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Josephson junctions arrays forming triangular (JJT) and Kagome (JJK) lattices and emulating dimer systems. JJT: The large capacitance C h joins hexagonal islands into electric units which are frustrated by a global gate to accept 1/2 Cooper pair. Cooper pairs resonating between hexagonal islands form dimers (shaded ellipses); dimer flips due to Ht are indicated by arrows. JJK: Cooper pairs on X-shaped islands are capacitively coupled through star-shaped islands. The gate is tuned to allow for 1/2 Cooper pair per hexagon. Dimers are pairs residing on X-shaped islands and polarizing adjacent star-shaped islands.
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All physical implementations of quantum bits (or qubits, the logical elements in a putative quantum computer) must overcome conflicting requirements: the qubits should be manipulable through external signals, while remaining isolated from their environment. Proposals based on quantum optics emphasize optimal isolation, while those following the sol...
Citations
... (A notable exception is Kitaev's honeycomb model [6].) While it is possible to design multi-spin interactions as effective couplings arising from physical, two-body interactions, these constructions tend to be either perturbative (they are exact in a classical limit) and break down in the presence of quantum dynamics [7][8][9][10][11][12][13][14][15][16], or require capabilities beyond those achievable in real materials or in programmable quantum devices [17][18][19][20][21]. ...
... where a n, j are integers such that q j=1 a n, j ≡ 0 (mod k), or equivalently q j=1 ζ a n, j k = 1, for all n. This matrix will satisfy the CGS invariance condition (15). In this case a general gauge transformation acts on the gauge degrees of freedom via a multiplication on the right of W k,q by the following diagonal matrix: ...
Combinatorial gauge symmetry is a principle that allows us to construct lattice gauge theories with two key and distinguishing properties: a) only one- and two-body interactions are needed; and b) the symmetry is exact rather than emergent in an effective or perturbative limit. The ground state exhibits topological order for a range of parameters. This paper is a generalization of the construction to any finite Abelian group. In addition to the general mathematical construction, we present a physical implementation in superconducting wire arrays, which offers a route to the experimental realization of lattice gauge theories with static Hamiltonians.
... Quantum dimer models allowed the study of a variety of physical phenomena [55][56][57][58], and it was found that they could be potentially simulated using cold atoms [59]. Quantum dimers have also potential applications in quantum computation, where it was found that they can be used to implement topologically stable qubits using quantum Josephson junction arrays [60]. On the other hand, qutrits and mixed spin chains with higher dimensional states have sparked much interest recently. ...
This research delves into the dynamical behavior of quantum correlations and coherence within a mixed Heisenberg dimer system under the intrinsic decoherence. Our approach involves the application of logarithmic negativity, local quantum uncertainty, and the ℓ 1 norm-based coherence as quantifiers for entanglement, skew information correlations, and quantum coherence in this qubit-qutrit model. Our primary objective is to explore the impact of various factors on the dynamics of quantum correlations and quantum coherence. These factors encompass the initial density matrix and its mixing parameter, the intrinsic decoherence rate (γ), the external magnetic field, as well as intrinsic system parameters, notably the XXZ and uniaxial single-ion anisotropies. Our results demonstrate that the introduction of intrinsic decoherence (ID) significantly erodes quantum resources. Particularly, for high values of the ID rate (γ), excessive damping occurs, leading to the absence of oscillations or a rapid decay of quantum resources, ultimately stabilizing in steady states. Furthermore, the presence of an external homogeneous magnetic field further diminishes quantum resources within the system. However, despite the degradation induced by the combined influence of intrinsic decoherence and high external magnetic field intensities, the judicious selection of the initial density matrix and precise adjustment of the uniaxial single-ion anisotropy enable the preservation of quantum resources within the mixed spin-(1/2, 1) Heisenberg dimer.
... The large kinetic inductance in superconductors makes it useful in superinductors [5][6][7][8], in constructing inductance-based qubits [9][10][11][12][13][14], inductive-shunted qubits [15][16][17], and for qubit protection [18][19][20][21][22][23][24][25]. It also has various applications in quantum information microwave circuits [26], such as readout and coupling resonators [4,[27][28][29], circulators [30], filters [23], and for circuit elements resilient in high magnetic field [29,31,32]. ...
Ultra-thin superconducting aluminum films of 3-nm grown on sapphire by molecule-beam epitaxy show excellent superconductivity and large kinetic inductance. This results in a record high Kerr non-linearity of 33 kHz and 3.62 MHz per photon in notch-type and transmission-type resonators, respectively. 4-wave mixing leverages this non-linearity to achieve 12 dB parametric amplification in transmission type resonator, making the ultra-thin film ideal for photon detection and amplification applications.
