Singlet-only always-on gapless exchange (SAGE) spin qubits are an alternative type of exchange-only (EO) qubits that encode a single qubit in the spins of four electrons located in four tunnel-coupled quantum dots. While conventional EO qubits are susceptible to local magnetic field gradients caused by local nuclear environments and g-factor variations, the SAGE qubit subspace is inherently protected from magnetic-gradient-induced Pauli errors by virtue of the singlet-only encoding, which is invariant under magnetic field gradients, and the always-on exchange couplings, which provide energetic leakage protection. However, the always-on operation simultaneously increases the qubit's sensitivity to charge noise. Here, starting from a Hubbard model describing the underlying electronic structure of the coupled quantum dots, we characterize the performance of SAGE qubits in the presence of 1/f charge noise that induces fluctuations in both the dot chemical potentials and the interdot tunnel couplings. We calculate SAGE idle coherence times and show that realistic CPMG-like pulse sequences can be used to significantly extend SAGE single-qubit coherence times for experimentally relevant charge noise strengths. We likewise study the fidelity of SAGE two-qubit gates in the presence of charge and magnetic noise and again propose a simple refocusing strategy to mitigate the noise, while increased ramp times of the entangling pulse suppress leakage into noncomputational states.

Gatemon qubits are based on a superconductor-quantum dot-superconductor (S-QD-S) junction which enables in situ electrostatic tuning via a gate electrode. For a single-channel QD this structure gives rise to two subgap Andreev bound states (ABSs), and generally leads to a richer quantum phase dynamics as compared to conventional transmons. In a recent work [Phys. Rev. B 111, 214503 (2025)] we derived the quantum phase dynamics from a many-body treatment which leads to an effective gate voltage-dependent Hamiltonian that self-consistently incorporates the phase quantization. It predicts (i) a renormalization of the junction's effective capacitance and (ii) the presence of gate voltage and occupation-dependent charge offsets in junctions with tunneling asymmetry. Here, we quantify the observable impact of these effects on the qubit's energy spectrum and anharmonicity, by studying the interplay of the two Andreev branches as a function of dot-gate voltages and junction transparencies. We show the relation of these predictions to simplified gatemon models and propose a protocol to experimentally detect the predicted charge offsets.

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 read-out 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 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 a 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 Floquet engineering of magnetic molecules via a time-periodic magnetic field that couples to the emergent total electronic spin of the metal center. By focusing on the low-lying energy levels using an S = 1 spin Hamiltonian containing the zero-field and Zeeman terms, we demonstrate their continuous tunability under the Floquet field. Remarkably, under the action of linearly polarized Floquet controls, the energy levels of a clock transition qubit retain their stability against variations in an external static magnetic field. This property is closely linked to having a net-zero total Zeeman shift, which results from both static and effective dynamical contributions. Furthermore, using second-order Van Vleck degenerate perturbation theory, we derived an effective Hamiltonian analytically, which explicitly shows the dependence of the renormalized zero-field tensor on the driving field. Based on our theoretical predictions, experimentalists will be able to dynamically tune qubit energy gaps to values that are useful in their specific laboratory settings, while retaining the spin decoherence suppressing effect of maintaining a clock transition.

Spin decoherence poses a significant challenge in molecular magnets, with the nuclear spin bath serving as a prominent source. Intriguingly, spin qubits at the clock transition exhibit remarkable insensitivity to the surrounding nuclear spins. Recent experimental studies have unveiled a correlation between the decoherence time and the density of spin qubits, prompting our investigation into the contribution of the qubit bath to spin decoherence. In this paper, we present a comprehensive theoretical analysis of a few S=1 spin qubits, focusing on their interaction at the clock transition. Employing the exact diagonalization and the cluster correlation expansion (CCE) method, we simulate the dynamics of spin decoherence while varying the density of the qubit bath. To ensure the realism of our simulations, we incorporate structural and energetic parameters derived from previous studies on the HoW10 crystal. Our findings indicate that when the energy mismatch between the energy splittings of two qubits exceeds their interaction strength, they can become effectively insensitive to each other, offering an explanation for the absence of observed changes in the T2 time during experiments with lower qubit densities. Understanding the role of qubit bath density in spin decoherence at the clock transition not only advances our knowledge of decoherence mechanisms but also provides insights for the development of strategies to protect coherence in molecular magnets and other quantum systems. By optimizing the density of spin qubits, we can enhance the coherence properties and pave the way for improved performance of quantum devices. Overall, this study offers valuable insights into the relationship between qubit bath density and spin decoherence at the clock transition, contributing to the broader understanding and control of quantum systems in molecular magnets.

