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Hybrid quantum information processing
Ulrik L. Andersen, Jonas S. Neergaard-Nielsen, Peter van Loock, Akira Furusawa
TL;DR
Quantum information processing has developed along separate discrete-variable and continuous-variable lines because their standard technologies were difficult to interconnect. This Review synthesizes recent efforts to combine them, covering state generation and hybrid protocols whose proposals and experiments have progressively blurred the boundary between the platforms.
Problem
Quantum information processing has traditionally followed separate discrete-variable and continuous-variable paths because interconnecting their standard technologies was experimentally difficult.
Method
The Review surveys recent progress in combining CV and DV methods, including nonclassical-state generation and hybrid quantum information-processing protocols.
Results
Hybridization has produced numerous theoretical proposals and experimental implementations, including deterministic optical hybrid teleportation, non-Gaussian state generation, and entanglement-distillation techniques.
Takeaways & Limitations
Combining DV and CV technologies is establishing a young research area with promising protocols for quantum information processing.
Takeaways & Limitations
Most demonstrations remain proof-of-principle experiments lacking high-fidelity operation, efficiency, and scalability.
Abstract
from arXiv · showhide
The development of quantum information processing has traditionally followed two separate and not immediately connected lines of study. The main line has focused on the implementation of quantum bit (qubit) based protocols whereas the other line has been devoted to implementations based on high-dimensional Gaussian states (such as coherent and squeezed states). The separation has been driven by the experimental difficulty in interconnecting the standard technologies of the two lines. However, in recent years, there has been a significant experimental progress in refining and connecting the technologies of the two fields which has resulted in the development and experimental realization of numerous new hybrid protocols. In this Review, we summarize these recent efforts on hybridizing the two types of schemes based on discrete and continuous variables.
I. INTRODUCTION
Quantum information processing spans discrete-variable and continuous-variable forms, distinguished by whether the relevant observable has discrete or continuous eigenvalues. This Review examines recent efforts to combine these approaches to overcome their individual limitations and realize hybrid protocols.
- Quantum information processing is pursued across many physical platforms, including light, ions, atoms, solid-state systems, superconducting systems, and nuclear magnetic resonance.
- Discrete-variable QIP uses observables with discretized eigenvalues, whereas continuous-variable QIP uses observables with a continuum of eigenvalues.
- Recent research has bridged DV and CV technologies to develop protocols intended to overcome limitations intrinsic to the individual schemes.
- The Review surveys hybrid CV-DV methods for quantum information processing, including nonclassical-state generation, teleportation, quantum repeaters, and quantum computing.
II. GENERATION OF NON-GAUSSIAN STATES
Non-Gaussian states can be generated either deterministically through strong coupling between continuous-variable oscillators and discrete two-level systems, or probabilistically through non-Gaussian detection. These hybrid approaches have enabled diverse state-generation experiments across electromagnetic and mechanical systems, while some proposed extensions remain unrealized.
- Gaussian states are relatively easy to produce with standard continuous-variable tools, but those tools alone cannot produce pure non-Gaussian states or arbitrary quantum states.Non-Gaussian transformations or measurements are needed to enter this regime.
- Deterministic generation: Deterministic schemes use strong coupling between a continuous-variable oscillator and a discrete two-level system to generate non-Gaussian states.Experiments include single photons, higher-order Fock states, Fock-state superpositions, Schrödinger cat states, and single-phonon mechanical states.
- Deterministic generation: The Purcell effect enables a strongly coupled cavity mode to harvest an emitted photon with large probability.Complete Wigner-function characterization has been achieved in selected microwave and optical experiments.
- Probabilistic generation: Probabilistic schemes use a finite-level detector to induce non-Gaussian transformations in otherwise Gaussian states.Examples include photon addition, single-photon heralding, photon subtraction, photonic-qubit engineering, and kitten-state generation.
- Combined techniques: Combining hybrid techniques has produced proposals and demonstrations for enlarging kitten and cat states, increasing entangled-state energy, and generating hybrid entanglement with microscopic systems.These approaches include conditional photon counting or homodyne detection, displacement, photon subtraction, and conditional squeezing.
- Experimental boundaries: Proposed photon-counting schemes for non-Gaussian spin and mechanical states remain experimentally challenging and have not yet been realized.Some progress toward a heralded non-Gaussian spin state has been reported.
III. QUANTUM INFORMATION PROCESSING
Hybrid quantum information processing combines DV and CV states, devices, and measurements to perform communication, computation, teleportation, and entanglement tasks. These schemes trade determinism, fidelity, efficiency, and implementation complexity in task-dependent ways.
- Hybridization supports quantum teleportation, error correction, entanglement distillation, Bell tests, Bell measurements, and quantum computation.
- Hybrid quantum teleportation: CV teleportation can deterministically transfer DV states, but perfectly faithful arbitrary-state transfer requires infinite Gaussian entanglement.Deterministic CV teleportation has been demonstrated for photonic qubits and a cat state.
- Hybrid quantum teleportation: DV teleportation can reach 100% fidelity for low-dimensional optical states, but linear-optical Bell measurements make its success probability fundamentally non-unit.Transmitting a high-dimensional CV state requires decomposing it into smaller states and performing many individual DV teleportations.
- Hybrid quantum teleportation: Hybrid teleportation therefore converts a probabilistic linear-optical qubit teleporter into a deterministic device, potentially at the expense of transfer fidelity.The reverse direction offers potentially high-fidelity CV transfer at the expense of non-unit success probability.
- Hybrid quantum teleportation: Cat-qubit teleportation uses entangled cat-qubit states and has been experimentally demonstrated for binary coherent states.The protocol is a critical element of cat-qubit quantum computing, where some probabilistic gates have been realized.
- Hybrid entanglement distillation and quantum communication: Photon subtraction combined with squeezing or displacement enables hybrid operations that can optimize entanglement distillation and engineer DV-qubit-type entanglement remotely.A heralded noiseless linear amplifier is another DV non-Gaussian tool for distilling CV and DV entangled states.
- Hybrid quantum computing: Universal hybrid optical gates use teleportation- or measurement-based processing, replacing selected DV elements with CV elements or selected CV elements with DV elements.Universality can place non-Gaussian resources in ancilla states or detectors, with implementation complexity guiding the choice.
IV. OUTLOOK
Hybrid DV–CV research has blurred a once-sharp platform boundary, producing theoretical proposals and experimental protocols while remaining an immature field. Moving beyond proof-of-principle demonstrations requires higher fidelity, efficiency, scalability, and miniaturized integrated systems.
- Recent advances combining DV and CV technologies have progressively smeared the formerly sharp boundary between the two platforms.
- The hybridization has generated numerous theoretical proposals and some experimental implementations of promising quantum information-processing protocols.
- Current demonstrations generally remain proof-of-principle experiments lacking high-fidelity operation, efficiency, and scalability.
- Higher-fidelity and more efficient systems are needed to support perfect error correction and fault-tolerant quantum information processing.
- Scalability will require miniaturization through integrated photonics, phononics, electronics, solid-state platforms, and on-chip detectors with real-time feedback.