Realization of the iSWAP-like gate among the superconducting qutrits

High-dimensional quantum systems, such as qutrits(quantum three-level systems), have multiple accessible energy levels beyond the two-level qubits. Therefore, qutrits can offer a larger state space to improve the efficiency of quantum computation. Here, we demonstrate a high-fidelity iSWAP-like gate operation on a frequency-tunable superconducting qutrits system. The superconducting quantum system consists of two qutrits that are coupled via a resonator with fixed qutrit-resonator coupling strengths. Through designing the frequency pulse profile and optimizing the parameter values,the gate error can be suppressed below 1.5 × 10^(-3). To bear out the feasibility of the proposal, we have conducted our study with experimentally accessible parameters. As the resonator can mediate the interaction between the irrelevant qutrits, the presented approach can also be used to couple multiple qutrits together, providing a good platform for quantum information processing.

Probabilistically implementing nonlocal operations between two distant qutrits

We propose a method to probabilistically implement a nonlocal operation, exp[iζUAUB], between two distant qutrits A and B, where ζ∈ C [0,2π] and UA, UB are local unitary and Hermitian operations for qutrits A and B respectively. The consumptions of resource for one performance of the method are a single non-maximally entangled qutrit state and 1-trit classical communication. For a given ζ, the successful probability of the method depends on the forms of both entanglement resource and Bob＇s partial-measurement basis. We systematically discuss the optimal successful probabilities and their corresponding conditions for three cases： adjustable entanglement resource, adjustable partial-measurement basis, adjustable entanglement resource and partial-measurement basis. It is straightforward to generalize the method for producing nonlocal unitary operations between any two N-level systems.

On Topics in Quantum Games

This work concentrates on simultaneous move non-cooperating quantum games. Part of it is evidently not new, but it is included for the sake self consistence, as it is devoted to introduction of the mathematical and physical grounds of the pertinent topics, and the way in which a simple classical game is modified to become a quantum game (a procedure referred to as a quantization of a classical game). The connection between game theory and information science is briefly stressed, and the role of quantum entanglement (that plays a central role in the theory of quantum games), is exposed. Armed with these tools, we investigate some basic concepts like the existence (or absence) of a pure strategy and mixed strategy Nash equilibrium and its relation with the degree of entanglement. The main results of this work are as follows: 1) Construction of a numerical algorithm based on the method of best response functions, designed to search for pure strategy Nash equilibrium in quantum games. The formalism is based on the discretization of a continuous variable into a mesh of points, and can be applied to quantum games that are built upon two-players two-strategies classical games, based on the method of best response functions. 2) Application of this algorithm to study the question of how the existence of pure strategy Nash equilibrium is related to the degree of entanglement (specified by a continuous parameter γ ). It is shown that when the classical game GC has a pure strategy Nash equilibrium that is not Pareto efficient, then the quantum game GQ with maximal entanglement (γ = π/2) has no pure strategy Nash equilibrium. By studying a non-symmetric prisoner dilemma game, it is found that there is a critical value 0γc such that for γγc there is a pure strategy Nash equilibrium and for γ≥γc there is no pure strategy Nash equilibrium. The behavior of the two payoffs as function of γ starts at that of the classical ones at (D, D) and approaches the cooperative classical ones at (C, C) (C = confess, D = don’t confess). 3) We then study Bayesian quantum games and show that under certain conditions, there is a pure strategy Nash equilibrium in such games even when entanglement is maximal. 4) We define the basic ingredients of a quantum game based on a two-player three strategies classical game. This requires the introduction of trits (instead of bits) and quantum trits (instead of quantum bits). It is proved that in this quantum game, there is no classical commensurability in the sense that the classical strategies are not obtained as a special case of the quantum strategies.

Fast population transfer with a superconducting qutrit via non-Hermitian shortcut to adiabaticity

Non-Hermitian dissipation dynamics,capable of turning the conventionally detrimental decoherence effects to useful resources for state engineering,is highly attractive to quantum information processing.In this work,an effective scheme is developed for implementing fast population transfer with a superconducting qutrit via the non-Hermitian shortcut to adiabaticity(STA).We first deal with aΛ-configuration interaction between the qutrit and microwave drivings,in which the dephasing-assisted qubit state inversion requiring an overlarge dephasing rate is constructed non-adiabatically.After introducing a feasible ancillary driving that directly acts upon the qubit states,the target state transfer can be well realized but with an accessible qubit dephasing rate.Moreover,a high fidelity could be numerically obtained in the considered system.The strategy could provide a new route towards the non-Hermitian shortcut operations on superconducting quantum circuits.

