Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Hybrid Methods in Quantum Information

Kevin Marshall

Published Nov 1, 2017• 0 citations
OpenAlex

Abstract

Today, the potential power of quantum information processing comes as no surprise to physicist or science-fiction writer alike. However, the grand promises of this field remain unrealized, despite significant strides forward, due to the inherent difficulties of manipulating quantum systems. Simply put, it turns out that it is incredibly difficult to interact, in a controllable way, with the quantum realm when we seem to live our day to day lives in a classical world. In an effort to solve this challenge, people are exploring a variety of different physical platforms, each with their strengths and weaknesses, in hopes of developing new experimental methods that one day might allow us to control a quantum system. One path forward rests in combining different quantum systems in novel ways to exploit the benefits of different systems while circumventing their respective weaknesses. In particular, quantum systems come in two different flavours: either discrete-variable systems or continuous-variable ones. The field of hybrid quantum information seeks to combine these systems, in clever ways, to help overcome the challenges blocking the path between what is theoretically possible and what is achievable in a laboratory. In this thesis we explore four topics in the context of hybrid methods in quantum information, in an effort to contribute to the resolution of existing challenges and to stimulate new avenues of research. First, we explore the manipulation of a continuous-variable quantum system consisting of phonons in a linear chain of trapped ions where we use the discretized internal levels to mediate interactions. Using our proposed interaction we are able to implement, for example, the acoustic equivalent of a beam splitter with modest experimental resources. Next we propose an experimentally feasible implementation of the cubic phase gate, a primitive non-Gaussian gate required for universal continuous-variable quantum computation, based off sequential photon subtraction. We then discuss the notion of embedding a finite dimensional state into a continuous-variable system, and propose a method of performing quantum computations on encrypted continuous-variable states. This protocol allows for a client, of limited quantum ability, to outsource a computation while hiding their information. Next, we discuss the possibility of performing universal quantum computation on discrete-variable logical states encoded in mixed continuous-variable quantum states. Finally, we present an account of open problems related to our results, and possible future avenues of research.

Related papers

Modular variables in quantum information

Andreas Ketterer

Quantum information can be processed in two fundamentally different ways, using either discrete or continuous variable implementations. Each one of them provides different practical advantages and drawbacks. In this thesis we study theoretical means allowing to implement quantum information protocols originally formulated for discrete quantum systems in physical objects characterized by continuous variables. At the heart of our considerations is the use of modular variables as helpful technique to reveal discrete structure in continuous-variable states, operations and observables. The present work is strongly guided by the experimental applicability of our ideas in quantum optics experiments, with a particular focus on the transverse degrees of freedom of single photons.One of the main themes of this thesis is the formulation of a framework for quantum information processing in phase-space based on the use of modular variables. The term modular variables refers to a specific class of observables that are periodic with respect to some pair of conjugate variables. In our framework we use these periodic observables in order to encode discrete quantum information in Hilbert spaces of infinite dimension. In particular, we consider protocols that involve measurements of judiciously chosen logical observables enabling the readout of the encoded discrete quantum information from the corresponding logical states. Using this framework we show how to perform tests of fundamental properties of quantum mechanics, such as entanglement, Bell nonlocality and contextuality, in Hilbert spaces of various dimensions. Particularly, we generalize known tests of each of these properties, that were originally formulated for measurements with discrete outcomes, to more general measurement contexts comprising the case of bounded continuous outcomes. Concerning experimental implementations of the presented theoretical elaborations we discuss the transverse degrees of freedom of single photons as a natural platform to manipulate and measure modular variables. In particular, we demonstrate how to process discrete quantum information encoded in the spatial distribution of single photons via the optical Talbot effect - a near-field interference effect. Finally, we show how to produce d-dimensional entangled Talbot photon pairs without post-selection, using spontaneous parametric down-conversion and linear optical elements only. As last topic we explore the nonlocal properties of a specific class of hybrid entanglement between particle-like and wave-like optical qubits. Using a hybrid measurement scheme of Pauli and displaced parity measurements we show that, even after including realistic experimental losses, a violation of local-realism is theoretically possible.

