arXiv subjects

Silas Hoffman

Publications and source records attributed to Silas Hoffman.

At least 19 recordsLinked to original sources

arXiv2026

Spin singlets are useful

We evaluate the utility of the spin-zero manifold of an exchange-coupled array of $N$ spins for tasks in quantum computation and quantum simulation. Since pairs of electrons can be readily initialized into a product state of singlets in semiconducting quantum dot arrays, the full spin-zero manifold is available with exchange-only control, providing a Hilbert space of approximate dimension $2^N/(N/2)^{3/2}$, asymptotically close to the $2^N$ dimension of the full spin Hilbert space. Leveraging the spin-zero manifold enables larger computational space in a given array compared to traditional exchange-only control, in which spin arrays are organized into modular units of $n$ spins comprising $N/n$ encoded qubits, limiting to the exponentially smaller Hilbert dimension $2^{N/n}$. Here we focus on benchmarking metrics for this resource utilization by generalizing cross-entropy benchmarking, mirror benchmarking, and out-of-time-ordered correlators to this system. We show that operating in the spin-zero manifold can accelerate the realization of computational quantum advantage applications in semiconductor-based spin qubits.

quant-ph↗

arXiv2026

Voltage-tunable Josephson Junctions on Germanium Quantum Wells with in-situ Aluminum Contacts

Voltage-tunable Josephson junctions (VT-JJs) are an emerging element in superconducting quantum electronics with potential to expand the functionality of conventional designs. While VT-JJs are largely compatible with wafer-scale semiconductor processing, their integration into quantum circuits remains a challenge due to unmitigated semiconductor microwave loss. Here, a deep mesa etch process, wherein the epitaxial material is removed except the VT-JJ device, will facilitate the integration of VT-JJs with low-microwave-loss circuit elements by allowing these circuit elements to be placed directly on a low-loss substrate. A Germanium quantum well is grown by Molecular Beam Epitaxy (MBE) on a float zone silicon substrate with in-situ deposited aluminum contacts. This combination allows the formation of an oxide-free superconductor-semiconductor interface. The deep mesa etch process is optimized to produce a sidewall taper sufficient for continuous metal deposition from the substrate to the top of the mesa for electrostatic gate electrodes and interconnects. The fabricated Josephson junctions demonstrate gate-tunable supercurrents with a maximum critical current over 100 nA and critical-current normal-resistance product of $8.63~\mu V$. These results demonstrate a pathway toward improved integration of voltage-tunable superconducting circuit elements with quantum electronic building blocks such as couplers and qubits.

cond-mat.mes-hall↗

arXiv2026

Gate-dependent offset charge shifts and anharmonicity in gatemon qubits in the weak tunneling regime

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.

cond-mat.mes-hall↗

arXiv2026

Singlet-only always-on gapless exchange (SAGE) spin qubits: Charge noise effects and two-qubit gates

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.

cond-mat.mes-hall↗

arXiv2026

Using near-flat-band electrons for read-out of molecular spin qubit entangled states

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.

cond-mat.mes-hall↗

arXiv2025

Floquet Engineering Clock Transitions in Magnetic Molecules

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. Further, using second-order Van Vleck degenerate perturbation theory, we derived analytically an effective Hamiltonian, 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.

quant-ph↗

arXiv2025

Dominant spin-spin relaxation mechanism at clock transition of the $Ho_{x}Y_{1-x}W_{10}$ complex at different concentrations

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.

quant-ph↗

arXiv2025

Singlet-only Always-on Gapless Exchange Qubits with Baseband Control

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, for instance 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.

quant-ph↗

arXiv2025

Measurement-based Simulation of Geometric Gates in Topological Qubits on NISQ Devices

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 $S^{(\dagger)}$-gates and entangling two-qubit gates is shown using two-physical-qubit joint measurements alone, whilst partial phase rotations such as a $T^{(\dagger)}$-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.

