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(a) The quantum version of the bit, a qubit, can be represented in the Bloch sphere with an arrow pointing north representing the |0⟩ state, while when pointing south it represents the |1⟩ state. Unlike the bit, the qubit can possess many more states, which can be viewed as an arrow pointing in any other direction of the sphere. These new states are quantum superposition of the |1⟩ and 0⟩ states, giving the computational power expected in quantum computers; (b) One qubit Hadamard gate acting on an initial qubit. After each operation superposition of states are obtained, all of them containing all possible combinations of states.
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Presently, one of the most ambitious technological goals is the development of devices working under the laws of quantum mechanics. One prominent target is the quantum computer, which would allow the processing of information at quantum level for purposes not achievable with even the most powerful computer resources. The large-scale implementation...
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Quantum computers are expected to be able to outperform classical computers. In fact, some computational problems such as integer factorization can be solved on quantum computers substantially faster than classical computers. Interestingly, these problems can be cast in a framework of the hidden symmetry subgroup problem. However, only a few of qua...
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... To be specific, molecular systems can be easily assembled to reach higher nuclearities and Hilbert space dimensions 4 , and their energy levels can be tailored via chemical modification. This field has been attracting increasing attention, and its development, prospects and remaining challenges have been thoroughly discussed 1,[5][6][7][8][9][10][11][12] . While an increasing number of candidate molecules showing sufficiently long spin relaxation times have been synthesized, pushing the limit to the millisecond scale 13 , fullerenes are uniquely advantageous because these allcarbon molecules have little intramolecular hyperfine interaction, which helps preserving the spin coherence, and the near-spherical symmetry of the cage configurations allows small zero-field splittings (ZFS) [14][15][16][17] . ...
High-spin magnetic molecules are promising candidates for quantum information processing because their intrinsic multiplicity facilitates information storage and computational operations. However, due to the absence of suitable sublevel splittings, their susceptibility to environmental disturbances and limitation from the selection rule, the arbitrary control of the quantum state of a molecular electron multiplet has not been realized. Here, we exploit the photoexcited triplet of C 70 as a molecular electron spin qutrit with pulsed electron paramagnetic resonance. We prepared the system into 3-level superposition states characteristic of a qutrit and validated them by the tomography of their density matrices. To further elucidate the coherence of the operation and the nature of the system as a qutrit, we demonstrated the quantum phase interference in the superposition. The interference pattern is further interpreted as a map of possible evolution paths in the space of phase factors, representing the quantum nature of the 3-level system.
... Different physical platforms can be used to implement high-dimensional quantum systems [15], such as photons [13,[16][17][18][19][20], trapped ions [21,22], superconducting systems [23,24], and molecules [25][26][27]. The practical application of these qudit-based systems is a very active research field with great potential. ...
The use of classical computers to simulate quantum computing has been successful in aiding the study of quantum algorithms and circuits that are too complex to examine analytically. Current implementations of quantum computing simulators are limited to two-level quantum systems. Recent advances in high-dimensional quantum computing systems have demonstrated the viability of working with multi-level superposition and entanglement. These advances allow an agile increase in the number of dimensions of the system while maintaining quantum entanglement, achieving higher encoding of information and making quantum algorithms less vulnerable to decoherence and computational errors. In this paper, we introduce QuantumSkynet, a novel high-dimensional cloud-based quantum computing simulator. This platform allows simulations of qudit-based quantum algorithms. We also propose a unified generalization of high-dimensional quantum gates, which are available for simulations in QuantumSkynet. Finally, we report simulations and their results for qudit-based versions of the Deutsch--Jozsa and quantum phase estimation algorithms using QuantumSkynet.
... Unlike qubits, the Lie algebra of such gates are not the native Hamiltonians, and thus implementation of this generating set is not straightforward. Different approaches have been studied to implement SU(d) gates [31][32][33][34][35]. One approach is to specify an arbitrary SU(d) unitary matrix through a sequence of so-called Givens rotations acting between pairs of levels [36]. ...