•Oct 14, 2016•4 citations

Universal hybrid quantum computing in trapped ions

R. T. Sutherland, R. Srinivas

Using discrete and continuous variable subsystems, hybrid approaches to quantum information could enable more quantum computational power for the same physical resources. Here, we propose a hybrid scheme that can be used to generate the necessary Gaussian and non-Gaussian operations for universal continuous variable quantum computing in trapped ions. This scheme utilizes two linear spin-motion interactions to generate a broad set of nonlinear effective spin-motion interactions including one- and two-mode squeezing, beam splitter, and trisqueezing operations in trapped ion systems. We discuss possible experimental implementations using laser-based and laser-free approaches.

arXiv:2105.05768•Physical Review A•Sep 14, 2021•28 citations

Hybrid Quantum Computing with Conditional Beam Splitter Gate in Trapped Ion System

Jaren Gan, Gleb Maslennikov, Ko-Wei Tseng +2 more

The hybrid approach to quantum computation simultaneously utilizes both discrete and continuous variables, which offers the advantage of higher density encoding and processing powers for the same physical resources. Trapped ions, with discrete internal states and motional modes that can be described by continuous variables in an infinite-dimensional Hilbert space, offer a natural platform for this approach. A nonlinear gate for universal quantum computing can be implemented with the conditional beam splitter Hamiltonian |e⟩⟨e|(a[over ^]^{†}b[over ^]+a[over ^]b[over ^]^{†}) that swaps the quantum states of two motional modes, depending on the ion's internal state. We realize such a gate and demonstrate its applications for quantum state overlap measurements, single-shot parity measurement, and generation of NOON states.

arXiv:1908.10117•Physical Review Letters•Apr 27, 2020•55 citations

Hybrid Teleportation Protocols for Heterogeneous Quantum Networks

Tom Darras, Adrien Cavaillès, Hanna Le Jeannic +4 more

The wave-particle duality of light has led to two different encodings of optical quantum information. One approach, referred to as the discrete-variable (DV) one, relies on finite dimensional quantum systems, while the other one, referred to as the continuous-variable (CV) one, is based on wave-like states belonging to an infinite dimensional Hilbert space. These two encodings have historically been separated, but recently, new hybrid protocols which aim at combining the advantages of the two encodings have emerged [1] . In that prospect our recent demonstration of the measurement-induced generation of hybrid entanglement between discrete- and continuous-variable quantum states [2] , [3] , located at distant places and connected by a lossy channel, has opened the way to the implementation of hybrid protocols and heterogeneous quantum networks. Following the first protocols based on this resource, such as the remote preparation of continuous-variable qubits [4] , or a violation of an Einstein-Podolsky-Rosen steering inequality [5] , we will here report our latest experimental results on entanglement swapping and quantum teleportation protocols using hybrid entangled states based on different encodings [6] .

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 21, 2021•0 citations

Universal continuous-variable quantum computation without cooling

Hoi-Kwan Lau, Martin Bodo Plenio

One limitation of the quantum computing capability of a continuous-variable system is determined by our ability to cool it to the ground state, because pure logical states, in which we accurately encode quantum information, are conventionally pure physical states that are constructed from the ground state. In this work, we present an alternative quantum computing formalism that encodes logical quantum information in mixed physical states. We introduce a class of mixed-state protocols that are based on a parity encoding, and propose an implementation of the universal logic gates by using realistic hybrid interactions. When compared with the conventional pure-state protocols, our formalism could relax the necessity, and hence the systemic requirements, of cooling. Additionally, the mixed-state protocols are inherently resilient to a wider class of noise processes and reduce the fundamental energy consumption in initialization. Our work broadens the range of candidates for continuous-variable quantum computers.

arXiv:1608.03213•Physical Review A•Feb 2, 2017•14 citations

Ancillas in Quantum Computation: Beyond Two-Level Systems

Timothy J Proctor

Quantum computers have the potential to solve problems that are believed to be classically intractable. However, building such a device is proving to be very challenging. In this thesis, two physically promising settings for quantum computation are investigated: the one-way quantum computer and ancilla-based quantum gates. The majority of both the theoretical and experimental focus in the field of quantum computation has been on computation using 2-level quantum systems, known as qubits. In contrast to this, in this thesis I consider the relatively less well-understood setting of quantum computation using continuous variables or d-level quantum systems, called qudits. I develop a simple notation that encompasses each different encoding, and is applicable to a `general quantum variable'. These ideas are then used to investigate computational depth (a proxy for time) in quantum circuits and one-way quantum computations in this general quantum variable setting. In doing so, the parallelism inherent in the one-way quantum computer is made precise. In the second half of this thesis, a range of techniques are proposed for implementing entangling gates on a well-isolated computational register via interactions with `ancillary' systems. In particular, ancilla-based quantum gates for general quantum variables are investigated - including the interesting case of hybrid quantum computation, whereby more than one encoding is used in tandem. The methods proposed herein each have their own unique advantages, such as: reducing gate-counts in certain circuits, allowing for inherently parallel computation, or minimising the physical requirements for universal quantum computation. In particular, the final gate techniques that are proposed in this thesis may implement any quantum computation using only a single fixed ancilla-register interaction gate and ancillas prepared in simple states. This then allows the computational register to consist of well-isolated `memory' quantum variables and the ancillas need only be optimised for a single high-quality fixed interaction gate. Hence, this provides a simple and highly promising setting for physically implementing a quantum computer.

