While molecular spin qubits (MSQs) are a promising platform for quantum computing, read-out has been largely limited to electron paramagnetic resonance which is often slow and requires a global system drive. Moreover, because one prerequisite for the Elzerman and Pauli spin blockade readout mechanisms typical of semiconductor spin qubits is tunneling of electrons between sites, these read-out modalities are unavailable in MSQs. Here, we theoretically demonstrate electrical read-out of entangled MSQs via driven many-electron spin unpolarized currents. In particular, using a time-dependent density matrix renormalization group approach we simulate a maximally entangled MSQ pair between two electronic leads. Driving itinerant electrons between the two leads, we find that the conductance is greater when the MSQs are in the entangled singlet state as compared to the entangled triplet state. This contrast in conductance is enhanced when the electronic density of states at the Fermi energy is large and for narrow bandwidth. Our results are readily applicable to molecules supramolecularly functionalizing semiconductors with relatively flat bands such as single-wall carbon nanotubes under a magnetic field.
While molecular spin qubits (MSQs) are a promising platform for quantum computing, read-out has been largely limited to electron paramagnetic resonance which is often slow and requires a global system drive. Moreover, because one prerequisite for the Elzerman and Pauli spin blockade readout mechanisms typical of semiconductor spin qubits is tunneling of electrons between sites, these read-out modalities are unavailable in MSQs. Here, we theoretically demonstrate electrical read-out of entangled MSQs via driven many-electron spin unpolarized currents. In particular, using a time-dependent density matrix renormalization group approach we simulate a maximally entangled MSQ pair between two electronic leads. Driving itinerant electrons between the two leads, we find that the conductance is greater when the MSQs are in the entangled singlet state as compared to the entangled triplet state. This contrast in conductance is enhanced when the electronic density of states at the Fermi energy is large and for narrow bandwidth. Our results are readily applicable to molecules supramolecularly functionalizing semiconductors with relatively flat bands such as single-wall carbon nanotubes under a magnetic field.
We theoretically study how a scattered electron can entangle molecular spin qubits (MSQs). This requires solving the inelastic transport of a single electron through a scattering region described by a tight-binding interacting Hamiltonian. We accomplish this using a Green's-function solution. We can model realistic physical implementations of MSQs by parametrizing the tight-binding Hamiltonian with first-principles descriptions of magnetic anisotropy and exchange interactions. We find that, for two-MSQ systems with inversion symmetry, projective measurement of the spin degree of freedom of the scattered electron offers probabilistic control of the degree of entanglement between the MSQs.
Electron spins confined in semiconductor quantum dots are emerging as a promising system to study quantum information science and to perform sensitive metrology. Their weak interaction with the environment leads to long coherence times and robust storage for quantum information, and the intrinsic tunability of semiconductors allows for controllable operations, initialization, and readout of their quantum state. These spin qubits are also promising candidates for the building block for a scalable quantum information processor due to their prospects for scalability and miniaturization. owever, several obstacles limit the performance of quantum information experiments in these systems. For example, the weak coupling to the environment makes inter-qubit operations challenging, and a fluctuating nuclear magnetic field limits the performance of single-qubit operations.\n\n\n\nThe focus of this thesis will be several experiments which address some of the outstanding problems in semiconductor spin qubits, in particular, singlet-triplet (S-T0) qubits. We use these qubits to probe both the electric field and magnetic field noise that limit the performance of these qubits. The magnetic noise bath is probed with high bandwidth and precision using novel techniques borrowed from the field of Hamiltonian learning, which are effective due to the rapid control and readout available in S-T0 qubits. These findings allow us to effectively undo the undesired effects of the fluctuating nuclear magnetic field by tracking them in real-time, and we demonstrate a 30-fold improvement in the coherence time T2*.\n\n\n\nWe probe the voltage noise environment of the qubit using coherent qubit oscillations, which is partially enabled by control of the nuclear magnetic field. We find that the voltage noise bath is frequency- dependent, even at frequencies as high as 1MHz, and it shows surprising and, as of yet, unexplained temperature dependence. We leverage this knowledge of the voltage noise environment, the nuclear magnetic field control, as well as new techniques for calibrated measurement of the density matrix in a singlet-triplet qubit to entangle two adjacent single-triplet qubits. We fully characterize the generated entangled states and prove that they are, indeed, entangled.\n\n\n\nThis work opens new opportunities to use qubits as sensors for improved metrological capabilities, as well as for improved quantum information processing. The singlet-triplet qubit is unique in that it can be used to probe two fundamentally different noise baths, which are important for a large variety of solid state qubits. More specifically, this work establishes the singlet-triplet qubit as a viable candidate for the building block of a scalable quantum information processor.