We study the ability to implement unitary maps on states of the I = 9/2 nuclear spin in 87 Sr, a d = 10 dimensional (qudecimal) Hilbert space, using quantum optimal control. Through a combination of nuclear spin-resonance and a tensor AC-Stark shift, by solely modulating the phase of a radio-frequency magnetic field, the system is quantum controllable. Alkaline earth atoms, such as 87 Sr, have a very favorable figure-of-merit for such control due to the long lifetimes of the intercombination lines and the large hyperfine splitting in the excited states. We numerically study the quantum speed-limit, optimal parameters, and the fidelity of arbitrary state preparation and full SU(10) maps including the presence of decoherence due to optical pumping induced by the light-shifting laser. We also study the use of robust control to mitigate some dephasing due to inhomogenieties in the light shift. We find that with an rf-Rabi frequency of Ω rf /2π = 2 kHz and 1% inhomogeneity in the the light shift we can prepare an arbitrary Haar-random state in a time T = 8π/Ω rf = 2 ms with average fidelity F ψ = 0.9996, and an arbitrary Haar-random SU(10) map in a time T = 42π/Ω rf = 10.5 ms with average fidelity FU = 0.9963. Ultracold ensembles of alkaline-earth atoms trapped in optical lattices or arrays of optical tweezers are a powerful platform for quantum information processing (QIP), including atomic clocks and sensors [1-5], simulators of many-body physics [6-11], and general purpose quantum computers [7, 12, 13]. The ability to optically manipulate coherence in single-atoms via ultranarrow optical resonances on the intercombination lines, together with the ability to create high-fidelity entangling interactions between atoms when they are excited to high-lying Ryd-berg states [14-16] provides tools that makes this system highly controllable for such applications. In addition, fermionic species have nuclear spin. As the ground state is a closed shell, there is no electron angular momentum, and the nuclear spin with its weak magnetic moment is highly isolated from the environment. Such nuclear spins in alkaline-earth atoms are thus natural carriers of quantum information given their long coherence times and our ability to coherently control them with magnetic and optical fields. Nuclear spins are also seen as excellent carriers of quantum information in the solid state as demonstrated in pioneering experiments including in NV-centers [17] and dopants in silicon [18-21]. Using magneto-optical fields to control qubits comprising an isolated pair of two nuclear-spin magnetic sub-levels levels in 87 Sr was recently demonstrated [22]. The nuclear spin in this atomic species, however, is not a two-level system; the spin is I = 9/2 and there are d = 2I + 1 = 10 nuclear magnetic sublevels. Such qudits, here "qudecimals," have potential advantage for QIP. First and foremost, one can encode a D = d n d = 2 n2 dimensional Hilbert space associated with n 2 qubits in n d = n 2 / log 2 d qudits. While only a logarithmic saving , this is meaningful for the qudecimal (log 2 d = 3.32), especially when trapping and control of each atom is at a premium. This savings extends to algorithmic efficiency , in that the number of elementary two-qudit gates necessary to implement a unitary map scales as O(n 2 d D 2) = O n 2 2 D 2 (log 2 d) 2 [23]. Moreover, qudits offer new opportunities for quantum error correction [24]. One can protect against dephasing errors by encoding a qubit in a nuclear spin qudit [25]. In addition, fault-tolerant operation of a quantum computer may be more favorable based on qudit vs. qubit codes [26, 27]. While QIP with qudits has great potential, there are substantial hurdles. State preparation and a readout are more challenging for systems with d > 2. Moreover, quantum logic with qudits is more complex. Universal quantum logic with qubits can be achieved with a set of logic gates that include the unitary-generators of SU(2) on each qubit, plus one entangling gate between qubits pairwise. In the case of qudits, in addition to the entangling gate, we require unitary-generators of SU(d) for each subsystem [23, 28-30]. Unlike qubits, the Lie algebra of such gates are not the native Hamiltonians, and thus implementation of this generating set is not straightforward. Different approaches have been studied to implement SU(d) gates [31-35]. One approach is to specify an arbitrary SU(d) unitary matrix through a sequence of so-called Givens rotations acting between pairs of levels [36]. Alternatively, one can employ the tools of quantum optimal control to numerically search for a time-dependent waveform that achieves the desired SU(d) unitary map when one has access to a Hamiltonian that makes the system universally "controllable" [37]. Optimal control is a powerful and flexible approach that does not require specific pairwise Givens rotations, can be high-fidelity and can be made robust to imperfections such as inhomogenieties through the tools of robust control [38].
... 5 Much effort has been put into investigations on the properties of superposition-state molecules, arising from not only fundamental interests in chemical dynamics 5,6 but also the potential applications in quantum information processing. [7][8][9] In principle, molecular structure and dynamics, besides electronic and nuclear spins, 9 offer rich scales that are at the heart of new protocols in quantum information. Therefore, it is full of meaning and imperative to establish practical methods to prepare the superpositionstate molecules. ...
... 5 Much effort has been put into investigations on the properties of superposition-state molecules, arising from not only fundamental interests in chemical dynamics 5,6 but also the potential applications in quantum information processing. [7][8][9] In principle, molecular structure and dynamics, besides electronic and nuclear spins, 9 offer rich scales that are at the heart of new protocols in quantum information. Therefore, it is full of meaning and imperative to establish practical methods to prepare the superpositionstate molecules. ...