•Mar 1, 2016•1 citation
Today, the potential power of quantum information processing comes as no surprise to physicist or science-fiction writer alike. However, the grand promises of this field remain unrealized, despite significant strides forward, due to the inherent difficulties of manipulating quantum systems. Simply put, it turns out that it is incredibly difficult to interact, in a controllable way, with the quantum realm when we seem to live our day to day lives in a classical world. In an effort to solve this challenge, people are exploring a variety of different physical platforms, each with their strengths and weaknesses, in hopes of developing new experimental methods that one day might allow us to control a quantum system. One path forward rests in combining different quantum systems in novel ways to exploit the benefits of different systems while circumventing their respective weaknesses. In particular, quantum systems come in two different flavours: either discrete-variable systems or continuous-variable ones. The field of hybrid quantum information seeks to combine these systems, in clever ways, to help overcome the challenges blocking the path between what is theoretically possible and what is achievable in a laboratory. In this thesis we explore four topics in the context of hybrid methods in quantum information, in an effort to contribute to the resolution of existing challenges and to stimulate new avenues of research. First, we explore the manipulation of a continuous-variable quantum system consisting of phonons in a linear chain of trapped ions where we use the discretized internal levels to mediate interactions. Using our proposed interaction we are able to implement, for example, the acoustic equivalent of a beam splitter with modest experimental resources. Next we propose an experimentally feasible implementation of the cubic phase gate, a primitive non-Gaussian gate required for universal continuous-variable quantum computation, based off sequential photon subtraction. We then discuss the notion of embedding a finite dimensional state into a continuous-variable system, and propose a method of performing quantum computations on encrypted continuous-variable states. This protocol allows for a client, of limited quantum ability, to outsource a computation while hiding their information. Next, we discuss the possibility of performing universal quantum computation on discrete-variable logical states encoded in mixed continuous-variable quantum states. Finally, we present an account of open problems related to our results, and possible future avenues of research.
Quantum information can be processed in two fundamentally different ways, using either discrete or continuous variable implementations. Each one of them provides different practical advantages and drawbacks. In this thesis we study theoretical means allowing to implement quantum information protocols originally formulated for discrete quantum systems in physical objects characterized by continuous variables. At the heart of our considerations is the use of modular variables as helpful technique to reveal discrete structure in continuous-variable states, operations and observables. The present work is strongly guided by the experimental applicability of our ideas in quantum optics experiments, with a particular focus on the transverse degrees of freedom of single photons.One of the main themes of this thesis is the formulation of a framework for quantum information processing in phase-space based on the use of modular variables. The term modular variables refers to a specific class of observables that are periodic with respect to some pair of conjugate variables. In our framework we use these periodic observables in order to encode discrete quantum information in Hilbert spaces of infinite dimension. In particular, we consider protocols that involve measurements of judiciously chosen logical observables enabling the readout of the encoded discrete quantum information from the corresponding logical states. Using this framework we show how to perform tests of fundamental properties of quantum mechanics, such as entanglement, Bell nonlocality and contextuality, in Hilbert spaces of various dimensions. Particularly, we generalize known tests of each of these properties, that were originally formulated for measurements with discrete outcomes, to more general measurement contexts comprising the case of bounded continuous outcomes. Concerning experimental implementations of the presented theoretical elaborations we discuss the transverse degrees of freedom of single photons as a natural platform to manipulate and measure modular variables. In particular, we demonstrate how to process discrete quantum information encoded in the spatial distribution of single photons via the optical Talbot effect - a near-field interference effect. Finally, we show how to produce d-dimensional entangled Talbot photon pairs without post-selection, using spontaneous parametric down-conversion and linear optical elements only. As last topic we explore the nonlocal properties of a specific class of hybrid entanglement between particle-like and wave-like optical qubits. Using a hybrid measurement scheme of Pauli and displaced parity measurements we show that, even after including realistic experimental losses, a violation of local-realism is theoretically possible.
