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Intramode encoding of continuous-variable quantum information in a single optical parametric oscillator (Conference Presentation)

Olivier Pfister

Published Apr 28, 2017• 0 citations
Publisher

Abstract

Quantum information can be encoded in a scalable manner over the continuous variables (CV) that are the canonically conjugate quantum amplitudes of the electromagnetic field, which are mathematical equivalents of the position and momentum of the quantum harmonic oscillator. Previous results in our group in Charlottesville and the groups of Akira Furusawa in Tokyo, of Nicolas Treps in Paris, and of Ping-Koy Lam in Canberra, have shown that CV quantum information is massively scalable. In addition, Nicolas Menicucci in Melbourne has shown that there exists a fault tolerance threshold for CV quantum computing with the Gottesman-Kitaev-Preskill qubit error encoding. Here, we report on our exploration of the extension of scalable CV encoding by way of intramode, rather than intermode, squeezing and entanglement. As is well known, single-mode squeezing can only be considered along with the "quasi-mode" approximation which assimilates the modes of the optical parametric oscillator cavity used in the experiment to delta functions. As Hans Bachor and Tim Ralph noted, when one ambles beyond this approximation, single-mode squeezing can be described as intramode two-mode squeezing. Here, we aim at generalizing this situation to the case of multipartite entangled cluster states.

DOI
10.1117/12.2253603

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Quantum information can be encoded in a scalable manner over the continuous variables (CV) that are the canonically conjugate quantum amplitudes of the electromagnetic field, which are mathematical equivalents of the position and momentum of the quantum harmonic oscillator. Previous results in our group in Charlottesville and the groups of Akira Furusawa in Tokyo, of Nicolas Treps in Paris, and of Ping-Koy Lam in Canberra, have shown that CV quantum information is massively scalable. In addition, Nicolas Menicucci in Melbourne has shown that there exists a fault tolerance threshold for CV quantum computing with the Gottesman-Kitaev-Preskill qubit error encoding. Here, we report on our exploration of the extension of scalable CV encoding by way of intramode, rather than intermode, squeezing and entanglement. As is well known, single-mode squeezing can only be considered along with the "quasi-mode" approximation which assimilates the modes of the optical parametric oscillator cavity used in the experiment to delta functions. As Hans Bachor and Tim Ralph noted, when one ambles beyond this approximation, single-mode squeezing can be described as intramode two-mode squeezing. Here, we aim at generalizing this situation to the case of multipartite entangled cluster states.
In the race to demonstrate a scalable and fault tolerant quantum computing (QC) platform, quantum photonics stands poised to have a major impact. In particular, by encoding quantum information over fields rather than photons (continuous-variable—CV, rather than discrete-variable—DV, quantum information), record-size quantum processors were demonstrated in spectral and in temporal quantum field combs. These demonstrations used the measurement-based QC paradigm, which is based on cluster entangled states. In this talk, I will outline two of our recent results: proposals for generating hypercubic cluster states by phase modulation of the quantum optical frequency comb and for generating fault-tolerant hybrid CV-DV encodings called Gottesman-Kitaev-Preskill states. The latter leverages CV cluster states along with our experimental ability to perform photon-number-resolving measurements up to 100 photons.
One-way quantum computing uses single-qubit projective measurements performed on a cluster state (a highly entangled state of multiple qubits) in order to enact quantum gates. The model is promising due to its potential scalability; the cluster state may be produced at the beginning of the computation and operated on over time. Continuous variables (CV) offer another potential benefit in the form of deterministic entanglement generation. This determinism can lead to robust cluster states and scalable quantum computation. Recent demonstrations of CV cluster states have made great strides on the path to scalability, utilizing either time or frequency multiplexing in optical parametric oscillators (OPO), both above and below threshold. The techniques relied on a combination of entangling operators and beam-splitter transformations. Here we show that an analogous transformation exists for amplifiers with Gaussian inputs states operating on multiple spatial modes. By judicious selection of local oscillators, the spatial mode distribution is analogous to the optical frequency comb consisting of axial modes in an OPO cavity. We outline an experimental system that generates cluster states across the spatial frequency comb, which can also scale the amount of quantum noise reduction to potentially larger than in other systems.
Summary form only given. The use of continuous-variable (CV) quantum computing allows information to be encoded and processed much more compactly and efficiently than with discrete-variable (qubit) computing. That is, with CV realizations, one can perform quantum information processes using fewer coupled quantum systems: a considerable advantage for the experimental realization of quantum computing. As a result, CV quantum information theory is of interest in quantum error correction, quantum cryptography and quantum teleportation. For example, quantum teleportation has recently been tested experimentally in the CV domain. The current proposed realization of CV quantum computation employs position eigenstates as a computational basis; these states are approximated in experiment using highly squeezed states. We introduce new CV representations, where the generalized Pauli group is generated by the number and phase operators for harmonic oscillators, and the computational basis is given by either harmonic oscillator energy eigenstates or phase eigenstates.
In the one-way model of quantum computing, quantum algorithms are implemented using only measurements on an entangled initial state. Much of the hard work is done upfront when creating this universal resource, known as a cluster state, on which the measurements are made. Here we detail a new proposal for a scalable method of creating cluster states using only a single multimode optical parametric oscillator (OPO). The method generates a continuous-variable cluster state that is universal for quantum computation and encoded in the quadratures of the optical frequency comb of the OPO. This work expands on the presentation in Menicucci, Flammia and Pfister (2008 Phys. Rev. Lett. 101 , 130501).
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The generation of continuous-variable (CV) scalable multipartite entanglement and non-Gaussian states is important for quantum information, in particular quantum computing. Non-Gaussian Wigner functions as well as macroscopic scaling of multipartite entanglement are both necessary ingredients for a CV quantum computer [1]. As a result it is necessary to find a reliable way to produce such states in a compact, manageable manner. Our group has shown that the use of concurrent second order nonlinearities and continuous variables can solve the scalability problem [2]. Second order cascaded nonlinearities could also be used in an optical parametric oscillator (OPO) to produce an effective third-order Hamiltonian, which is needed to produce non-Gaussian states.