Based on the geometrical nature of quantum phases, non-adiabatic holonomic quantum control (NHQC) has become a standard technique for enhancing robustness in constructing quantum gates. However, the conventional approach of NHQC is sensitive to control instability, as it requires the driving pulses to cover a fixed pulse area. Furthermore, even for small-angle rotations, all operations need to be completed with the same duration of time. Here we experimentally demonstrate a time-optimal and unconventional approach of NHQC (called TOUNHQC), which can optimize the operation time of any holonomic gate. Compared with the conventional approach, TOUNHQC provides an extra layer of robustness to decoherence and control errors. The experiment involves a scalable architecture of superconducting circuit, where we achieved a fidelity of 99.51% for a single qubit gate using interleaved randomized benchmarking. Moreover, a two-qubit holonomic control-phase gate has been implemented where the gate error can be reduced by as much as 18% compared with NHQC.
We prove that a generic three-qubit quantum logic gate can be implemented using at most 98 one-qubit rotations about the $y$- and $z$-axes and 40 CNOT gates, beating an earlier bound of 64 CNOT gates.
Among the many proposals for the realization of a quantum computer, holonomic quantum computation (HQC) is distinguished from the rest in that it is geometrical in nature and thus expected to be robust against decoherence. Here we analyze the realization of various quantum gates by solving the inverse problem: Given a unitary matrix, we develop a formalism by which we find loops in the parameter space generating this matrix as a holonomy. We demonstrate for the first time that such a one-qubit gate as the Hadamard gate and such two-qubit gates as the CNOT gate, the SWAP gate and the discrete F…
We implement a non-adiabatic universal set of holonomic quantum gates based on abelian holonomies using dynamical invariants, by Lie-algebraic methods. Unlike previous implementations, presented scheme does not rely on secondary methods such as double-loop or spin-echo and avoids associated experimental difficulties. It turns out that such gates exist purely in the non-adiabatic regime for these systems.
Atomic Interferometer has two quantum unitary gates that must be realized for quantum sensing purposes from atomic gravimeter and atomic interferometer gyroscope. An optimal cost function which define the distance between two unitary operator is defines and based on it a pulse based stochastic gradient descent algorithm is derived for implementation of atomic mirror and atomic beam-splitter gates. By using numerical optimal control for those gate realization, we achieved to gate fidelity of 0.995 and 0.998 for mirror and beam-splitter gates, respectively. For this research, a two-level atomic …
We relate gate fidelities of experimentally realized quantum operations to the broadcasting property of their ideal operations, and show that the more parties a given quantum operation can broadcast to, the higher gate fidelities of its experimental realization are in general. This is shown by establishing the correspondence between two operational quantities, quantum state shareability and quantum broadcasting. This suggests that, to assess an experimental realization using gate fidelities, the worst case of realization such as noisy operations should be taken into account and then compared t…
Using virtual spin formalism it is shown that a quantum particle with eight energy levels can store three qubits. The formalism allows to realize a universal set of quantum gates. Feasible formalism implementation is suggested which uses nuclear spin-7/2 as a storage medium and radio frequency pulses as the gates. One pulse realization of all universal gates has been found, including three-qubit Toffoli gate.
The three-qubit conditional swap gate(Fredkin gate) is a universal gate that can be used to create any logic circuit and has many direct usages. In this paper, we experimentally realized Fredkin gate with only three transition pulses in solution of alanine. It appears that no experimental realization of Fredkin gate with fewer pulses has yet been reported up to now. In addition, the simple structure of our scheme makes it easy to be implemented in experiments.
The controlled-not gate and the single qubit gates are considered elementary gates in quantum computing. It is natural to ask how many such elementary gates are needed to implement more elaborate gates or circuits. Recall that a controlled-U gate can be realized with two controlled-not gates and four single qubit gates. We prove that this implementation is optimal if and only if the matrix U satisfies the conditions tr U != 0, tr UX != 0, and det U != 1. We also derive optimal implementations in the non-generic cases.
