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.
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.
An important problem in quantum computation is to characterize the resources required for a computational speedup over classical computation. Veitch et al. showed that one necessary condition for a computational speedup in the model of quantum computation with magic states is that the discrete Wigner function representing the input state of the quantum circuit must take negative values. The amount of negativity in the discrete Wigner function quantifies the complexity of classical simulation of a quantum computation with simulation being efficient if the Wigner function is nonnegative everywhere. In this sense, negativity of the Wigner quasiprobability representation serves as an indicator of quantumness from a computational perspective. However, this result only holds for systems of qudits where the local Hilbert space dimension is odd. The first main result discussed in this thesis relates to a discrete Wigner function suitable for describing quantum computation with magic states defined for any local Hilbert space dimension. When the local Hilbert space dimension is odd it subsumes the standard discrete Wigner function. When the local Hilbert space dimension is even, as a result of state-independent proofs of contextuality among multiqubit (or multi-even-dimensional-qudit) Pauli observables, the phase space over which the Wigner function is defined becomes much larger. However, for systems of qubits, the properties required for simulation of quantum computation with magic states remain. This simulation method effectively extends the result described above for odd-dimensional qudits to qubits. Although in the even-dimensional case the phase space is much larger, points in multiqubit phase space can be characterized and classified and some structure can be imparted on the phase space. The second main result discussed here is a hidden variable model for quantum computation with magic states on qubits. This model is similar in structure to quasiprobability representations like the discrete Wigner function, but unlike those representations the model is capable of representing all elements of any quantum computation---states, operations, and measurements---using only classical probabilities. No negativity is required. This calls into question the role of negativity in quasiprobability representations as an indicator of quantumness for models of quantum computation.
Stabilizer states constitute an important class of quantum states that can be generated from computational-basis states using Pauli operators and Clifford gates. Although they may exhibit substantial multipartite entanglement, quantum circuits restricted to stabilizer operations can be efficiently simulated classically and therefore cannot, by themselves, provide a quantum computational advantage. Such an advantage requires non-stabilizer resources, commonly referred to as quantum magic. In this paper, we investigate the non-stabilizerness of quantum states arising in a class of spin Hamiltonians by computing their stabilizer Rényi entropies. Using real-space renormalization-group techniques, we obtain a closed-form expression valid in the low-energy, large-distance regime. We analyze how quantum magic evolves under coarse-graining and explore its behavior across different parameter regimes and quantum phases.
Magic refers to the degree of “quantumness” in a system that cannot be fully described by stabilizer states and Clifford operations alone. In quantum computing, stabilizer states and Clifford operations can be efficiently simulated on a classical computer, even though they may appear complicated from the perspective of entanglement. In this sense, magic is a crucial resource for unlocking the unique computational power of quantum computers to address problems that are classically intractable. Magic can be quantified by measures such as Wigner negativity and mana that satisfy fundamental properties such as monotonicity under Clifford operations. In this paper, we generalize the statistical mechanical mapping methods of large- q random circuits to the calculation of Rényi Wigner negativity and mana. Based on this, we find: (1) a precise formula describing the competition between magic and entanglement in many-body states prepared under Haar random circuits; (2) a formula describing the spreading and scrambling of magic in states evolved under random Clifford circuits; (3) a quantitative description of magic “squeezing” and “teleportation” under measurements. Finally, we comment on the relation between coherent information and magic.
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.
We study the non-stabilizerness (quantum magic) content of the Hubbard dimer, an analytically solvable, yet completely non-trivial, model of strongly correlated fermions. We consider zero- and finite-temperature properties as well as the time evolution after a quantum quench drives the system out of equilibrium. We evaluate local and nonlocal non-stabilizerness using both the robustness of magic and the stabilizer Renyi entropy, demonstrating how the latter often fails in detecting the mixed stabilizer states that are typically found in this kind of systems. Finally, we compare the non-stabilizerness with other genuine resources of quantum-state complexity, i.e., the fermionic non-Gaussianity and the superselected two-site entanglement. Our findings corroborate the role of non-stabilizerness as a fundamental quantum resource, capturing aspects of quantum complexity that elude traditional information-theoretic measures and providing a novel perspective on fermionic systems with tunable interactions.
Abstract To achieve universal quantum computation via general fault-tolerant schemes, stabilizer operations must be supplemented with other non-stabilizer quantum resources. Motivated by this necessity, we develop a resource theory for magic quantum channels to characterize and quantify the quantum ‘magic’ or non-stabilizerness of noisy quantum circuits. For qudit quantum computing with odd dimension d , it is known that quantum states with non-negative Wigner function can be efficiently simulated classically. First, inspired by this observation, we introduce a resource theory based on completely positive-Wigner-preserving quantum operations as free operations, and we show that they can be efficiently simulated via a classical algorithm. Second, we introduce two efficiently computable magic measures for quantum channels, called the mana and thauma of a quantum channel. As applications, we show that these measures not only provide fundamental limits on the distillable magic of quantum channels, but they also lead to lower bounds for the task of synthesizing non-Clifford gates. Third, we propose a classical algorithm for simulating noisy quantum circuits, whose sample complexity can be quantified by the mana of a quantum channel. We further show that this algorithm can outperform another approach for simulating noisy quantum circuits, based on channel robustness. Finally, we explore the threshold of non-stabilizerness for basic quantum circuits under depolarizing noise.