While the adiabatic exchange of Majorana zero modes (MZMs) enables a non-universal set of geometrically protected gates, realising an experimental implementation of MZM braiding remains challenging. In an alternative proposal, charge-parity measurement of two neighboring MZMs supports braiding by teleportation. Moreover, owing to the lack of definitive evidence of MZMs in semiconducting systems, there have been several simulations of MZMs on NISQ devices which more naturally lend themselves to braiding. In this work, measurement-based braiding about MZM Y-junctions are simulated by multi-qubit Pauli-parity measurements of a logical qubit. Logical single-qubit geometric S^(†)-gates and entangling two-qubit gates is shown using two-physical-qubit joint measurements alone, whilst partial phase rotations such as a T^(†)-gates require at least one three-qubit joint measurement. These relatively small scale circuits offer both novel measurement-based geometric gates as well as a measurement-based demonstration of quantum Hamiltonian simulation.

We simulate the non-Abelian exchange of Majorana zero modes (MZMs) on a quantum computer. Rather than utilizing MZMs at the boundaries of quantum Ising chains, which are typically represented as nonlocal operators on a quantum computer, using a Kitaev lattice allows us to exploit a local representation of MZMs. We detail the protocol for braiding two and four MZMs in terms of a spin Hamiltonian, i.e. physical qubit Hamiltonian. Projecting this onto a subspace of states, we extract an effective Hamiltonian which drives a nonAbelian Berry phase. Using several approximations, we construct a set of gates which mimics this accumulation of non-Abelian phase and process this construction on a quantum computer. For two and four MZMs, we realize braiding fidelities of approximately 85 and 47%, respectively.

While the adiabatic exchange of Majorana zero modes (MZMs) enables a nonuniversal set of geometrically protected gates, realizing an experimental implementation of MZM braiding remains challenging. In an alternative proposal, charge-parity measurement of two neighboring MZMs supports braiding by teleportation. Moreover, owing to the lack of definitive evidence of MZMs in semiconducting systems, there have been several simulations of MZMs on noisy intermediate-scale quantum devices which more naturally lend themselves to braiding. In this work, measurement-based braiding about MZM Y junctions is simulated by multiqubit parity measurements of a logical qubit. Logical single-qubit geometric S(dagger) and entangling two-qubit braiding operations are shown using two-physical-qubit joint measurements alone, while T (dagger) gates corresponding to a kind of partial-braiding operation require at least one three-qubit joint measurement. These relatively small-scale circuits demonstrate potential applications of both measurement-based geometric gates and a measurementbased demonstration of quantum Hamiltonian simulation.

Andreev spin qubits (ASQs) are a promising platform for quantum information processing which benefit from both the small footprint of semiconducting spin qubits and the long range connectivity of superconducting qubits. While state-of-the-art experiments have developed ASQs in InAs nanowires, these realizations are coherence-time limited by nuclear magnetic noise which cannot be removed by isotopic purification. In Ge-based Josephson junctions, which can be isotopically purified, Andreev states have been experimentally observed but spin-resolved Andreev states remain elusive. Here, we theoretically demonstrate that the geometry of the Josephson junction can limit the qubit frequency to values below typical experimental temperatures and render the ASQ effectively invisible. ASQs could be experimentally resolved by judiciously choosing the geometry of the junction and filling of the underlying Ge. Our comprehensive study of ASQ frequency on in situ and ex situ experimentally controllable parameters provides design guidance of Ge-based Josephson junctions and paves the way towards realization of high-coherence ASQs.