Molecular electronic or vibrational states can be superimposed temporarily in an extremely short laser pulse, and the superposition-state transients formed therein receive much attention, owing to the extensive interest in molecular fundamentals and the potential applications in quantum information processing. Using the crossed-beam ion velocity map imaging technique, we disentangle two distinctly different pathways leading to the forward-scattered N 2 + yields in the large impact-parameter charge transfer from low-energy Ar + to N 2. Besides the ground-state (X 2 Σg +) N 2 + produced in the energy-resonant charge transfer, a few slower N 2 + ions are proposed to be in the superpositions of the X 2 Σg +-A 2 Πu and A 2 Πu-B 2 Σu + states on the basis of the accidental degeneracy or energetic closeness of the vibrational states around the X 2 Σg +-A 2 Πu and A 2 Πu-B 2 Σu + crossings in the non-Franck-Condon region. This finding potentially shows a brand-new way to prepare the superposition-state molecular ion. Published under an exclusive license by AIP Publishing. https://doi.
... Over the last two decades, coordination compounds of trivalent Ln ions also acquired a prominent role in molecular magnetism since the discovery that they can show slow relaxation of the magnetization and the opening up of a hysteresis loop [10][11][12][13], offering a glance at the possibility to create a single-molecule version of bulk permanent magnets for high-density memory storage. Interestingly, the possibility of obtaining Ln complexes with very long magnetic moment lifetimes [14,15] also makes them optimal candidates for the realization of multi-level quantum bits (qudits) [16][17][18]. ...
The unique electronic and magnetic properties of Lanthanides molecular complexes place them at the forefront of the race towards high-temperature single-ion magnets and magnetic quantum bits. The design of compounds of this class has so far been almost exclusively driven by static crystal field considerations, with emphasis on increasing the magnetic anisotropy barrier. This guideline has now reached its maximum potential and new progress can only come from a deeper understanding of spin-phonon relaxation mechanisms. In this work we compute relaxation times fully ab initio and unveil the nature of all spin-phonon relaxation mechanisms, namely Orbach and Raman pathways, in a prototypical Dy single-ion magnet. Computational predictions are in agreement with the experimental determination of spin relaxation time and crystal field anisotropy, and show that Raman relaxation, dominating at low temperature, is triggered by low-energy phonons and little affected by further engineering of crystal field axiality. A comprehensive analysis of spin-phonon coupling mechanism reveals that molecular vibrations beyond the ion's first coordination shell can also assume a prominent role in spin relaxation through an electrostatic polarization effect. Therefore, this work shows the way forward in the field by delivering a novel and complete set of chemically-sound design rules tackling every aspect of spin relaxation at any temperature
... Before proceeding further, we briefly explain the necessity of developing qudit-based NHQC. Compared to qubit settings, qudit-based processors can store exponentially larger amounts of information and thereby provide reduction of the circuit complexity and simplification of the experimental setup [53][54][55]. Qudit-based processors can also enable enhancement of the algorithm efficiency, favorable error thresholds, and high-fidelity magic-state distillation [56][57][58][59][60][61]. This benefits quantum error corrections and is essential for scalable quantum computation. ...
Nonadiabatic holonomic quantum computation (NHQC) provides a method to implement error resilient gates and that has attracted considerable attention recently. Since it was proposed, three-level Λ systems have become the typical building block for NHQC and a number of NHQC schemes have been developed based on such systems. In this paper, we investigate the realization of NHQC beyond the standard three-level setting. The central idea of our proposal is to improve NHQC by enlarging the Hilbert space of the building block system and letting it have a bipartite graph structure in order to ensure purely holonomic evolution. Our proposal not only improves conventional qubit-based NHQC by efficiently reducing its duration, but also provides implementations of qudit-based NHQC. Therefore, our proposal provides a further development of NHQC that can contribute significantly to the physical realization of efficient quantum information processors.
... 34 It is also possible to make use of the metal ions' nuclear spin states. 35,36 The hyperfine coupling to the electronic spin splits these levels and considerably speeds up the rates at which such states can be coherently manipulated by electromagnetic pulses. [37][38][39] The different strategies can also be combined to further increase the qudit dimension. ...
Artificial magnetic molecules can contribute to progressing towards large scale quantum computation by: a) integrating multiple quantum resources and b) reducing the computational costs of some applications. Chemical design, guided by theoretical proposals, allows embedding nontrivial quantum functionalities in each molecular unit, which then acts as a microscopic quantum processor able to encode error protected logical qubits or to implement quantum simulations. Scaling up even further requires 'wiring-up' multiple molecules. We discuss how to achieve this goal by the coupling to on-chip superconducting resonators. The potential advantages of this hybrid approach and the challenges that still lay ahead are critically reviewed.
... Li et al. proposed the slime mould algorithm (SMA) [19] in 2020 and achieved good optimization results. en, Moreno-Pineda et al. proposed the improved dragonfly algorithm (DA) [20]; the method can be used as a useful, auxiliary tool for solving complex optimization problems. Next, Yu et al. proposed a moth flame optimizer [21], which has achieved remarkable results in solving complex optimization problems. ...