We investigate the effects of systematic errors of the control parameters on single-qubit gates based on non-adiabatic non-Abelian geometric holonomies and those relying on purely dynamical evolution. It is explicitly shown that the systematic error in the Rabi frequency of the control fields affects these two kinds of gates in different ways. In the presence of this systematic error, the transformation produced by the non-adiabatic non-Abelian geometric gate is not unitary in the computational space, and the resulting gate infidelity is larger than that with the dynamical method. Our results …
We present a computational circuit which realizes contextually the Tele-UNOT gate and the universal optimal quantum cloning machine (UOQCM). We report the experimental realization of the probabilistic UOQCM with polarization encoded qubits. This is achieved by combining on a symmetric beam-splitter the input qubit with an ancilla in a fully mixed state.
Quantum controlled-logic gates, including controlled NOT gate and Toffoli gate, play critical roles in lots of quantum information processing schemes. We design and experimentally demonstrate deterministic Toffoli gate by utilizing orbital-angular-momentum and polarization degrees of freedom of a single photon. In addition, we generate Bell states by using the controlled NOT gate. The effective conversion rate of the Toffoli gate in our experiment is $(95.1\pm3.2)\%$. Furthermore, our experimental setup does not require any auxiliary photons and probabilistic post selections.
We present a linear-optical implementation of a class of two-qubit partial SWAP gates for polarization states of photons. Different gate operations, including the SWAP and entangling square root of SWAP, can be obtained by changing a classical control parameter -- namely the path difference in the interferometer. Reconstruction of output states, full process tomography and evaluation of entanglement of formation prove very good performance of the gates.
The controlled-NOT gate and controlled square-root NOT gate play an important role in quantum algorithm. This article reports the experimental results of these two universal quantum logic gates (controlled square-root NOT gate and controlled-NOT gate) on a 7-qubit NMR quantum computer. Further, we propose a simple experimental method to measure and correct the error in the controlled phase-shift gate, which is helpful to construct a more perfect phase-shift gate experimentally and can also be used in more qubits discrete Fourier transformation.
Nonadiabatic holonomic quantum computation has received increasing attention due to its robustness against control errors as well as high-speed realization. The original protocol of nonadiabatic holonomic one-qubit gates has been experimentally demonstrated with superconducting transmon qutrit. However, the original protocol requires two noncommuting gates to realize an arbitrary one-qubit gate, which doubles the exposure time of gates to error sources and therefore makes the gates vulnerable to environment-induced decoherence. Single-shot protocol was subsequently proposed to realize an arbit…
By a significant modification of the standard protocol of quantum state Teleportation two processes ''forbidden'' by quantum mechanics in their exact form, the Universal NOT gate and the Universal Optimal Quantum Cloning Machine, have been implemented contextually and optimally by a fully linear method. In particular, the first experimental demonstration of the Tele-UNOT Gate, a novel quantum information protocol has been reported (cfr. quant-ph/0304070). A complete experimental realization of the protocol is presented here.
The geometric aspects of quantum mechanics are underlined most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a closed path in Hilbert space. The geometric phase is determined only by the shape of this path and is -- in its simplest form -- a real number. However, if the system contains degenerate energy levels, matrix-valued geometric phases, termed non-abelian holonomies, can emerge. They play an important role for the creation of synthetic gauge fields in cold atomic gases and the description of non-abelian anyon statistics. Moreov…
Squeezing is a nonlinear Gaussian operation that is the key component in construction of other nonlinear Gaussian gates. In our implementation of the squeezing gate, the amount and the orientation of the squeezing can be controlled by an external driving signal with 1 MHz operational bandwidth. This opens a brand new area of dynamic Gaussian processing. In particular, the gate can be immediately employed as the feed-forward needed for the deterministic implementation of the quantum cubic gate, which is a key piece of universal quantum information processing.
Algorithms for quantum information processing are usually decomposed into sequences of quantum gate operations, most often realized with single- and two- qubit gates[1]. While such operations constitute a universal set for quantum computation, gates acting on more than two qubits can simplify the implementation of complex quantum algorithms[2]. Thus, a single three-qubit operation can replace a complex sequence of two-qubit gates, which in turn promises faster execution with potentially higher Fidelity. One important three-qubit operation is the quantum Toffoli gate which performs a NOT operat…
We investigate two models for performing topological quantum gates with the Aharonov-Bohm (AB) and Aharonov-Casher (AC) effects. Topological one- and two-qubit Abelian phases can be enacted with the AB effect using charge qubits, whereas the AC effect can be used to perform all single-qubit gates (Abelian and non-Abelian) for spin qubits. Possible experimental setups suitable for a solid state implementation are briefly discussed.
