# Efficient classical simulation of continuous variable quantum information processes.

@article{Bartlett2002EfficientCS, title={Efficient classical simulation of continuous variable quantum information processes.}, author={Stephen D. Bartlett and Barry C. Sanders and Samuel L. Braunstein and Kae Nemoto}, journal={Physical review letters}, year={2002}, volume={88 9}, pages={ 097904 } }

We obtain sufficient conditions for the efficient simulation of a continuous variable quantum algorithm or process on a classical computer. The resulting theorem is an extension of the Gottesman-Knill theorem to continuous variable quantum information. For a collection of harmonic oscillators, 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…

## 258 Citations

### Continuous variable quantum computing , and universality

- Computer Science
- 2014

This work introduces an specific proposal for continuous variable quantum computing, discusses universality of computation under this model, and shows how to implement a larger set of Hamiltonians from an initial set.

### Non-Gaussian states of light as an offline resource for universal continuous variable quantum information processing

- Computer ScienceSPIE Optics + Photonics
- 2005

We prove that continuous variable quantum information processing via Gaussian preserving operations, with Gaussian input states plus a (highly nonclassical) Fock number state, and subject to homodyne…

### 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.

### Practical Framework for Conditional Non-Gaussian Quantum State Preparation

- Physics
- 2020

We develop a general formalism, based on the Wigner function representation of continuous-variable quantum states, to describe the action of an arbitrary conditional operation on a multimode Gaussian…

### Efficient classical simulation of optical quantum information circuits.

- PhysicsPhysical review letters
- 2002

This simulatability result places powerful constraints on the capability to realize exponential quantum speedups as well as on inducing an optical nonlinear transformation via linear optics, photodetection-based measurement, and classical feedforward of measurement results, optimal cloning, and a wide range of other processes.

### Limitations on continuous variable quantum algorithms with Fourier transforms

- Physics
- 2009

We study quantum algorithms implemented within a single harmonic oscillator, or equivalently within a single mode of the electromagnetic field. Logical states correspond to functions of the canonical…

### Quantum entanglement beyond Gaussian criteria

- PhysicsProceedings of the National Academy of Sciences
- 2009

The experimental observation of genuine non-Gaussian entanglement using spatially entangled photon pairs is reported, which shows that the photons exhibit a variety ofEntanglement that cannot be reproduced by Gaussian states.

### Efficient classical computation of expectation values in a class of quantum circuits with an epistemically restricted phase space representation

- PhysicsScientific reports
- 2020

We devise a classical algorithm which efficiently computes the quantum expectation values arising in a class of continuous variable quantum circuits wherein the final quantum observable—after the…

### Universal quantum computation with continuous-variable cluster states.

- Computer Science, PhysicsPhysical review letters
- 2006

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…

### Universal Continuous Variable Quantum Computation in the Micromaser

- Computer ScienceUC
- 2010

It is shown how to generate a set of operations in the micromaser which can be used to achieve universal CVQC and the proof is easily adaptable to other potential physical systems.

## References

SHOWING 1-10 OF 36 REFERENCES

### 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…

### The Heisenberg Representation of Quantum Computers

- Physics
- 1998

Since Shor`s discovery of an algorithm to factor numbers on a quantum computer in polynomial time, quantum computation has become a subject of immense interest. Unfortunately, one of the key features…

### Teleportation of continuous quantum variables

- PhysicsTechnical Digest. Summaries of Papers Presented at the International Quantum Electronics Conference. Conference Edition. 1998 Technical Digest Series, Vol.7 (IEEE Cat. No.98CH36236)
- 1998

Summary form only given. A particularly startling discovery by Bennett et al. is the possibility for teleportation of a quantum state, whereby an unknown state of a spin-1/2 particle is transported…

### 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…

### Classical simulation of noninteracting-fermion quantum circuits

- PhysicsArXiv
- 2001

It is shown that a class of quantum computations that was recently shown to be efficiently simulatable on a classical computer by Valiant corresponds to a physical model of noninteracting fermions in one dimension.

### Error Correction for Continuous Quantum Variables

- Computer Science
- 1998

This work uses an error correction coding algorithm for continuous quantum variables to construct a highly efficient 5-wave-packet code which can correct arbitrary single wave-packets errors.

### Secure quantum key distribution using squeezed states

- Physics, Computer Science
- 2001

This proof employs quantum error-correcting codes that encode a finite-dimensional quantum system in the infinite-dimensional Hilbert space of an oscillator, and protect against errors that shift the canonical variables p and q.

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

- Physics
- 2002

Although universal continuous-variable quantum computation cannot be achieved via linear optics (including squeezing), homodyne detection, and feed-forward, inclusion of ideal photon-counting…

### How to share a continuous-variable quantum secret by optical interferometry

- Physics
- 2002

We develop the theory of continuous-variable quantum secret
sharing and propose its interferometric realization using
passive and active optical elements. In the ideal case of
infinite squeezing, a…

### Unconditional quantum teleportation

- PhysicsScience
- 1998

The first realization of unconditional quantum teleportation where every state entering the device is actually teleported is realized, using squeezed-state entanglement.