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Työväentutkimus Vuosikirja

Generation of magic by interaction with bosonic systems

Ron Nyström

Published Apr 8, 2025• 0 citations
OpenAlex

Abstract

Magic is a quantum resource characterising quantum advantage. It is required for fault-tolerant application of non-Clifford gates, which may yield algorithms faster than their classical counterparts. Magic generation is therefore a concept of great importance. In this thesis, we present a novel method of generating magic by interaction with bosonic systems. Most notably, we show that it is possible to generate magic by interaction with a quantum scalar field in the vacuum state and with a single quantum harmonic oscillator. This work was inspired by the concept of entanglement harvesting, where two space-like separated probes become entangled when coupled to a quantum field. As a continuation of this, we show that another resource, specifically magic, may also be harvested by interaction with a quantum field. This is done for both a point-like and a spatially smeared detector. As a corollary, we study a simpler case of magic generation using the Jaynes–Cummings model for a qutrit. After presenting the relevant methods for numerical simulations, this interaction is simulated for various initial states and values of the relevant parameters. These simulations demonstrate magic generation to be possible through interaction with a quantum harmonic oscillator as well. We use mana as the resource monotone evaluating the magic of a state. Mana is defined through the negativity of the discrete Wigner function, which is only defined for odd-dimensional systems. Hence, we will employ a quantum system with three levels, a qutrit, to study magic generation of this kind. When considering interaction with a quantum field, this qutrit will function as a three-level Unruh–DeWitt detector.

Related papers

Harvesting magic from the vacuum

Ron Nyström, Nicola Pranzini, Esko Keski-Vakkuri

Magic is the quantum resource allowing a quantum computer to perform operations that cannot be simulated efficiently by classical computation. As such, generating magic in a quantum system is crucial for achieving quantum advantage. This article shows that magic can be harvested by a three-level Unruh-DeWitt detector (a qutrit) interacting with a quantum field in an initial vacuum state. While the idea of extracting resources from Quantum Field Theories (QFT) was born from the harvesting of entanglement, our result extends the protocol to evolve a qutrit from a nonmagical state to a magical one, making it possible to generate magic from QFT.

arXiv:2409.11473•Physical Review Research•Jun 23, 2025•7 citations

Mutual Mana: Converting Local Magic into Correlations via Discrete Beamsplitters

Linshuai Zhang, Huihui Li

Magic (non-stabilizerness) is a key resource for achieving universal fault-tolerant quantum computation beyond classical computation. While previous studies have primarily focused on magic in single systems, its interactions and distribution in multipartite settings remain largely unexplored. In this work, we introduce mutual mana as a measure of magic correlations defined in close analogy with quantum mutual information. Our definition builds upon mana, which is the established quantifier of magic based on discrete Wigner function negativity. We characterize magic correlations generated by discrete beamsplitters, whose Gaussian counterparts are fundamental components in quantum optics and quantum technologies. We show that coupling a magic state with a stabilizer vacuum state via a discrete beamsplitter will induce a full conversion of local magic into mutual mana, thereby establishing a mechanism for redistributing magic resources as magic correlations. We reveal the fundamental properties of mutual mana and derive its explicit expressions for several prototypical qutrit states subject to a discrete beamsplitter. We make a comparative study of mutual mana with several established quantifiers of correlations generated by the qutrit beamsplitter, including quantum mutual information, mutual $L^1$-norm magic, and mutual stabilizer 2-Rényi entropy.

quant-pharXiv:2511.08004•Annals of Physics•Nov 12, 2025•0 citations

Entanglement and quantum gate processes in the one-dimensional quantum harmonic oscillator

