Schrieffer-Wolff transformation for quantum many-body systems
TL;DR: The Schrieffer-Wolff (SW) method as mentioned in this paper is a version of degenerate perturbation theory in which the low energy effective Hamiltonian H eff is obtained from the exact Hamiltonian by a unitary transformation decoupling the low-energy and high-energy subspaces.
About: This article is published in Annals of Physics.The article was published on 2011-10-01 and is currently open access. It has received 253 citations till now. The article focuses on the topics: Unitary transformation & Hamiltonian (quantum mechanics).
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TL;DR: The field of circuit quantum electrodynamics (QED) as discussed by the authors was initiated by Josephson-junction-based superconducting circuits and has become an independent and thriving field of research in its own right.
Abstract: Quantum-mechanical effects at the macroscopic level were first explored in Josephson-junction-based superconducting circuits in the 1980s. In recent decades, the emergence of quantum information science has intensified research toward using these circuits as qubits in quantum information processors. The realization that superconducting qubits can be made to strongly and controllably interact with microwave photons, the quantized electromagnetic fields stored in superconducting circuits, led to the creation of the field of circuit quantum electrodynamics (QED), the topic of this review. While atomic cavity QED inspired many of the early developments of circuit QED, the latter has now become an independent and thriving field of research in its own right. Circuit QED allows the study and control of light-matter interaction at the quantum level in unprecedented detail. It also plays an essential role in all current approaches to gate-based digital quantum information processing with superconducting circuits. In addition, circuit QED provides a framework for the study of hybrid quantum systems, such as quantum dots, magnons, Rydberg atoms, surface acoustic waves, and mechanical systems interacting with microwave photons. Here the coherent coupling of superconducting qubits to microwave photons in high-quality oscillators focusing on the physics of the Jaynes-Cummings model, its dispersive limit, and the different regimes of light-matter interaction in this system are reviewed. Also discussed is coupling of superconducting circuits to their environment, which is necessary for coherent control and measurements in circuit QED, but which also invariably leads to decoherence. Dispersive qubit readout, a central ingredient in almost all circuit QED experiments, is also described. Following an introduction to these fundamental concepts that are at the heart of circuit QED, important use cases of these ideas in quantum information processing and in quantum optics are discussed. Circuit QED realizes a broad set of concepts that open up new possibilities for the study of quantum physics at the macro scale with superconducting circuits and applications to quantum information science in the widest sense.
773 citations
TL;DR: Turner et al. as mentioned in this paper used forward scattering approximation to describe the structure and physical properties of quantum scarred eigenstate properties of the same model and found that the majority of the eigenstates exhibit anomalous thermalization: the observable expectation values converge to their Gibbs ensemble values, but parametrically slower compared to the predictions of the Eigenstate thermalization hypothesis.
Abstract: Recent realization of a kinetically constrained chain of Rydberg atoms by Bernien et al., [Nature (London) 551, 579 (2017)] resulted in the observation of unusual revivals in the many-body quantum dynamics. In our previous work [C. J. Turner et al., Nat. Phys. 14, 745 (2018)], such dynamics was attributed to the existence of “quantum scarred” eigenstates in the many-body spectrum of the experimentally realized model. Here, we present a detailed study of the eigenstate properties of the same model. We find that the majority of the eigenstates exhibit anomalous thermalization: the observable expectation values converge to their Gibbs ensemble values, but parametrically slower compared to the predictions of the eigenstate thermalization hypothesis (ETH). Amidst the thermalizing spectrum, we identify nonergodic eigenstates that strongly violate the ETH, whose number grows polynomially with system size. Previously, the same eigenstates were identified via large overlaps with certain product states, and were used to explain the revivals observed in experiment. Here, we find that these eigenstates, in addition to highly atypical expectation values of local observables, also exhibit subthermal entanglement entropy that scales logarithmically with the system size. Moreover, we identify an additional class of quantum scarred eigenstates, and discuss their manifestations in the dynamics starting from initial product states. We use forward scattering approximation to describe the structure and physical properties of quantum scarred eigenstates. Finally, we discuss the stability of quantum scars to various perturbations. We observe that quantum scars remain robust when the introduced perturbation is compatible with the forward scattering approximation. In contrast, the perturbations which most efficiently destroy quantum scars also lead to the restoration of “canonical” thermalization.