... Disorder in two-dimensional electronic systems leads to a wide range of topological phenomena, including integer and fractional quantum Hall effects, in which impurities resulting from the sample fabrication process break the degeneracies of Landau levels and localize the wave functions at almost all energies (1)(2)(3)(4). Such localization is the direct cause of quantized plateaus in the Hall conductance, as the localized states do not contribute to the particle transport and the quantization plateaus would cease to exist in an ideal clean sample (1,(5)(6). ...
Complex networks play a fundamental role in understanding phenomena from the collective behavior of spins, neural networks, and power grids to the spread of diseases. Topological phenomena in such networks have recently been exploited to preserve the response of systems in the presence of disorder. We propose and demonstrate topological structurally disordered systems with a modal structure that enhances nonlinear phenomena in the topological channels by inhibiting the ultrafast leakage of energy from edge modes to bulk modes. We present the construction of the graph and show that its dynamics enhances the topologically protected photon pair generation rate by an order of magnitude. Disordered nonlinear topological graphs will enable advanced quantum interconnects, efficient nonlinear sources, and light-based information processing for artificial intelligence.
... Topological physics in superconducting quantum circuits with many qubits is also explored. For example, topologically protected qubits and quantum coherence were proposed by using Josephson junction arrays [18] and superconducting qubits [19]. A two-component fermion model with anyonic excitations was constructed by two capacitively coupled chains of superconducting quantum circuits [20]. ...
Kitaev fermionic chain is one of the important physical models for studying topological physics and quantum computing. We here propose an approach to simulate the one-dimensional Kitaev model by a chain of superconducting qubit circuits. Furthermore, we study the environmental effect on topological quantum states of the Kitaev model. Besides the independent environment surrounding each qubit, we also consider the common environment shared by two nearest neighboring qubits. Such common environment can result in an effective non-Hermitian dissipative coupling between two qubits. Through theoretical analysis and numerical calculations, we show that the common environment can significantly change properties of topological states in contrast to the independent environment. In addition, we also find that dissipative couplings at the edges of the chain can be used to more easily tune the topological properties of the system than those at other positions. Our study may open a new way to explore topological quantum phase transition and various environmental effects on topological physics using superconducting qubit circuits.
... (A notable exception is Kitaev's honeycomb model [5].) While it is possible to design multi-spin interactions as effective couplings arising from physical, twobody interactions, these constructions: (a) tend to be either perburbative (they are only exact in a classical limit and break down in the presence of quantum dynamics) [6][7][8][9][10][11][12][13][14][15], or (b) require capabilities beyond those achievable in real materials or in programmable quantum devices [16][17][18][19][20]. ...
... (2,7,12,17,22) (3,8,13,18,23)(4,9,14,19,24),(5,10,15,20,25)} and L 12 = perm{(1, 2, 3, 4, 5)(6, 7, 8, 9, 10) (11, 12, 13, 14, 15)(16, 17, 18, 19, 20)(21, 22, 23, 24, 25)} where perm{σ} denotes the permutation matrix corresponding to the permutation σ. ...
Combinatorial gauge symmetry is a novel principle that allows us to construct lattice gauge theories with two key and distinguishing properties: (a) the construction only requires one- and two-body interactions; and (b) the symmetry is exact rather than emergent in an effective or perturbative limit. Systems with these properties can feature topologically ordered ground states for a range of parameters. This paper presents a generalization of combinatorial gauge symmetry to any finite Abelian group. Apart from the general mathematical construction, we present a physical implementation in superconducting wire arrays, which offers a route to the experimental realization of lattice gauge theories with static Hamiltonians.
... Josephson junction arrays (JJAs) have for decades provided model systems for investigating classical and quantum phase transitions with competing ground states, frustration, and complex dynamics [1,2], 2D superconductivity [3,4], and more recently as a basis for quantum simulatation [5], quantum matter [6], and protected quantum information [7,8]. It is generally accepted that JJAs exhibit a quantum phase transition between superconducting and insulating phases controlled by the ratio E C /E J of charging energy, E C , of a single island to the Josephson energy, E J , between neighboring islands. ...
We investigate the Berezinskii-Kosterlitz-Thouless (BKT) transition in a semiconductor-superconductor two-dimensional Josephson junction array. Tuned by an electrostatic top gate, the system exhibits separate superconducting (S), anomalous metal (M*), and insulating (I) phases, bordered by separatrices of the temperature-dependent of sheet resistance, $R_{s}$. We find that the gate-dependent BKT transition temperature falls to zero at the S-M* boundary, suggesting incomplete vortex-antivortex pairing in the M* phase. In the S phase, $R_{s}$ is roughly proportional to perpendicular magnetic field at the BKT transition, as expected, while in the M* phase $R_{s}$ deviates from its zero-field value as a power-law in field with exponent close to 1/2 at low temperature. An in-plane magnetic field eliminates the M* phase, leaving a small scaling exponent at the S-I boundary, which we interpret as a remnant of the incipient M* phase.