E. T. Owen

Quantum states can contain correlations which are stronger than is possible in classical systems. Quantum information technologies use these correlations, which are known as entanglement, as a resource for implementing novel protocols in a diverse range of fields such as cryptography, teleportation and computing. However, current methods for generating the required entangled states are not necessarily robust against perturbations in the proposed systems. In this thesis, techniques will be developed for robustly generating the entangled states needed for these exciting new technologies. The thesis starts by presenting some basic concepts in quantum information proccessing. In Ch. 2, the numerical methods which will be used to generate solutions for the dynamic systems in this thesis are presented. It is argued that using a GPU-accelerated staggered leapfrog technique provides a very efficient method for propagating the wave function. In Ch. 3, a new method for generating maximally entangled two-qubit states using a pair of interacting particles in a one-dimensional harmonic oscillator is proposed. The robustness of this technique is demonstrated both analytically and numerically for a variety of interaction potentials. When the two qubits are initially in the same state, no entanglement is generated as there is no direct qubit-qubit interaction. Therefore, for an arbitrary initial state, this process implements a root-of-swap entangling quantum gate. Some possible physical implementations of this proposal for low-dimensional semiconductor systems are suggested. One of the most commonly used qubits is the spin of an electron. However, in semiconductors, the spin-orbit interaction can couple this qubit to the electron's momentum. In order to incorporate this e ffect into our numerical simulations, a new discretisation of this interaction is presented in Ch. 4 which is signi ficantly more accurate than traditional methods. This technique is shown to be similar to the standard discretisation for magnetic fields. In Ch. 5, a simple spin-precession model is presented to predict the eff ect of the spin-orbit interaction on the entangling scheme of Ch. 3. It is shown that the root-of-swap quantum gate can be restored by introducing an additional constraint on the system. The robustness of the gate to perturbations in this constraint is demonstrated by presenting numerical solutions using the methods of Ch. 4.

•Jul 9, 2013•0 citations

Magic states in the asymmetric quantum Rabi model

A. Campos-Uscanga, E. Benítez Rodríguez, E. Piceno Martínez +1 more

Magic or non-stabilizerness is a resource for quantum computing that has been extensively studied in qudit networks. It describes the degree to which Clifford gates cannot generate a given state, capturing the advantage of quantum over classical computing. However, its definition in continuous variables and general composite systems remains an open issue. We study magic in a bipartite system, the Asymmetric Quantum Rabi model, a paradigmatic model from quantum optics. We explore the presence of magic in the qubit-reduced system throughout the Hamiltonian parameter space, the role of light-matter interactions in its generation, and the manifestation of Wigner function negativity in the corresponding bosonic degree of freedom. Finally, we discuss our results for magic state preparation in the strong and ultra-strong coupling regimes within the context of quantum informational systems.

arXiv:2508.00765•Physical Review A•Dec 1, 2025•2 citations

Harvesting contextuality from the vacuum

Philip A. LeMaitre

Quantum contextuality is the notion that certain measurement scenarios do not admit a global description of their statistics and has been implicated as the source of quantum advantage in a number of quantum information protocols. It has been shown that contextuality generalizes the concepts of nonlocal entanglement and magic and is an equivalent notion of nonclassicality to Wigner negativity. In this paper, the protocol of contextuality harvesting is introduced, and it is shown that Unruh-DeWitt models are capable of harvesting quantum contextuality from the vacuum of a massless scalar quantum field. In particular, it is shown that gapless systems can be made to harvest contextuality given a suitable choice of measurements. The harvested contextuality is also seen to behave similarly to harvested magic and can be larger in magnitude for specific parameter regimes. An Unruh-DeWitt qubit-qutrit system is also investigated, where it is shown that certain tradeoffs exist between the harvested contextuality of the qutrit and the harvested entanglement between the systems and that there are regimes where the two resources can both be present. Some of the tools of contextuality, namely the contextual fraction, are also imported and used as general measures for any form of harvested contextuality, including nonlocal entanglement and magic. Additionally, new criteria for genuine harvesting are put forward that also apply to individual systems, revealing new permissible harvesting parameter regimes.

arXiv:2508.11773•Physical review. D/Physical review. D.•Jan 8, 2026•2 citations

Optimality of T-gate for generating magic resource

Xiaohui Li, Shunlong Luo

Abstract In the stabilizer formalism of fault-tolerant quantum computation, stabilizer states serve as classical objects, while magic states (non-stabilizer states) are a kind of quantum resource (called magic resource) for promoting stabilizer circuits to universal quantum computation. In this framework, the T-gate is widely used as a non-Clifford gate which generates magic resource from stabilizer states. A natural question arises as whether the T-gate is in some sense optimal for generating magic resource. We address this issue by employing an intuitive and computable quantifier of magic based on characteristic functions (Weyl transforms) of quantum states. We demonstrate that the qubit T-gate, as well as its qutrit extension, the qutrit T-gate, are indeed optimal for generating magic resource among the class of diagonal unitary operators. Moreover, up to Clifford equivalence, the T-gate is essentially the only gate having such an optimal property. This reveals some intrinsic optimal features of the T-gate. We further compare the T-gate with general unitary gates for generating magic resource.