330 citations
TL;DR: QuSpin this paper is an open-source Python package for exact diagonalization and quantum dynamics of spin-photon chains, supporting the use of various symmetries in 1-dimensional and (imaginary) time evolution for chains up to 32 sites in length.
Abstract: We present a new open-source Python package for exact diagonalization and quantum dynamics of spin(-photon) chains, called QuSpin, supporting the use of various symmetries in 1-dimension and (imaginary) time evolution for chains up to 32 sites in length. The package is well-suited to study, among others, quantum quenches at finite and infinite times, the Eigenstate Thermalisation hypothesis, many-body localisation and other dynamical phase transitions, periodically-driven (Floquet) systems, adiabatic and counter-diabatic ramps, and spin-photon interactions. Moreover, QuSpin's user-friendly interface can easily be used in combination with other Python packages which makes it amenable to a high-level customisation. We explain how to use QuSpin using four detailed examples: (i) Standard exact diagonalisation of XXZ chain (ii) adiabatic ramping of parameters in the many-body localised XXZ model, (iii) heating in the periodically-driven transverse-field Ising model in a parallel field, and (iv) quantised light-atom interactions: recovering the periodically-driven atom in the semi-classical limit of a static Hamiltonian.
220 citations
TL;DR: In this article, a review summarizes and discusses the various theoretical attempts to find a workable scenario for a passive quantum memory, for which a suitably designed interaction Hamiltonian will naturally protect the coherence of low-lying states from decoherence induced by a thermal environment.
Abstract: While the typical scenario for quantum error correction involves active intervention there are advantages to a passive quantum memory, for which a suitably designed interaction Hamiltonian will naturally protect the coherence of low-lying states from decoherence induced by a thermal environment. This review summarizes and discusses the various theoretical attempts to find a workable scenario for a passive quantum memory.
212 citations
TL;DR: A generalizable and extensible scheme for a two-qu bit coupler switch that controls the qubit-qubit coupling by modulating the coupler frequency is proposed, thereby promising a higher gate fidelity with current technologies.
Abstract: The prospect of computational hardware with quantum advantage relies critically on the quality of quantum-gate operations. Imperfect two-qubit gates are a major bottleneck for achieving scalable quantum-information processors. Here, we propose a generalizable and extensible scheme for a two-qubit tunable coupler that controls the qubit-qubit coupling by modulating the coupler frequency. Two-qubit gate operations can be implemented by operating the coupler in the dispersive regime, which is noninvasive to the qubit states. We investigate the performance of the scheme by simulating a universal two-qubit gate on a superconducting quantum circuit, and find that errors from known parasitic effects are strongly suppressed. The scheme is compatible with existing high-coherence hardware, thereby promising a higher gate fidelity with current technologies.
183 citations
References
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TL;DR: In this article, a spin-1/2 system on a honeycomb lattice is studied, where the interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength.
4,032 citations
TL;DR: In this article, a phone directory containing $N$ names arranged in completely random order is presented, and the desired phone number can be obtained in only O(sqrt{N})$ accesses to the database.
Abstract: Quantum mechanics can speed up a range of search applications over unsorted data. For example, imagine a phone directory containing $N$ names arranged in completely random order. To find someone's phone number with a probability of 50%, any classical algorithm (whether deterministic or probabilistic) will need to access the database a minimum of $0.5N$ times. Quantum mechanical systems can be in a superposition of states and simultaneously examine multiple names. By properly adjusting the phases of various operations, successful computations reinforce each other while others interfere randomly. As a result, the desired phone number can be obtained in only $O(\sqrt{N})$ accesses to the database.
3,955 citations