Constructing Entanglers in 2-Players–N-Strategies Quantum Game

In quantum games based on 2-player-N-strategies classical games, each player has a quNit (a normalized vector in an N-dimensional Hilbert space HN) upon which he applies his strategy (a matrix U∈SU(N)). The players draw their payoffs from a state . Here ?and J (both determined by the game’s referee) are respectively an unentangled 2-quNit (pure) state and a unitary operator such that ?is partially entangled. The existence of pure strategy Nash equilibrium in the quantum game is intimately related to the degree of entanglement of . Hence, it is practical to design the entangler J= J(β) to be dependent on a single real parameter β that controls the degree of entanglement of , such that its von-Neumann entropy SN(β) is continuous and obtains any value in . Designing J(β) for N=2 is quite standard. Extension to N>2 is not obvious, and here we suggest an algorithm to achieve it. Such construction provides a special quantum gate that should be a useful tool not only in quantum games but, more generally, as a special gate in manipulating quantum information protocols.

Three-Qutrit Topological SWAP Logic Gate for ISK(I=1,S=1,K=1)Spin System

Three Zeeman levels of spin-1 electron or nucleus are called as qutrits in quantum computation. Then, ISK (I = 1, S = 1, K = 1) spin system can be represented as three-qutrit states. Quantum circuits and algorithms consist of quantum logic gates. By using SWAP logic gate, two quantum states are exchanged. Topological quantum computing can be applied in quantum error correction. In this study, first, Yang-Baxter equation is modified for ISK (I = 1, S = 1, K = 1) spin system. Then three-qutrit topological SWAP logic gate is obtained. This SWAP logic gate is applied for three-qutrit states of ISK (I = 1, S = 1, K = 1) spin system. Three-qutrit SWAP logic gate is also applied to the product operators of ISK (I = 1, S = 1, K = 1) spin system. For these two applications, expected exchange results are found.

High-dimension multiparty quantum secret sharing scheme with Einstein-Podolsky-Rosen pairs

In this paper a high-dimension multiparty quantum secret sharing scheme is proposed by using Einstein-Podolsky-Rosen pairs and local unitary operators. This scheme has the advantage of not only having higher capacity, but also saving storage space. The security analysis is also given.

Nonlocal multi-target controlled controlled gate using Greenberger–Horne–Zeilinger channel and qutrit catalysis

We present a scheme for implementing locally a nonlocal N-target controlled–controlled gate with unit probability of success by harnessing two（N＋1）-qubit Greenberger–Horne–Zeilinger（GHZ） states as quantum channel and N qutrits as catalyser. The quantum network that implements this nonlocal（N＋2）-body gate is built entirely of local single-body and two-body gates, and has only（3N＋2） two-body gates. This result suggests that both the computational depth of quantum network and the quantum resources required to perform this nonlocal gate might be significantly reduced. This scheme can be generalized straightforwardly to implement a nonlocal N-target and M-control qubits gate.

Reduction of entropy uncertainty for qutrit system under non-Markov noisy environment

We explore the entropy uncertainty for qutrit system under non-Markov noisy environment and discuss the effects of the quantum memory system and the spontaneously generated interference(SGI)on the entropy uncertainty in detail.The results show that,the entropy uncertainty can be reduced by using the methods of quantum memory system and adjusting of SGI.Particularly,the entropy uncertainty can be decreased obviously when both the quantum memory system and the SGI are simultaneously applied.

Thermal entanglement in two-qutrit spin-1 anisotropic Heisenberg model with inhomogeneous magnetic field

The thermal entanglement of a two-qutrit spin-1 anisotropic Heisenberg XXZ chain in an inhomogeneous magnetic field is studied in detail. The effects of the external magnetic field （B）, a parameter b which controls the inhomogeneity of B, and the bilinear interaction parameters Jx = Jy ≠ Jz on the thermal variation of the negativity are studied in detail. It is found that negativity N decreases when the values of magnetic field, inhomogeneity b and temperature are increasing. In addition, N remains at higher temperatures for higher values of Jz and lower values of B and b.