Emotion recognition is a research hotspot in the field of artificial intelligence. If the human-computer interaction system can sense human emotion and express emotion, it will make the interaction between the robot and human more natural. In this paper, a multimodal emotion recognition model based on many-objective optimization algorithm is proposed for the first time. The model integrates voice information and facial information and can simultaneously optimize the accuracy and uniformity of recognition. This paper compares the emotion recognition algorithm based on many-objective algorithm optimization with the single-modal emotion recognition model proposed in this paper and the ISMS_ALA model proposed by recent related research. The experimental results show that compared with the single-mode emotion recognition, the proposed model has a great improvement in each evaluation index. At the same time, the accuracy of emotion recognition is 2.88% higher than that of the ISMS_ALA model. The experimental results show that the many-objective optimization algorithm can effectively improve the performance of the multimodal emotion recognition model.
... Q uantum information processing (QIP) schemes, such as quantum computing, quantum storage, and quantum communication, use the quantum nature of materials to process and manipulate information [1][2][3][4] . In QIP, a dramatic improvement in computation time and secure data transmission can be achieved by creating superposition states with long coherence lifetimes (T 2 ) 5,6 . ...
... To the best of our knowledge, transient SHB in a molecular REI system-especially in an Eu(III) complex-is yet to be reported. Therefore, performing SHB studies in REI-based molecular systems to elucidate a light-mediated contol over nuclear spin states is a starting point towards the realization of REI molecules-based photonic quantum materials 3,35 . ...
The success of the emerging field of solid-state optical quantum information processing (QIP) critically depends on the access to resonant optical materials. Rare-earth ion (REI)-based molecular systems, whose quantum properties could be tuned taking advantage of molecular engineering strategies, are one of the systems actively pursued for the implementation of QIP schemes. Herein, we demonstrate the efficient polarization of ground-state nuclear spins—a fundamental requirement for all-optical spin initialization and addressing—in a binuclear Eu(III) complex, featuring inhomogeneously broadened 5D0 → 7F0 optical transition. At 1.4 K, long-lived spectral holes have been burnt in the transition: homogeneous linewidth (Γh) = 22 ± 1 MHz, which translates as optical coherence lifetime (T2opt) = 14.5 ± 0.7 ns, and ground-state spin population lifetime (T1spin) = 1.6 ± 0.4 s have been obtained. The results presented in this study could be a progressive step towards the realization of molecule-based coherent light-spin QIP interfaces. Rare-earth ion (REI)-doped systems are well suited for realising coherent light-spin interfaces, but demonstrations of spectral hole burning (SHB) in optical transitions of REI-based systems have been so far limited to REIs dispersed in matrices. Here, the authors report on transient SHB in a binuclear Eu(III) complex.
... The syn-syn bond between them, characteristic of carboxylate-based metal complex, yields a short intermolecular separation of 2.68(2) Å [21,22]. This provides a nearly-ideal realization of an isolated two-qubit system [31][32][33]. It is worth noting that, despite the specificity of the present LDMC, this behavior is actually encountered in a broad range of metal complexes, thanks to their large intramolecular interaction energy, as compared to the intermolecular ones [22,[24][25][26][31][32][33][34]. ...
... This provides a nearly-ideal realization of an isolated two-qubit system [31][32][33]. It is worth noting that, despite the specificity of the present LDMC, this behavior is actually encountered in a broad range of metal complexes, thanks to their large intramolecular interaction energy, as compared to the intermolecular ones [22,[24][25][26][31][32][33][34]. The energy of the two coupled qubit system is provided by the following Hamiltonian: ...
... In this regard, a charging and discharging steps of a major cycle can be presented for this QB, as sketched in Fig. 1b: (I) an external stimulus (e.g., electromagnetic field pulses [32,33], or pressure [25,29]), lowers the degree of quantum discord of the system, drives it to the triplet state subspace (more specifically the state |↓↓ ), discharging the battery by consuming the stored work [13,14,18,44]; (II) removing the stimulus, the material, in thermal equilibrium with a reservoir, returns to the singlet ground-state by increasing the population of |β − , charging the battery (see top figure of the chargingdischarging process). It is worth noting that these two steps belong to a major cycle and further discussions will be presented elsewhere. ...
The study of advanced quantum devices for energy storage has attracted the attention of the scientific community in the past few years. Although several theoretical progresses have been achieved recently, experimental proposals of platforms operating as quantum batteries under ambient conditions are still lacking. In this context, this work presents a feasible realization of a quantum battery in a carboxylate-based metal complex, which can store a finite amount of extractable work under the form of quantum discord at room temperature, and recharge by thermalization with a reservoir. Moreover, the stored work can be evaluated through non-destructive measurements of the compound's magnetic susceptibility. These results pave the way for the development of enhanced energy storage platforms through material engineering.