We review the progress made in integrating magnetic molecules containing transition metal ions into nanoelectronic solid-state devices and using them as molecular spin qubits. Molecular spin qubits offer numerous advantages over other material platforms, such as being inherently quantum systems with discrete energy levels, having a rich variety of possible chemical designs, and being synthesizable in large quantities with atomic precision. However, the integration of magnetic molecules into practical and scalable molecular spin qubit devices (MSQDs) that offer initialization, coherent control, and readout of quantum spin states remains one of the major bottlenecks on the way toward applications of these systems in quantum computing technologies. We discuss the evolution of the field of MSQDs and review the first successful implementation of essential qubit operations in a single-molecule transistor based on a TbPc 2 molecule. Further development has been achieved through the merging of molecular electronics with the circuit quantum electrodynamics (cQED) approach where molecular spin states can be manipulated by the microwave frequency photons confined in a superconducting waveguide resonator. We discuss examples of such hybrid devices operating via coupling of a superconducting resonator to large spin ensembles, such as bulk samples and thin films. We also review a possible architecture for single-molecule cQED devices and the potential advantages that it offers. Then, we highlight the possibility and benefits of the optical initialization and readout of molecular spin states. This approach has been realized by using an optical pumping technique for the initialization and changes in photoluminescence for the readout of large molecular spin ensembles coupled to a superconducting resonator. The field of MSQDs is highly interdisciplinary, bringing together progress in synthetic chemistry, molecular electronics, cQED, and optical measurements. While it is still in its infancy, there are promising theoretical designs and encouraging proof-of-concept experiments, and we discuss several proposed device architectures that are eagerly awaiting experimental realization. Advances in hybrid MSQDs will open horizons for quantum technologies.
One-dimensional (1D) magnetic systems offer rich phenomena in the quantum limit, proving more chemically accessible than zero-dimensional or higher-dimensional frameworks. Single-walled carbon nanotubes (SWCNT) have recently been used to encapsulate trimetric nickel(II) acetylacetonate [Nanoscale, 2019, 11, 10615–10621]. Here, we investigate the magnetization on spin chains based on nickel trimers by Matrix Product State (MPS) simulations. Our findings reveal plateaus in the exchange/magnetic-field phase diagram for three coupling configurations, showcasing effective dimeric and trimeric spin-ordering with similar or staggered entanglement across chains. These ordered states allow the qubit-like tuning of specific local magnetic moments, exhibiting disengagement or uniform coupling in entanglement plateaus. This behavior is consistent with the experimental transition from frustrated (3D) to non-frustrated (1D) molecules, corresponding to large and smaller SWCNT diameters. Our study offers insights into the potential of 1D-confined trimers for quantum computation, extending beyond the confinement of trimetric nickel-based molecules in one dimension.
The Kondo effect of a single magnetic impurity embedded in the Lieb lattice is studied by the numerical renormalization group. When the band flatness is present in the local density of states at the impurity site, it quenches the participation of all dispersive electrons in the Kondo singlet formation and reduces the many-body Kondo problem to a two-electron molecular Kondo problem. A quantum entanglement of two spins, which is the two-electron molecular analog of the many-body Kondo singlet, is stable at low temperature, and the impurity contributions to thermodynamical and dynamical quantities are qualitatively different from that obtained in the many-body Kondo effect. The conditions for existence of the molecular Kondo effect in narrow band systems are also presented.
The entanglement of flying qubits with static qubits in the solid state is important in the development of quantum computing. It has recently been shown theoretically that the spin-dependent scattering of a propagating electron from a bound electron is sufficient to give full entanglement between the qubits embodied in their respective spins [J. H. Jefferson et al., Europhys. Lett. 74, 764 (2006); D. Gunlycke et al., J. Phys.: Condens. Matter 18, S851 (2006)]. In this paper a generalized, real-space Anderson model is introduced for a quasi-one-dimensional structure consisting of a binding site coupled to ideal leads. Degeneracy of both the binding site and the leads is incorporated to represent, for example, conduction band degeneracy in carbon nanotubes. The model is used to calculate the spin-dependent scattering behavior and resultant static-flying qubit entanglement created by the scattering process. Degeneracy (and more generally, multiplicity) in the binding site gives rise to inelastic scattering processes. In the elastic scattering regime, a degenerate binding site gives rise to antiresonant structures in the transmission spectrum. Additional degeneracy in the leads restricts this effect to the second set of leads, raising the possibility of spin filtration, though this is eliminated in the inelastic scattering regime. Degeneracy in the binding site also gives rise to multiple resonances in transmission that will improve the probability of obtaining entangled pairs relative to the nondegenerate case. This effect is maximized when the components of the degenerate binding site are symmetrically coupled to the leads.