arXiv subjects

Alexander McDonald

Publications and source records attributed to Alexander McDonald.

18 recordsLinked to original sources

arXiv2026

Measurement-induced state transitions in multi-qubit transmon processors

Dispersive readout of the transmon qubit in circuit QED is known to lose its quantum non-demolition character at small to moderate measurement drive amplitudes. This phenomenon is understood to originate from Laundau-Zener transitions at accidental multi-photon resonances, where $n$ drive photons can promote the transmon by $m$ levels. This interpretation has been shown to be in agreement with experiments characterizing the dispersive readout of a single transmon. The impact of these measurement-induced state transition (MIST) of a transmon embedded in a multi-qubit chip, however, remains largely unexplored. Here, we show that the presence of other components, such as qubits and couplers, can affect the MIST threshold of a measured transmon. To arrive at these results, we present a general method to characterize measurement-induced transition when the qubit under readout is coupled to other circuit elements, a ubiquitous situation in circuit QED-based quantum processors. As an example, we consider the case of two transmon qubits, and we show that the spectator qubit can be impacted by the measurement-induced transition of the readout qubit and, conversely, that the presence of the spectator qubit can lower the MIST threshold of the readout qubit. Finally, we explore how adding a coupler mode between the two qubits further modifies these effects.

quant-ph↗

arXiv2026

Measurement-induced state transitions across the fluxonium qubit landscape

Understanding the mechanisms that limit high-fidelity readout in circuit quantum electrodynamics is essential for its optimization. Multi-photon resonances are understood to be a limiting factor, causing population transfer from the computational states to higher-energy states under drive. This effect, known as measurement-induced state transitions, has been extensively studied for the transmon qubit. While this exploration has begun for the fluxonium qubit, a systematic study of this effect is lacking. Here, we bridge this gap by theoretically studying measurement-induced state transitions in the fluxonium qubit over a wide range of parameters, comprising essentially all experimentally explored ranges. We find that lighter fluxoniums are less susceptible to these state transitions when compared to their heavier counterparts. We attribute this effect to the combination of lower density of multi-photon resonances, a smaller requisite coupling for a given dispersive shift, and a more harmonic-like structure of the charge operator. We confirm the validity of our analysis by performing time-dependent readout simulations. Finally, we consider the impact of the superinductor's array modes on measurement-induced state transitions over a large range of parameters.

quant-ph↗

arXiv2025

Exponentially enhanced sensing through nonreciprocal light propagation

Non-reciprocity is a key resource for pushing the performance of photonic devices beyond the fundamental limits imposed by Lorentz reciprocity. Here, we report on the realization of an optical sensor where non-reciprocal light propagation allows detecting small perturbations with a signal-to-noise ratio (SNR) that scales exponentially with system size. Our approach is based on encoding two Hatano-Nelson (HN) chains, which is equivalent to the bosonic Kitaev model, within the resonant modes of an electro-optics frequency comb. Non-reciprocal light propagation in the frequency domain is realized through simultaneous phase and amplitude modulation of the circulating field inside the optical fiber cavity. We demonstrate the sensing of a small modulating tone coupling the two HN chains with a SNR that scales exponentially with the lattice size, formed from up to 70 frequency modes per chain. Our results open a new paradigm in non-Hermitian sensing, with potential applications in remote sensing including the optical readout of superconducting circuits.

physics.optics↗

arXiv2025

Non-perturbative switching rates in bistable open quantum systems: from driven Kerr oscillators to dissipative cat qubits

In this work, we use path integral techniques to predict the switching rate in a single-mode bistable open quantum system. While analytical expressions are well-known to be accessible for systems subject to Gaussian noise obeying classical detailed balance, we generalize this approach to a class of quantum systems, those which satisfy the recently-introduced hidden time-reversal symmetry [1]. In particular, in the context of quantum computing, we deliver precise estimates of bit-flip error rates in cat-qubit architectures, circumventing the need for costly numerical simulations. Our results open new avenues for exploring switching phenomena in multistable single- and many-body open quantum systems.