Effects of colored noise on the dynamics of quantum entanglement of a one-parameter qubit-qutrit system

We analyzed the effect of colored noise on the negativity dynamics of a hybrid system consisting of a qubit-qutrit and not interacting,prepared from the start in an entangled one-parameter state and acting with noise in local and non-local environments.In this pink and brown noise we investigated two different situations:in the first situation,the noise is produced by a bistable oscillator with an unknown exchange rate;however,in the second situation,the noise is generated by a set of bistable oscillators.We found that entanglement decreases with time to zero,and undergoes the phenomenon of sudden death and rebirth.The pink noise is more prone to entanglement than the brown noise and the non-local environment is more prone to entanglement than the local one.When the number of fluctuators is increased,entanglement decays faster and finally,for certain parameters of the initial state,the subsystems are not affected by the noise.

Robust generation of qutrit entanglement via adiabatic passage of dark states

We propose a scheme for the deterministic generation of qutrit entanglement for two atoms trapped in an optical cavity. Taking advantage of the adiabatic passage, the operation is immune to atomic spontaneous emission as the atomic excited states are never populated; under certain conditions, the probability that the cavity is excited is negligible. We also study the influences of the dissipation due to the atomic spontaneous emission and cavity decay.

Quantum discord of two-qutrit system under quantum-jump-based feedback control

This paper studies quantum discord of two qutrits coupled to their own environments independently and coupled to the same environment simultaneously under quantum-jump-based feedback control. Our results show that spontaneous emission, quantum feedback parameters, classical driving, initial state, and detection efficiency all affect the evolution of quantum discord in a two-qutrit system. We find that under the condition of designing proper quantum-jump-based feedback parameters, quantum discord can be protected and prepared. In the case where two qutrits are independently coupled to their own environments, classical driving, spontaneous emission, and low detection efficiency have negative effect on the protection of quantum discord. For different initial states, it is found that the evolution of quantum discord under the control of appropriate parameters is similar. In the case where two qutrits are simultaneously coupled to the same environment,the classical driving plays a positive role in the generation of quantum discord, but spontaneous emission and low detection efficiency have negative impact on the generation of quantum discord. Most importantly, we find that the steady discord depends on feedback parameters, classical driving, and detection efficiency, but not on the initial state.

One-step generation of qutrit entanglement via adiabatic passage in cavity quantum electrodynamics

A scheme is proposed for generating a three-dimensional entangled state for two atoms trapped in a cavity by one step via adiabatic passage. In the scheme, the two atoms are always in ground states and the field mode of the cavity excited is negligible under a certain condition. Therefore, the scheme is very robust against decoherence. Furthermore, it needs neither the exact control of all parameters nor the accurate control of the interaction time. It is shown that qutrit entanglement can be generated with a high fidelity.

Demonstration of quantum permutation parity determine algorithm in a superconducting qutrit

A quantum algorithm provides a new way in solving certain computing problems and usually faster than classical algorithms. Here we report an implementation of a quantum algorithm to determine the parity of permutation in a single three-dimensional（3D） superconducting transmon qutrit system. The experiment shows the capacity to speed up in a qutrit,which can also be extended to a multi-level system for solving high-dimensional permutation parity determination problem.