We propose a singlet-only always-on gapless exchange (SAGE) spin qubit that encodes a single qubit in the spins of four electrons while allowing universal baseband control. While conventional exchange-only qubits suffer from magnetic-field-gradient-induced leakage and coherent errors due to local nuclear environments and variations in the g-factor, the SAGE qubit subspace is protected from coherent errors due to local magnetic field gradients, and leakage out of the computational subspace is energetically suppressed due to the exchange interactions between electrons being always on. Consequently, we find that when magnetic gradient noise dominates over charge noise, coherence times and single-qubit gate infidelities of the SAGE qubit improve by an order of magnitude compared to conventional exchange-only qubits. Moreover, using realistic parameters, two-qubit gates can be performed with a single interqubit exchange pulse with times comparable in duration to conventional exchange-only qubits but with a significantly simplified pulse sequence.

We simulate the coherence of two coupled electron spins interacting with a bath of nuclei using the generalized cluster correlation expansion method. An exchange interaction between the electrons facilitates a family of entangling gates that can be spoiled by nuclear-induced dephasing. Consequently, we study the dephasing of the coherent two-electron system by characterizing the T2 and T2* of the two-electron reduced density matrix for various system parameters in the range mimicking magnetic molecules, including magnetic field strength and orientation, exchange interaction strength, distance between the two spins, minimum distance between electron and nuclei and between nuclei, and nuclei density. We find the optimal regime for each parameter in which the coherence time is maximized and provide a physical understanding of it.

Spin superfluids enable long-distance spin transport through classical ferromagnets by developing topologically stable magnetic textures. For small spins at low dimensions, however, the topological protection suffers from strong quantum fluctuations. We study the remanence of spin superfluidity inherited from the classical magnet by considering the two-terminal spin transport through a finite spin-1/2 magnetic chain with planar exchange. By fermionizing the system, we recast the spin-transport problem in terms of quasiparticle transmission through a superconducting region. We show that the topological underpinnings of a semiclassical spin superfluid relate to the topological superconductivity in the fermionic representation. In particular, we find an efficient spin transmission through the magnetic region of a characteristic resonant length, which can be related to the properties of the boundary Majorana zero modes.

The ability to design quantum systems that decouple from environmental noise sources is highly desirable for development of quantum technologies with optimal coherence. The chemical tunability of electronic states in magnetic molecules combined with advanced electron spin resonance techniques provides excellent opportunities to address this problem. Indeed, so-called clock transitions have been shown to protect molecular spin qubits from magnetic noise, giving rise to significantly enhanced coherence. Here we conduct a spectroscopic and computational investigation of this physics, focusing on the role of the nuclear bath. Away from the clock transition, linear coupling to the nuclear degrees of freedom causes a modulation and decay of electronic coherence, as quantified via electron spin echo signals generated experimentally and in silico. Meanwhile, the effective hyperfine interaction vanishes at the clock transition, resulting in electron-nuclear decoupling and an absence of quantum information leakage to the nuclear bath, providing opportunities to characterize other decoherence sources.

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 parameterizing the tight-binding Hamiltonian with first-principles descriptions of magnetic anisotropy and exchange interactions. We find that for two-MSQ systems with inversion symmetry, the spin degree of freedom of the scattered electron offers probabilistic control of the degree of entanglement between the MSQs.

We propose a logical qubit based on the Blume-Capel model: a higher spin generalization of the Ising chain and which allows for an on-site anisotropy preserving rotational invariance around the Ising axis. We show that such a spin-3/2 Blume-Capel model can also support localized Majorana bound states at the ends of the chain. Inspired by known braiding protocols of these Majorana bound states, upon appropriate manipulation of the system parameters, we demonstrate a set of universal gate operations which act on qubits encoded in the doubly degenerate ground states of the chain.