... A promising route to creating protected qubits is to rely on circuits with underlying symmetries and encode the qubit into distinct eigenstates of the corresponding symmetry operator [1][2][3][4][5]. Such circuits satisfy the requirements of a protected qubit because (1) the vanishing transition matrix elements between states with different symmetries prevent bit-flip errors, and (2) the near degeneracy of the qubit states suppresses phase-flip errors. ...
... Besides protection against energy relaxation as well as fluctuations of charge and flux, two additional features are noteworthy. (1) The gate tunability of the semiconductor Josephson junctions allows the interferometers to be tuned into balance using gate voltages rather than additional fluxes. This feature is critical because the proposed concatenation approach enhances the protection only if the elements are pairwise balanced. ...
... We can gain insight into the origin of protection against flux errors by examining the simplest extension, with N = 2 interferometer loops. In this case, the Josephson energy of the setup, −E (1) J ,2 cos 2φ 1 − E (2) J ,2 cos 2φ 2 , has four minima in the unit cell at positions {(0, 0), (0, π), (π , 0), (π , π)}. We denote the linear combinations of the four lowest-energy Bloch waves with support in each of the four minima by {ψ ↑↑,n g , ψ ↑↓,n g , ψ ↓↑,n g , ψ ↓↓,n g }, and use them to define Wannier functions that are localized in a particular valley of the two-dimensional phase lattice, ...
We propose a protected qubit based on a modular array of superconducting islands connected by semiconductor Josephson interferometers. The individual interferometers realize effective cos2ϕ elements that exchange “pairs of Cooper pairs” between the superconducting islands when gate tuned into balance and frustrated by a half-flux quantum. If a large capacitor shunts the ends of the array, the circuit forms a protected qubit because its degenerate ground states are robust to offset-charge and magnetic field fluctuations for a sizable window around zero offset charge and half-flux quantum. This protection window broadens upon increasing the number of interferometers if the individual elements are balanced. We use an effective spin model to describe the system and show that a quantum phase transition sets the critical flux value at which protection is destroyed.
... One way of protecting the qubits is to enclose them in a medium of almost identical structures. Indeed, this gives a quantum error correction capability to the systems such that the effects of local noise become exponentially small as the size of the lattice increases [7,6]. The enclosure of a central plaquette is the focus of this next investigation. ...
... Another very promising form of quantum computation using superconducting systems is that of the topologically protected system [7,6], of which the spin-star is a subset. Josephson junction arrays imitate dimers, as we saw for the pyramid structure, when composed of triangular or kagome networks.A Josephson junction network with protected ground state degeneracies is one of the most promising long term solutions to the issues surrounding decoherence. ...
The $\pi$-ring qubit array is described using quasiclassical approaches that are shown to be accurate and give clarity to the complex energy landscape of connected vortex qubits. Using the techniques, large arrays of Josephson junction systems can be designed, including phase shift devices. Herein, connected arrays of loops containing $\pi$ junctions are described. These techniques are useful for design of quantum computers based on superconducting technologies, hybrid quantum technologies and quantum networks.
... Arguably the best-understood example of this is a one-dimensional (1D) spin-1/2 antiferromagnetic (AFM) chain where the spinons describe the spin domain wall dynamics [7][8][9][10][11][12][13][14][15]. QSLs in higher dimensions are harder to identify, but hold promise for realizing novel topological order and intrinsic long-range quantum entanglement with potential applications in quantum information [16,17]. Several studies have provided evidence for spinons in twodimensional (2D) or three-dimensional (3D) systems such as triangular, Kagome, Kitaev honeycomb, or pyrochlore lattices [18][19][20][21][22][23], while definitive material-realization remains controversial and is a major target of research. ...
Spinons are well-known as the elementary excitations of one-dimensional antiferromagnetic chains, but means to realize spinons in higher dimensions is the subject of intense research. Here, we use resonant x-ray scattering to study the layered trimer iridate Ba4Ir3O10, which shows no magnetic order down to 0.2 K. An emergent one-dimensional spinon continuum is observed that can be well-described by XXZ spin-1/2 chains with magnetic exchange of ~55 meV and a small Ising-like anisotropy. With 2% isovalent Sr doping, magnetic order appears below TN=130 K along with sharper excitations, indicating that the spinons become more confined in (Ba1-xSrx)4Ir3O10. We propose that the frustrated intra-trimer interactions effectively reduce the system into decoupled spin chains, the subtle balance of which can be easily tipped by perturbations such as chemical doping. Our results put Ba4Ir3O10 between the one-dimensional chain and two-dimensional quantum spin liquid scenarios, illustrating a new way to suppress magnetic order and realize fractional spinons.