It from Qutrit: Braided Loop Metaheuristic

Cosmologies are developed by physicists and philosophers to explain our experiences of the evolving cosmos. Intelligent deep-learning metaheuristics provide original frameworks for cosmologies which are founded on quantum information. Mathematical standard models of physical cosmology and particle physics formalize an abundance of observations, yet there is no scientific consensus about how these models include our conscious experiences and fundamental philosophies of information. Furthermore, Naturalness in physics is coupled to the related problem of fine-tuning. To address these foundational problems, within the quantum information paradigm, whilst aligning with standard scientific models, I introduce a topological deep-learning cosmology metaheuristic. Braided, 3-coloured, world-strands are proposed to be the fundamental quantum information tracts (ethereal fibre bundles) of our evolving Triuniverse. This Braided Loop Metaheuristic comprises eternally evolving deep-learning feedback loops of superposed, braided, 3-coloured, quantum information world-strands, which process (in 3-level qutrit states) foundational properties coined Algebrus (labelled red), Algorithmus (labelled green) and Geometrus (labelled blue). Braids split from 1→2→3 (in knot representation respectively: closed loop→trefoil knot→Borromean loops) thence combine from 3→2→1 to form eternally evolving deep-learning loops. This cosmology metaheuristic simultaneously incorporates initial Laws of Form;Emergentism (from substrate Mathematics, through Quantum Physics to Life);Consciousness (as a superposed triunity of Implicate Order, Process Philosophy and Aesthetic Relationalism);Reductionism (from Life, through Quantum Physics to Pure Mathematics expressed as Logical Axioms, Laws of Parsimony and Ideal Form);and the Braided Loop Metaheuristic reboots its eternal cycle with the initial Laws of Form. An agent’s personal anthropic Braided Loop Metaheuristic represents one of many-worlds, a meridional loop in a multiverse with horn-torus topology, where Nature’s physical parameters vary equatorially. Fundamental information processing is driven by ψ-Epistemic Drive, the Natural appetite for information selected for advantageous knowledge. The meridional loops are ψ-Epistemic Field lines emanating from an epistemic dipole at the horn-torus core. Equatorial parameter fine-tuning in many-worlds quantum physics and the many-species of Darwinian Life are similar deep-learning optimizations in the Braided Loop Metaheuristic.

Lithium Quantum Consciousness

Conscious agency is considered to be founded upon a quantum state of mind . An original synthesis, called “Lithium Quantum Consciousness” (LQC), proposes that this quantum state utilises lithium-6 (spin-1) qutrit nuclear magnetic resonance (NMR) quantum information processing (QIP) in the connectome (brain-graph). In parallel to the connectome’s processing of physiological controls, perception, cognition and intelligence via quantum electrodynamics (QED), the connectome also functions via its dynamic algebraic topology as a unitary transceiver antenna laced with lithium-6 nuclei which are spin-entangled with each other and with the environmental vortical gluon field via quantum chromodynamics (QCD). This unitary antenna (connectome) bestows the self its unity of consciousness within an intertwined-history multi-agent environment. An equivalence is proposed between Whitehead’s occasions of experience and topological spacetime instantons in the vortical gluon field. Topological spacetime instantons pervade the vortical gluon field in a quantum information network of vortex interactions, herein termed the “instanton-net”, or “Instanet” [sic]. The fermionic isotope lithium-6 has a very low nuclear binding energy and the smallest non-zero nuclear electric quadrupole moment of any stable nucleus making it susceptible to quantum chromodynamic (QCD) interaction with the vortical gluon field and ideal for spin-1 qutrit NMR-QIP. The compact spherical atomic orbital of lithium provides ideal rotational freedom inside tetrahedral water cages in organo6Li+(H2O)4 within which the lithium nucleus rapidly tumbles for NMR motional narrowing and long decoherence times. Nuclear spin-entanglement, among water-caged lithium-6 nuclei in the connectome, is a spin-1 qutrit NMR-QIP resource for conscious agency. By contrast, similar tetrahedral xenon cages in organo6Li+Xe4 excimers are postulated to decohere the connectome’s NMR-QIP due to xenon’s NMR signal being extremely sensitive to its molecular environment. By way of this quantum neurochemistry, lithium is an effective psychiatric medication for enhancing mood and xenon is an effective anaesthetic.

两Qutrit门的Cartan分解

用逐次进行Cartan分解的方法,讨论了两Qutrit门对应的矩阵分解,并利用李群和李代数之间的关系将其写成指数形式,使其可能与实现该门的哈密顿和控制场相联系起来.最后具体地讨论了三进制SWAP门的分解.

Controllable entanglement sudden birth of Heisenberg spins

We investigate the Entanglement Sudden Birth （ESB） of two Heisenberg spins A and B. The third controller, qutrit C is introduced, which only has the Dzyaloshinskii-Moriya （DM） spin-orbit interaction with qubit B. We find that the DM interaction is necessary to induce the Entanglement Sudden Birth of the system qubits A and B, and the initial states of the system qubits and the qurit C are also important to control its Entanglement Sudden Birth.