quant-ph↗

arXiv2025

Simulated Non-Abelian Statistics of Majorana Zero Modes from a Kitaev Lattice

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 non-Abelian Berry's 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

quant-ph↗

arXiv2025

Resolving Andreev spin qubits in germanium-based Josephson junctions

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.

cond-mat.mes-hall↗

arXiv2025

Quantum dynamics of semiconductor quantum dot Josephson junctions

Josephson junctions constructed from superconductor-semiconductor-superconductor heterostructures have been used to realize a variety of voltage-tunable superconducting quantum devices, including qubits and parametric amplifiers. To date theoretical descriptions of these systems have been restricted to small quantum fluctuations of the junction phase, making them inapplicable to many experiments. In this work we relax this, employing a path-integral formulation where the phase quantum dynamics is obtained self-consistently from an underlying many-body formalism. Our method recovers previously-known results for small phase fluctuations, and predicts new effects outside of that limit: (i) system capacitances undergo a gate-voltage-dependent renormalization; and (ii) an additional charge offset appears for asymmetric junctions. Our main results can be summarized in terms of a single-particle Hamiltonian, which can be directly compared to that of an ordinary Josephson junction. This more general theory could be a first step towards designing new quantum devices that go qualitatively beyond voltage-tunable variants of previously-known circuits.

cond-mat.mes-hall↗

arXiv2024

Decoherence in Andreev spin qubits

We theoretically study the dephasing of an Andreev spin qubit (ASQ) due to electric and magnetic noise. Using a tight-binding model, we calculate the Andreev states formed in a Josephson junction where the link is a semiconductor with strong spin-orbit interaction. As a result of both the spin-orbit interaction and induced superconductivity, the local charge and spin of these states varies as a function of externally controllable parameters: the phase difference between the superconducting leads, an applied magnetic field, and filling of the underlying semiconductor. Concomitantly, coupling to fluctuations of the electric or magnetic environment will vary, which informs the rate of dephasing. We qualitatively predict the dependence of dephasing on the nature of the environment, magnetic field, phase difference between the junction, and filling of the semiconductor. Comparing the simulated electric- and magnetic-noise-induced dephasing rate to experiment suggests that the dominant source of noise is magnetic. Moreover, by appropriately tuning these external parameters, we find sweet-spots at which we predict an enhancement in ASQ coherence times.

cond-mat.mes-hall↗

arXiv2024

Simulating decoherence of two coupled spins using the generalized cluster correlation expansion

We simulate the coherence of two coupled electron spins interacting with a bath of nuclei using the generalized cluster correlation expansion (gCCE) 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 $T_2$ and $T_2^*$ 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.

quant-ph↗

arXiv2022

Demonstration of electron-nuclear decoupling at a spin clock transition

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 (CTs) 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 CT, 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 $\textit{in silico}$. Meanwhile, the effective hyperfine interaction vanishes at the CT, resulting in electron-nuclear decoupling and an absence of quantum information leakage to the nuclear bath, providing opportunities to characterize other decoherence sources.

quant-ph↗

arXiv2022

Scattering solution of interacting Hamiltonian for electronic control of molecular spin qubits

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.

quant-ph↗

arXiv2022

Superconducting Quantum Interference in Edge State Josephson Junctions

We study superconducting quantum interference in a Josephson junction linked via edge states in two-dimensional (2D) insulators. We consider two scenarios in which the 2D insulator is either a topological or a trivial insulator supporting one-dimensional (1D) helical or nonhelical edge states, respectively. In equilibrium, we find that the qualitative dependence of critical supercurrent on the flux through the junction is insensitive to the helical nature of the mediating states and can, therefore, not be used to verify the topological features of the underlying insulator. However, upon applying a finite voltage bias smaller than the superconducting gap to a relatively long junction, the finite-frequency interference pattern in the non-equilibrium transport current is qualitatively different for helical edge states as compared to nonhelical ones.

cond-mat.mes-hall↗

arXiv2021

Majorana Zero Modes Emulated in a Magnetic Molecule Chain

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.

cond-mat.mes-hall↗