit nonlinearity, and we discuss how it can be implemented in a CV system using a Kerr interaction (or another nonlinear Hamiltonian) and homodyne measurement. The resource requirements of this measurement scheme compared with using linear optics and current photodetectors are outlined.
Although universal continuous-variable quantum computation cannot be achieved via linear optics (including squeezing), homodyne detection, and feed-forward, inclusion of ideal photon-counting measurements overcomes this obstacle. These measurements are sometimes described by arrays of beam splitters to distribute the photons across several modes. We show that such a scheme cannot be used to implement ideal photon counting and that such measurements necessarily involve nonlinear evolution. However, this requirement of nonlinearity can be moved ``off-line,'' thereby permitting universal continuous-variable quantum computation with linear optics.
We describe a generalization of the cluster-state model of quantum computation to continuous-variable systems, along with a proposal for an optical implementation using squeezed-light sources, linear optics, and homodyne detection. For universal quantum computation, a nonlinear element is required. This can be satisfied by adding to the toolbox any single-mode non-Gaussian measurement, while the initial cluster state itself remains Gaussian. Homodyne detection alone suffices to perform an arbitrary multimode Gaussian transformation via the cluster state. We also propose an experiment to demonstrate cluster-based error reduction when implementing Gaussian operations.
We propose feasible implementations of basic continuous-variable (CV) interactions (squeezer, parametric amplifier, and quantum nondemolition interaction) between light modes without the requirement for in-line nonlinear couplings in a strongly pumped optical medium. The method is based entirely on linear optics, homodyne detection, and off-line squeezed ancillary states and therefore represents the CV analog of the measurement-induced nonlinearity approach, previously used in single-photon qubit experiments to probabilistically implement a controlled-NOT gate.
Summary form only given. Quantum computers are expected to increase the efficiency of solving problems such as factoring large integers. However an experimental implementation of even relatively simple quantum information processing with a few to a dozen qubits presents an enormous technological challenge. One of the earliest proposals for quantum computation is based on implementing a quantum bit with two optical modes containing one photon. The proposal is appealing due to the ease with which photon interference can be observed. However these early proposals required huge single photon optical nonlinearities. Unfortunately currently available optical nonlinearities are too weak and too noisy to be useful. Recently however we have discovered that efficient quantum computation is possible using only beam splitters, phase shifters, single photon sources and photodetectors. Our methods exploit feed forward from photo-detectors and are robust against errors from photon loss and detector inefficiency. In this tutorial I will outline this scheme, highlighting the technical challenges required to implement it. The tutorial will be relatively self contained with a brief introduction to quantum optics and quantum computation.
We present strictly efficient schemes for scalable measurement-based quantum computing using continuous-variable systems: These schemes are based on suitable non-Gaussian resource states, ones that can be prepared using interactions of light with matter systems or even purely optically. Merely Gaussian measurements such as optical homodyning as well as photon counting measurements are required, on individual sites. These schemes overcome limitations posed by Gaussian cluster states, which are known not to be universal for quantum computations of unbounded length, unless one is willing to scale the degree of squeezing with the total system size. We establish a framework derived from tensor networks and matrix product states with infinite physical dimension and finite auxiliary dimension general enough to provide a framework for such schemes. Since in the discussed schemes the logical encoding is finite dimensional, tools of error correction are applicable. We also identify some further limitations for any continuous-variable computing scheme from which one can argue that no substantially easier ways of continuous-variable measurement-based computing than the presented one can exist.
Continuous-variable cluster states offer a potentially promising method of implementing a quantum computer. This paper extends and further refines theoretical foundations and protocols for experimental implementation. We give a cluster-state implementation of the cubic phase gate through photon detection, which, together with homodyne detection, facilitates universal quantum computation. In addition, we characterize the offline squeezed resources required to generate an arbitrary graph state through passive linear optics. Most significantly, we prove that there are universal states for which the offline squeezing per mode does not increase with the size of the cluster. Simple representations of continuous-variable graph states are introduced to analyze graph state transformations under measurement and the existence of universal continuous-variable resource states.