A two qubit quantum gate, namely the C-Phase, has been realized by exploiting the longitudinal momentum (i.e. the optical path) degree of freedom of a single photon. The experimental setup used to engineer this quantum gate represents an advanced version of the high stability closed-loop interferometric setup adopted to generate and characterize 2-photon 4-qubit Phased Dicke states. Some experimental results, dealing with the characterization of multipartite entanglement of the Phased Dicke states are also discussed in detail.
Fast robust two-qubit gate operation with low susceptibility to crosstalk are the key to scalable quantum information processing. Parametrically driven gate is inherently insensitive to crosstalk while superadiabatic control can speed up the gate without losing accuracy. We propose and experimentally implement superadiabatic two-qubit gates using parametric modulation on superconducting quantum circuits. Our results demonstrate the preservation of adiabaticity at a gate speed close to the quantum limit, in addition to robustness against control instability. We demonstrate a CZ gate with error …
In this paper, we propose a scheme to realize three-qubit controlled phase gate and multiqubit controlled-NOT gate of one qubit simultaneously controlling n target qubit with four level quantum system in a cavity. Adjustment of level spacing during the gates implementation is not required. Implementation time for multiqubit controlled NOT gate is independent of number of qubit. Three-qubit phase gate is generalized to n-qubit phase gate with multiple control qubit and the number of steps (complexity) reduces linearly as compare to conventional gate decomposition method. Our scheme can be appli…
A simultaneous realization of the Universal Optimal Quantum Cloning Machine (UOQCM) and of the Universal-NOT gate by a quantum injected optical parametric amplification (QIOPA), is reported. The two processes, forbidden in their exact form for fundamental quantum limitations, are found universal and optimal, and the measured fidelity F<1 is found close to the limit values evaluated by quantum theory. This work may enlighten the yet little explored interconnections of fundamental axiomatic properties within the deep structure of quantum mechanics.
We show that with the assistance of a third level of the qubits an n-qubit phase gate can be constructed from $2n-4$ two-qutrit conditional swap gates, a single qutrit-qubit controlled phase gate, and two single-qutrit operations. Unlike previous schemes, our scheme uses the auxiliary level to "expose" some state to the qutrit-qubit controlled phase gate, instead of using it to "hide" states from the conditional dynamics. Neither the number of the additional levels nor that of single-qutrit operations needs to increase with $n$. We propose a physical implementation of the required elementary g…
We propose a Lyapunov control design to achieve specific (or a family of) unitary time-evolution operators, i.e., quantum gates in the Schrödinger picture by tracking control. Two examples are presented. In the first, we illustrate how to realize the Hadamard gate in a single-qubit system, while in the second, the controlled-NOT (CNOT) gate is implemented in two-qubit systems with the Ising and Heisenberg interactions. Furthermore, we demonstrate that the control can drive the time-evolution operator into the local equivalence class of the CNOT gate and the operator keeps in this class forever…
We report the first experimental demonstration of a quantum controlled-NOT gate for different photons, which is classically feed-forwardable. In the experiment, we achieved this goal with the use only of linear optics, an entangled ancillary pair of photons and post-selection. The techniques developed in our experiment will be of significant importance for quantum information processing with linear optics.
We have studied a system composed by two endohedral fullerene molecules. We have found that this system can be used as good candidate for the realization of Quantum Gates Each of these molecules encapsules an atom carrying a spin,therefore they interact through the spin dipole interaction. We show that a phase gate can be realized if we apply on each encased spin static and time dependent magnetic field. We have evaluated the operational time of a $π$-phase gate, which is of the order of ns. We made a comparison between the theoretical estimation of the gate time and the experimental decoheren…
Broadband implementations of time-optimal geodesic pulse elements are introduced for the efficient creation of effective trilinear coupling terms for spin systems consisting of three weakly coupled spins 1/2. Based on these pulse elements, the time-optimal implementation of indirect SWAP operations is demonstrated experimentally. The duration of indirect SWAP gates based on broadband geodesic sequence is reduced by 42.3% compared to conventional approaches.
