# Universal quantum computation with continuous-variable cluster states.

@article{Menicucci2006UniversalQC, title={Universal quantum computation with continuous-variable cluster states.}, author={Nicolas C. Menicucci and Peter van Loock and Mile Gu and Christian Weedbrook and Timothy C. Ralph and Michael A. Nielsen}, journal={Physical review letters}, year={2006}, volume={97 11}, pages={ 110501 } }

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…

## 478 Citations

### Quantum Computing with Continuous-Variable Clusters

- Computer Science
- 2009

It is proved that there are universal states for which the offline squeezing per mode does not increase with the size of the cluster and the existence of universal continuous-variable resource states is found.

### Optical Quantum Computation with Continuous-Variable Cluster States

- Physics2007 Conference on Lasers and Electro-Optics - Pacific Rim
- 2007

We describe an extension of the cluster-state model for universal quantum computation from qubits to qumodes (quantized harmonic oscillators), i.e., a translation from discrete to continuous quantum…

### Optical Quantum Computation with Continuous-Variable Cluster States

- Physics
- 2007

We describe an extension of the cluster-state model for universal quantum computation from qubits to qumodes (quantized harmonic oscillators), i.e., a translation from discrete to continuous quantum…

### Universal quantum computation with temporal-mode bilayer square lattices

- Physics
- 2018

We propose an experimental design for universal continuous-variable quantum computation that incorporates recent innovations in linear-optics-based continuous-variable cluster state generation and…

### Compact Gaussian quantum computation by multi-pixel homodyne detection

- Physics
- 2013

This method is based on a multi-pixel homodyne detection system recently demonstrated experimentally, which includes classical data post-processing and allows the incorporation of the linear optics network in the stage of the measurement.

### One-way quantum computing with arbitrarily large time-frequency continuous-variable cluster states from a single optical parametric oscillator

- Computer Science, Physics
- 2016

A generalized measurement protocol is introduced to enable improved computational performance on this entanglement resource and create a scalable architecture in which a single optical parametric oscillator and simple interferometer entangle into a computationally universal continuous-variable cluster state.

### Non-Gaussian ancilla states for continuous variable quantum computation via Gaussian maps

- Physics
- 2006

We investigate non-Gaussian states of light as ancillary inputs for generating nonlinear transformations required for quantum computing with continuous variables. We consider a recent proposal for…

### Demonstration of unconditional one-way quantum computations for continuous variables.

- PhysicsPhysical review letters
- 2011

This work implements three different levels of squeezing operations and a Fourier transformation, all of which are accessible by selecting the correct quadrature measurement angles of the homodyne detections, necessary for universal quantum computation.

### Cluster States from Gaussian States: Essential Diagnostic Tools for Continuous-Variable One-Way Quantum Computing

- Computer Science, PhysicsPRX Quantum
- 2021

By a detailed analysis of the structure of Gaussian states, an algorithm is derived that reveals hidden entanglement in an arbitrary Gaussian state and optimizes its use for one-way quantum computing.

### Ultracompact generation of continuous-variable cluster states

- Physics
- 2007

We propose an experimental scheme that has the potential for large-scale realization of continuous-variable (CV) cluster states for universal quantum computation. We do this by mapping CV…

## References

SHOWING 1-10 OF 31 REFERENCES

### Resource-efficient linear optical quantum computation.

- PhysicsPhysical review letters
- 2005

This work introduces a scheme for linear optics quantum computation, that makes no use of teleported gates, and requires stable interferometry over only the coherence length of the photons, and demonstrates the universality and usefulness of generic parity measurements.

### Optical quantum computation using cluster States.

- PhysicsPhysical review letters
- 2004

An approach to optical quantum computation in which a deterministic entangling quantum gate may be performed using a few hundred coherently interacting optical elements using the abstract cluster-state model of quantum computation.

### Continuous-variable Gaussian analog of cluster states

- Physics
- 2006

We present a continuous-variable CV Gaussian analog of cluster states, a new class of CV multipartite entangled states that can be generated from squeezing and quantum nondemolition coupling HI…

### Efficient classical simulation of continuous variable quantum information processes.

- Physics, MathematicsPhysical review letters
- 2002

It is obtained that any quantum process that begins with unentangled Gaussian states, performs only transformations generated by Hamiltonians that are quadratic in the canonical operators, and involves only measurements of canonical operators and suitable operations conditioned on these measurements can be simulated efficiently on a classical computer.

### Quantum Computation over Continuous Variables

- Physics
- 1999

This paper provides necessary and sufficient conditions for constructing a universal quantum computer over continuous variables. As an example, it is shown how a universal quantum computer for the…

### Squeezing as an irreducible resource

- Physics
- 2005

Using the Bloch-Messiah reduction we show that squeezing is an ``irreducible'' resource which remains invariant under transformations by linear optical elements. In particular, this gives a…

### A scheme for efficient quantum computation with linear optics

- PhysicsNature
- 2001

It is shown that efficient quantum computation is possible using only beam splitters, phase shifters, single photon sources and photo-detectors and are robust against errors from photon loss and detector inefficiency.

### Encoding a qubit in an oscillator

- Physics
- 2001

Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes…

### Noise thresholds for optical quantum computers.

- PhysicsPhysical review letters
- 2006

The results show that scalable optical quantum computing is possible for photon loss probabilities <3 x 10(-3), and for depolarization probabilities <10(-4).