Communications in Theoretical Physics•Dec 30, 2022•19 citations
Magic is a quantum resource characterising quantum advantage. It is required for fault-tolerant application of non-Clifford gates, which may yield algorithms faster than their classical counterparts. Magic generation is therefore a concept of great importance. In this thesis, we present a novel method of generating magic by interaction with bosonic systems. Most notably, we show that it is possible to generate magic by interaction with a quantum scalar field in the vacuum state and with a single quantum harmonic oscillator. This work was inspired by the concept of entanglement harvesting, where two space-like separated probes become entangled when coupled to a quantum field. As a continuation of this, we show that another resource, specifically magic, may also be harvested by interaction with a quantum field. This is done for both a point-like and a spatially smeared detector. As a corollary, we study a simpler case of magic generation using the Jaynes–Cummings model for a qutrit. After presenting the relevant methods for numerical simulations, this interaction is simulated for various initial states and values of the relevant parameters. These simulations demonstrate magic generation to be possible through interaction with a quantum harmonic oscillator as well. We use mana as the resource monotone evaluating the magic of a state. Mana is defined through the negativity of the discrete Wigner function, which is only defined for odd-dimensional systems. Hence, we will employ a quantum system with three levels, a qutrit, to study magic generation of this kind. When considering interaction with a quantum field, this qutrit will function as a three-level Unruh–DeWitt detector.
Magic is the quantum resource allowing a quantum computer to perform operations that cannot be simulated efficiently by classical computation. As such, generating magic in a quantum system is crucial for achieving quantum advantage. This article shows that magic can be harvested by a three-level Unruh-DeWitt detector (a qutrit) interacting with a quantum field in an initial vacuum state. While the idea of extracting resources from Quantum Field Theories (QFT) was born from the harvesting of entanglement, our result extends the protocol to evolve a qutrit from a nonmagical state to a magical one, making it possible to generate magic from QFT.
Magic (non-stabilizerness) is a key resource for achieving universal fault-tolerant quantum computation beyond classical computation. While previous studies have primarily focused on magic in single systems, its interactions and distribution in multipartite settings remain largely unexplored. In this work, we introduce mutual mana as a measure of magic correlations defined in close analogy with quantum mutual information. Our definition builds upon mana, which is the established quantifier of magic based on discrete Wigner function negativity. We characterize magic correlations generated by discrete beamsplitters, whose Gaussian counterparts are fundamental components in quantum optics and quantum technologies. We show that coupling a magic state with a stabilizer vacuum state via a discrete beamsplitter will induce a full conversion of local magic into mutual mana, thereby establishing a mechanism for redistributing magic resources as magic correlations. We reveal the fundamental properties of mutual mana and derive its explicit expressions for several prototypical qutrit states subject to a discrete beamsplitter. We make a comparative study of mutual mana with several established quantifiers of correlations generated by the qutrit beamsplitter, including quantum mutual information, mutual L1L^1L1-norm magic, and mutual stabilizer 2-Rényi entropy.
Quantum states can contain correlations which are stronger than is possible in classical systems. Quantum information technologies use these correlations, which are known as entanglement, as a resource for implementing novel protocols in a diverse range of fields such as cryptography, teleportation and computing. However, current methods for generating the required entangled states are not necessarily robust against perturbations in the proposed systems. In this thesis, techniques will be developed for robustly generating the entangled states needed for these exciting new technologies. The thesis starts by presenting some basic concepts in quantum information proccessing. In Ch. 2, the numerical methods which will be used to generate solutions for the dynamic systems in this thesis are presented. It is argued that using a GPU-accelerated staggered leapfrog technique provides a very efficient method for propagating the wave function. In Ch. 3, a new method for generating maximally entangled two-qubit states using a pair of interacting particles in a one-dimensional harmonic