Holonomies, arising from non-Abelian geometric transformations of quantum states in Hilbert space, offer a promising way for quantum computation. These holonomies are not commutable and thus can be used for the realization of a universal set of quantum logic gates, where the global geometric feature may result in some noise-resilient advantages. Here we report the first on-chip realization of a non-Abelian geometric controlled-Not gate in a superconducting circuit, which is a building block for constructing a holonomic quantum computer. The conditional dynamics is achieved in an all-to-all con…
Rabi nutations of a single nuclear spin in a solid have been observed. The experiments were carried out on a single electron and a single 13C nuclear spin of a single nitrogen vacancy defect center in diamond. The system was used for implementation of quantum logical NOT and a conditional two-qubit gate (CROT). Density matrix tomography of the CROT gate shows that the gate fidelity achieved in our experiments is up to 0.9, good enough to be used in quantum algorithms.
We present a scheme to achieve maximally entangled states, controlled phase-shift gate, and SWAP gate for two superconducting-quantum-interference-device (SQUID) qubits, by placing SQUIDs in a microwave cavity. We also show how to transfer quantum information from one SQUID qubit to another. In this scheme, no transfer of quantum information between the SQUIDs and the cavity is required, the cavity field is only virtually excited and thus the requirement on the quality factor of the cavity is greatly relaxed.
Quantum state manipulation with gates based on geometric phases acquired during cyclic operations promises inherent fault-tolerance and resilience to local fluctuations in the control parameters. Here we create a general non-Abelian and non-adiabatic holonomic gate acting in the $(\ket{0},\ket{2})$ subspace of a three-level transmon fabricated in a fully coplanar design. Experimentally, this is realized by simultaneously coupling the first two transitions by microwave pulses with amplitudes and phases defined such that the condition of parallel transport is fulfilled. We demonstrate the creati…
We investigate the feasibility of single-shot Toffoli- and Fredkin-gate realizations in qubit arrays with Heisenberg-type exchange interactions between adjacent qubits. As follows from the Lie-algebraic criteria of controllability, such an array is rendered completely controllable -- equivalent to allowing universal quantum computation -- by a Zeeman-like control field with two orthogonal components acting on a single "actuator" qubit. Adopting this local-control setting, we start our analysis with piecewise-constant control fields and determine the global maxima of the relevant figure of meri…
Nonadiabatic holonomic quantum computation has received increasing attention due to its robustness against control errors. However, all the previous schemes have to use at least two sequentially implemented gates to realize a general one-qubit gate. Based on two recent works, we construct two Hamiltonians and experimentally realized nonadiabatic holonomic gates by a single-shot implementation in a two-qubit nuclear magnetic resonance (NMR) system. Two noncommuting one-qubit holonomic gates, rotating along $\hat{x}$ and $\hat{z}$ axes respectively, are implemented by evolving a work qubit and a…
We report the implementation of a perceptron quantum gate in an ion-trap quantum computer. In this scheme, a perceptron's target qubit changes its state depending on the interactions with several qubits. The target qubit displays a tunable sigmoid switching behaviour becoming a universal approximator when nested with other percetrons. The procedure consists on the adiabatic ramp-down of a dressing-field applied to the target qubit. We also use two successive perceptron quantum gates to implement a XNOR-gate, where the perceptron qubit changes its state only when the parity of two input qubits …
We present a numerical study of the robustness of a specific class of non-abelian holonomic quantum gates . We take into account the parametric noise due to stochastic fluctuations of the control fields which drive the time-dependent Hamiltonian along an adiabatic loop. The performance estimator used is the state fidelity between noiseless and noisy holonomic gates. We carry over our analysis with different correlation times and we find out that noisy holonomic gates seem to be close to the noiseless ones for 'short' and 'long' noise correlation times. This result can be interpreted as a conse…
Cavity QED is a versatile tool to explore small scale quantum information processing. Within this setting, we describe a particular protocol for implementing a Toffoli gate with Rydberg atoms and a cavity field. Our scheme uses both resonant and non resonant interactions, and in particular a cavity assisted atomic collision. The experimental feasibility of the protocol is carefully analyzed with the help of numerical simulations and takes into account the decoherence process. Moreover, we show that our protocol is optimal within the constraints imposed by the experimental setting.
