# Quantum Computation over Continuous Variables

@article{Lloyd1999QuantumCO, title={Quantum Computation over Continuous Variables}, author={S. Lloyd and Samuel L. Braunstein}, journal={Physical Review Letters}, year={1999}, volume={82}, pages={1784-1787} }

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 amplitudes of the electromagnetic field might be constructed using simple linear devices such as beam splitters and phase shifters, together with squeezers and nonlinear devices such as Kerr-effect fibers and atoms in optical cavities. Such a device could in principle perform “floating point…

## 615 Citations

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

- Physics, MathematicsPhysical review letters
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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.

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

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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.

### Continuous variable quantum computing , and universality

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### Hybrid Quantum Computing

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Necessary and sufficient conditions are given for the construction of a hybrid quantum computer that operates on both continuous and discrete quantum variables that are more efficient than conventional quantum computers for performing a variety of quantum algorithms.

### 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.

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We present a scheme to perform universal quantum computation using global control with an arbitrary subsystem dimension not necessarily finite. The scheme is developed over a one spatial dimension…

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

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Quantum computation and quantum control operate by building unitary transformations out of sequences of elementary quantum logic operations or applications of control fields. This paper puts upper…

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

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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…

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