oscillator is proposed. The robustness of this technique is demonstrated both analytically and numerically for a variety of interaction potentials. When the two qubits are initially in the same state, no entanglement is generated as there is no direct qubit-qubit interaction. Therefore, for an arbitrary initial state, this process implements a root-of-swap entangling quantum gate. Some possible physical implementations of this proposal for low-dimensional semiconductor systems are suggested. One of the most commonly used qubits is the spin of an electron. However, in semiconductors, the spin-orbit interaction can couple this qubit to the electron's momentum. In order to incorporate this e ffect into our numerical simulations, a new discretisation of this interaction is presented in Ch. 4 which is signi ficantly more accurate than traditional methods. This technique is shown to be similar to the standard discretisation for magnetic fields. In Ch. 5, a simple spin-precession model is presented to predict the eff ect of the spin-orbit interaction on the entangling scheme of Ch. 3. It is shown that the root-of-swap quantum gate can be restored by introducing an additional constraint on the system. The robustness of the gate to perturbations in this constraint is demonstrated by presenting numerical solutions using the methods of Ch. 4.
Magic or non-stabilizerness is a resource for quantum computing that has been extensively studied in qudit networks. It describes the degree to which Clifford gates cannot generate a given state, capturing the advantage of quantum over classical computing. However, its definition in continuous variables and general composite systems remains an open issue. We study magic in a bipartite system, the Asymmetric Quantum Rabi model, a paradigmatic model from quantum optics. We explore the presence of magic in the qubit-reduced system throughout the Hamiltonian parameter space, the role of light-matter interactions in its generation, and the manifestation of Wigner function negativity in the corresponding bosonic degree of freedom. Finally, we discuss our results for magic state preparation in the strong and ultra-strong coupling regimes within the context of quantum informational systems.
Quantum contextuality is the notion that certain measurement scenarios do not admit a global description of their statistics and has been implicated as the source of quantum advantage in a number of quantum information protocols. It has been shown that contextuality generalizes the concepts of nonlocal entanglement and magic and is an equivalent notion of nonclassicality to Wigner negativity. In this paper, the protocol of contextuality harvesting is introduced, and it is shown that Unruh-DeWitt models are capable of harvesting quantum contextuality from the vacuum of a massless scalar quantum field. In particular, it is shown that gapless systems can be made to harvest contextuality given a suitable choice of measurements. The harvested contextuality is also seen to behave similarly to harvested magic and can be larger in magnitude for specific parameter regimes. An Unruh-DeWitt qubit-qutrit system is also investigated, where it is shown that certain tradeoffs exist between the harvested contextuality of the qutrit and the harvested entanglement between the systems and that there are regimes where the two resources can both be present. Some of the tools of contextuality, namely the contextual fraction, are also imported and used as general measures for any form of harvested contextuality, including nonlocal entanglement and magic. Additionally, new criteria for genuine harvesting are put forward that also apply to individual systems, revealing new permissible harvesting parameter regimes.
Abstract In the stabilizer formalism of fault-tolerant quantum computation, stabilizer states serve as classical objects, while magic states (non-stabilizer states) are a kind of quantum resource (called magic resource) for promoting stabilizer circuits to universal quantum computation. In this framework, the T-gate is widely used as a non-Clifford gate which generates magic resource from stabilizer states. A natural question arises as whether the T-gate is in some sense optimal for generating magic resource. We address this issue by employing an intuitive and computable quantifier of magic based on characteristic functions (Weyl transforms) of quantum states. We demonstrate that the qubit T-gate, as well as its qutrit extension, the qutrit T-gate, are indeed optimal for generating magic resource among the class of diagonal unitary operators. Moreover, up to Clifford equivalence, the T-gate is essentially the only gate having such an optimal property. This reveals some intrinsic optimal features of the T-gate. We further compare the T-gate with general unitary gates for generating magic resource.