Based on a `shortcut-to-adiabaticity' (STA) scheme, we theoretically design and experimentally realize a set of high-fidelity single-qubit quantum gates in a superconducting Xmon qubit system. Through a precise microwave control, the qubit is driven to follow a fast `adiabatic' trajectory with the assistance of a counter-diabatic field and the correction of derivative removal by adiabatic gates. The experimental measurements of quantum process tomography and interleaved randomized benchmarking show that the process fidelities of our STA quantum gates are higher than 94.9% and the gate fideliti…
We propose an approach to realize an $n$-qubit controlled-$U$ gate with superconducting quantum interference devices (SQUIDs) in cavity QED. In this approach, the two lowest levels of a SQUID represent the two logical states of a qubit while a higher-energy intermediate level serves the gate manipulation. Our method operates essentially by creating a single photon through one of the control SQUIDs and then performing an arbitrary unitrary transformation on the target SQUID with the assistance of the cavity photon. In addition, we show that the method can be applied to implement an $n $% -qubit…
For a frequency-tunable two-qubit system, a controlled-Z (CZ) gate can be realized by adiabatically driving the qubit system through an avoided level crossing between an auxiliary state and computational levels. Here, we theoretically propose a fast CZ gate using a shortcut-to-adiabaticity (STA). Experimentally, the STA CZ gate is implemented with a 52 ns control pulse for two coupled superconducting Xmon qubits. Measured fidelity of the STA CZ gate is higher than 96.0%, in both quantum process tomography and randomized benchmarking. The protocol allows a flexible design of the evolution time …
A practical quantum computer must be capable of performing high fidelity quantum gates on a set of quantum bits (qubits). In the presence of noise, the realization of such gates poses daunting challenges. Geometric phases, which possess intrinsic noise-tolerant features, hold the promise for performing robust quantum computation. In particular, quantum holonomies, i.e., non-Abelian geometric phases, naturally lead to universal quantum computation due to their non-commutativity. Although quantum gates based on adiabatic holonomies have already been proposed, the slow evolution eventually compro…
The universality theorem in quantum computing states that any quantum computational task can be decomposed into a finite set of logic gates operating on one and two qubits. However, the process of such decomposition is generally inefficient, often leading to exponentially many gates to realize an arbitrary computational task. Practical processor designs benefit greatly from availability of multi-qubit gates that operate on more than two qubits to implement the desired circuit. In 1995, Cirac and Zoller proposed a method to realize native multi-qubit controlled-$Z$ gates in trapped ion systems,…
In this paper, with the weak cross-Kerr nonlinearity, we first present a special experimental scheme called C-path gate with which the realization of all possible bipartite POVMs of two-photon polarization states can be simpler and nearly deterministic. Following the same technique, the schemes of the realization of quantum control gates have been proposed, including the CNOT gate (1/2), Fredkin gate (1/8), Toffoli gate (2/23), CU gate and even MCU gate. All these gates are scalable with the certain probabilities which are larger than those gates in linear optics. Less resource are required an…
Nonadiabatic holonomic quantum computation uses non-Abelian geometric phases to implement a universal set of quantum gates that are robust against control imperfections and decoherence. Until now, a number of three-level-based schemes of nonadiabatic holonomic computation have been put forward, and several of them have been experimentally realized. However, all these works are based on the same class of nonadiabatic paths, which originates from the first nonadiabatic holonomic proposal. Here, we propose a universal set of nonadiabatic holonomic gates based on an extended class of nonadiabatic …
We experimentally demonstrate a programmable single-qubit quantum gate. This device applies a unitary phase shift operation to a data qubit with the value of the phase shift being fully determined by the state of a program qubit. Our linear optical implementation is based on the encoding of qubits into polarization states of single photons, two-photon interference on a polarizing beam splitter, and measurement on the output program qubit. We fully characterize the programmable gate by quantum process tomography. The achieved average quantum process fidelity exceeding 97% illustrates very good …
It is proposed that high-speed universal quantum gates can be realized by using non-Abelian holonomic transformation. A cyclic evolution path which brings the system periodically back to a degenerate qubit subspace is crucial to holonomic quantum computing. The cyclic nature and the resulting gate operations are fully dependent on the precise control of driving parameters, such as the modulated envelop function of Rabi frequency and the control phases. We investigate the effects of fluctuations in these driving parameters on the transformation fidelity of a universal set of single-qubit quantu…