Department of Physics, University of Florida, Gainesville, FL 32611, USA Quantum Theory Project, University of Florida, Gainesville, FL 32611, USA Center for Molecular Magnetic Quantum Materials National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL 32310, USA Department of Physics, Florida State University, Tallahassee, FL 32306, USA Instituto de Ciencia Molecular (ICMol), Universitat de València, Paterna, Spain Department of Chemistry, University of Florida, Gainesville, FL 32611, USA

Novel many-body and topological electronic phases can be created in assemblies of interacting spins coupled to a superconductor, such as one-dimensional topological superconductors with Majorana zero modes (MZMs) at their ends. Understanding and controlling interactions between spins and the emergent band structure of the in-gap Yu-Shiba-Rusinov (YSR) states they induce in a superconductor are fundamental for engineering such phases. Here, by precisely positioning magnetic adatoms with a scanning tunneling microscope (STM), we demonstrate both the tunability of exchange interaction between spins and precise control of the hybridization of YSR states they induce on the surface of a bismuth (Bi) thin film that is made superconducting with the proximity effect. In this platform, depending on the separation of spins, the interplay among Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, spin-orbit coupling, and surface magnetic anisotropy stabilizes different types of spin alignments. Using high-resolution STM spectroscopy at millikelvin temperatures, we probe these spin alignments through monitoring the spin-induced YSR states and their energy splitting. Such measurements also reveal a quantum phase transition between the ground states with different electron number parity for a pair of spins in a superconductor tuned by their separation. Experiments on larger assemblies show that spin-spin interactions can be mediated in a superconductor over long distances. Our results show that controlling hybridization of the YSR states in this platform provides the possibility of engineering the band structure of such states for creating topological phases.

We propose molecular magnets as a platform to emulate Majorana zero modes (MZMs). Using a quantum chemistry approach, we identify several candidates and predict a Co trimer to have sufficient properties to host MZMs. Parameters of the quantum spin Hamiltonian describing the three coupled magnetic centers are extracted from ab initio calculations. The low-energy subspace of this material realizes an effective anisotropic spin-1/2 chain. We show the presence of MZMs in this system and find that their response to electronic paramagnetic resonance provides an experimentally realizable signature.

Clock transitions (CTs) have been shown to protect qubits against various sources of decoherence. Here, we present a joint experimental and theoretical investigation of the decoupling of a central electron spin qubit from the surrounding nuclear spin bath by studying the so-called Electron Spin Echo Envelope Modulation (ESEEM) effect in the vicinity of a magnetic CT. Experimentally, ESEEM spectra are collected for a HoW$_{10}$ molecular spin qubit, and suppression of the modulation at a CT is clearly demonstrated. The effect is then simulated theoretically by exact quantum time evolution using a simple model Hamiltonian of a central electron spin with an avoided Zeeman crossing coupled to a finite number of nuclear bath spins. The results reproduce key experimental observations and reveal that, due to the quadratic energy dependence on magnetic field at the avoided crossing, fluctuations of the nuclear spin bath that couple linearly to the central spin do not affect its quantum dynamics at the CT. Consequently, hyperfine coupling effectively vanishes, leading to a complete suppression of ESEEM and electron-nuclear decoherence at the CT.

We theoretically study the spectrum induced by one and two magnetic impurities near the boundary of a one-dimensional nanowire in proximity to a conventional $s$-wave superconductor and extract the ground state magnetic configuration. We show that the energies of the subgap states, supported by the magnetic impurities, are strongly affected by the boundary for distances less than the superconducting coherence length. In particular, when the impurity is moved towards the boundary, multiple quantum phase transitions periodically occur in which the parity of the superconducting condensate oscillates between even and odd. We find that the magnetic ground state configuration of two magnetic impurities depends not only on the distance between them but also explicitly on their distance away from the boundary of the nanowire. As a consequence, the magnetic ground state can switch from ferromagnetic to antiferromagnetic while keeping the inter-impurity distance unaltered by simultaneously moving both impurities away from the boundary. The ground state magnetic configuration of two impurities is found analytically in the weak coupling regime and exactly for an arbitrary impurity coupling strength using numerical tight-binding simulations.