Using discrete and continuous variable subsystems, hybrid approaches to quantum information could enable more quantum computational power for the same physical resources. Here, we propose a hybrid scheme that can be used to generate the necessary Gaussian and non-Gaussian operations for universal continuous variable quantum computing in trapped ions. This scheme utilizes two linear spin-motion interactions to generate a broad set of nonlinear effective spin-motion interactions including one- and two-mode squeezing, beam splitter, and trisqueezing operations in trapped ion systems. We discuss possible experimental implementations using laser-based and laser-free approaches.
The hybrid approach to quantum computation simultaneously utilizes both discrete and continuous variables, which offers the advantage of higher density encoding and processing powers for the same physical resources. Trapped ions, with discrete internal states and motional modes that can be described by continuous variables in an infinite-dimensional Hilbert space, offer a natural platform for this approach. A nonlinear gate for universal quantum computing can be implemented with the conditional beam splitter Hamiltonian |e⟩⟨e|(a[over ^]^{†}b[over ^]+a[over ^]b[over ^]^{†}) that swaps the quantum states of two motional modes, depending on the ion's internal state. We realize such a gate and demonstrate its applications for quantum state overlap measurements, single-shot parity measurement, and generation of NOON states.
The wave-particle duality of light has led to two different encodings of optical quantum information. One approach, referred to as the discrete-variable (DV) one, relies on finite dimensional quantum systems, while the other one, referred to as the continuous-variable (CV) one, is based on wave-like states belonging to an infinite dimensional Hilbert space. These two encodings have historically been separated, but recently, new hybrid protocols which aim at combining the advantages of the two encodings have emerged [1] . In that prospect our recent demonstration of the measurement-induced generation of hybrid entanglement between discrete- and continuous-variable quantum states [2] , [3] , located at distant places and connected by a lossy channel, has opened the way to the implementation of hybrid protocols and heterogeneous quantum networks. Following the first protocols based on this resource, such as the remote preparation of continuous-variable qubits [4] , or a violation of an Einstein-Podolsky-Rosen steering inequality [5] , we will here report our latest experimental results on entanglement swapping and quantum teleportation protocols using hybrid entangled states based on different encodings [6] .
One limitation of the quantum computing capability of a continuous-variable system is determined by our ability to cool it to the ground state, because pure logical states, in which we accurately encode quantum information, are conventionally pure physical states that are constructed from the ground state. In this work, we present an alternative quantum computing formalism that encodes logical quantum information in mixed physical states. We introduce a class of mixed-state protocols that are based on a parity encoding, and propose an implementation of the universal logic gates by using realistic hybrid interactions. When compared with the conventional pure-state protocols, our formalism could relax the necessity, and hence the systemic requirements, of cooling. Additionally, the mixed-state protocols are inherently resilient to a wider class of noise processes and reduce the fundamental energy consumption in initialization. Our work broadens the range of candidates for continuous-variable quantum computers.
Quantum computers have the potential to solve problems that are believed to be classically intractable. However, building such a device is proving to be very challenging. In this thesis, two physically promising settings for quantum computation are investigated: the one-way quantum computer and ancilla-based quantum gates. The majority of both the theoretical and experimental focus in the field of quantum computation has been on computation using 2-level quantum systems, known as qubits. In contrast to this, in this thesis I consider the relatively less well-understood setting of quantum computation using continuous variables or d-level quantum systems, called qudits. I develop a simple notation that encompasses each different encoding, and is applicable to a `general quantum variable'. These ideas are then used to investigate computational depth (a proxy for time) in quantum circuits and one-way quantum computations in this general quantum variable setting. In doing so, the parallelism inherent in the one-way quantum computer is made precise. In the second half of this thesis, a range of techniques are proposed for implementing entangling gates on a well-isolated computational register via interactions with `ancillary' systems. In particular, ancilla-based quantum gates for general quantum variables are investigated - including the interesting case of hybrid quantum computation, whereby more than one encoding is used in tandem. The methods proposed herein each have their own unique advantages, such as: reducing gate-counts in certain circuits, allowing for inherently parallel computation, or minimising the physical requirements for universal quantum computation. In particular, the final gate techniques that are proposed in this thesis may implement any quantum computation using only a single fixed ancilla-register interaction gate and ancillas prepared in simple states. This then allows the computational register to consist of well-isolated `memory' quantum variables and the ancillas need only be optimised for a single high-quality fixed interaction gate. Hence, this provides a simple and highly promising setting for physically implementing a quantum computer.