Developing quantum computers for real-world applications requires understanding theoretical sources of quantum advantage and applying those insights to design more powerful machines. Toward that end, we introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis (CCPHASE$(θ)$). We estimate the process fidelity for this scheme via Cycl…
We propose and experimentally demonstrate that a Mach-Zehnder interferometer composed of polarized beam splitters and a pentaprism in the place of one of the mirrors works as a linear optical quantum controlled-NOT (CNOT) gate. To perform the information processing, the polarization and orbital angular momentum (OAM) of the photons act as the control and target qubits, respectively. The readout process is simple, requiring only a linear polarizer and a triangular diffractive aperture before detection. The viability and stability of the experiment makes the present proposal a valuable candidate…
Nonadiabatic holonomic quantum computation in decoherence-free subspaces has attracted increasing attention recently, as it allows for high-speed implementation and combines both the robustness of holonomic gates and the coherence stabilization of decoherence-free subspaces. Since the first protocol of nonadiabatic holonomic quantum computation in decoherence-free subspaces, a number of schemes for its physical implementation have been put forward. However, all previous schemes require two noncommuting gates to realize an arbitrary one-qubit gate, which doubles the exposure time of gates to er…
The possibility of realization of quantum gates by means of the non-adiabatic geometric phase is considered. It is shown that the non-adiabatic phase can be used for quantum gates realization as well as the adiabatic one.
High-fidelity two-qubits gates are essential for the realization of large-scale quantum computation and simulation. Tunable coupler design is used to reduce the problem of parasitic coupling and frequency crowding in many-qubit systems and thus thought to be advantageous. Here we design a extensible 5-qubit system in which center transmon qubit can couple to every four near-neighbor qubit via a capacitive tunable coupler and experimentally demonstrate high-fidelity controlled-phase (CZ) gate by manipulating center qubit and one near-neighbor qubit. Speckle purity benchmarking (SPB) and cross e…
We present a novel method to realize a multi-target-qubit controlled phase gate with one microwave photonic qubit simultaneously controlling $n-1$ target microwave photonic qubits. This gate is implemented with $n$ microwave cavities coupled to a superconducting flux qutrit. Each cavity hosts a microwave photonic qubit, whose two logic states are represented by the vacuum state and the single photon state of a single cavity mode, respectively. During the gate operation, the qutrit remains in the ground state and thus decoherence from the qutrit is greatly suppressed. This proposal requires onl…
In recent investigations, it has been found that conservation laws generally lead to precision limits on quantum computing. Lower bounds of the error probability have been obtained for various logic operations from the commutation relation between the noise operator and the conserved quantity or from the recently developed universal uncertainty principle for the noise-disturbance trade-off in general measurements. However, the problem of obtaining the precision limit to realizing the quantum NOT gate has eluded a solution from these approaches. Here, we develop a new method for this problem ba…
Quantum computation with quantum gates induced by geometric phases is regarded as a promising strategy in fault tolerant quantum computation, due to its robustness against operational noises. However, because of the parametric restriction of previous schemes, the main robust advantage of holonomic quantum gates is smeared. Here, we experimentally demonstrate a solution scheme, demonstrating nonadiabatic holonomic single qubit quantum gates with optimal control in a trapped Yb ion based on three level systems with resonant drives, which also hold the advantages of fast evolution and convenient …
Experimental realization of a universal set of quantum logic gates is the central requirement for implementation of a quantum computer. An all-geometric approach to quantum computation offered a paradigm for implementation where all the quantum gates are achieved based on the Berry phases and their non-abelian extensions, the holonomies, from geometric transformation of quantum states in the Hilbert space. Apart from its fundamental interest and rich mathematical structure, the geometric approach has some built-in noise-resilient features. On the experimental side, geometric phases and holonom…
Topological quantum computation (TQC) is one of the most striking architectures that can realize fault-tolerant quantum computers. In TQC, the logical space and the quantum gates are topologically protected, i.e., robust against local disturbances. The topological protection, however, requires rather complicated lattice models and hard-to-manipulate dynamics; even the simplest system that can realize universal TQC--the Fibonacci anyon system--lacks a physical realization, let alone braiding the non-Abelian anyons. Here, we propose a disk model that can realize the Fibonacci anyon system, and c…