quant-ph↗

arXiv2024

Robustness of longitudinal transmon readout to ionization

Multi-photon processes deteriorate the quantum non-demolition (QND) character of the dispersive readout in circuit QED, causing readout to lag behind single and two-qubit gates, in both speed and fidelity. Alternative methods such as the longitudinal readout have been proposed, however, it is unknown to what extent multi-photon processes hinder this approach. Here we investigate the QND character of the longitudinal readout of the transmon qubit. We show that the deleterious effects that arise due to multi-photon transitions can be heavily suppressed with detuning, owing to the fact that the longitudinal interaction strength is independent of the transmon-resonator detuning. We consider the effect of circuit disorder, the selection rules that act on the transmon, as well as the description of longitudinal readout in the classical limit of the transmon to show qualitatively that longitudinal readout is robust. We show that fast, high-fidelity QND readout of transmon qubits is possible with longitudinal coupling.

quant-ph↗

arXiv2024

High-fidelity gates in a transmon using bath engineering for passive leakage reset

Leakage, the occupation of any state not used in the computation, is one of the of the most devastating errors in quantum error correction. Transmons, the most common superconducting qubits, are weakly anharmonic multilevel systems, and are thus prone to this type of error. Here we demonstrate a device which reduces the lifetimes of the leakage states in the transmon by three orders of magnitude, while protecting the qubit lifetime and the single-qubit gate fidelties. To do this we attach a qubit through an on-chip seventh-order Chebyshev filter to a cold resistor. The filter is engineered such that the leakage transitions are in its passband, while the qubit transition is in its stopband. Dissipation through the filter reduces the lifetime of the transmon's $f$ state, the lowest energy leakage state, by three orders of magnitude to 33 ns, while simultaneously keeping the qubit lifetime to greater than 100 $\mu$s. Even though the $f$ state is transiently populated during a single qubit gate, no negative effect of the filter is detected with errors per gate approaching 1e-4. Modelling the filter as coupled linear harmonic oscillators, our theoretical analysis of the device corroborate our experimental findings. This leakage reduction unit turns leakage errors into errors within the qubit subspace that are correctable with traditional quantum error correction. We demonstrate the operation of the filter as leakage reduction unit in a mock-up of a single-qubit quantum error correcting cycle, showing that the filter increases the seepage rate back to the qubit subspace.

quant-ph↗

arXiv2024

Measurement-Induced Transmon Ionization

Despite the high measurement fidelity that can now be reached, the dispersive qubit readout of circuit quantum electrodynamics is plagued by a loss of its quantum nondemolition character and a decrease in fidelity with increased measurement strength. In this work, we elucidate the nature of this dynamical process, which we refer to as transmon ionization. We develop a comprehensive framework which provides a physical picture of the origin of transmon ionization. This framework consists of three complementary levels of descriptions: a fully quantized transmon-resonator model, a semiclassical model where the resonator is treated as a classical drive on the transmon, and a fully classical model. Crucially, all three approaches preserve the full cosine potential of the transmon and lead to similar predictions. This framework identifies the multiphoton resonances responsible for transmon ionization. It also allows one to efficiently compute numerical estimates of the photon number threshold for ionization, which are in remarkable agreement with recent experimental results. The tools developed within this work are both conceptually and computationally simple, and we expect them to become an integral part of the theoretical underpinning of all circuit QED experiments.

quant-ph↗

arXiv2023

Fast Flux-Activated Leakage Reduction for Superconducting Quantum Circuits

Quantum computers will require quantum error correction to reach the low error rates necessary for solving problems that surpass the capabilities of conventional computers. One of the dominant errors limiting the performance of quantum error correction codes across multiple technology platforms is leakage out of the computational subspace arising from the multi-level structure of qubit implementations. Here, we present a resource-efficient universal leakage reduction unit for superconducting qubits using parametric flux modulation. This operation removes leakage down to our measurement accuracy of $7\cdot 10^{-4}$ in approximately $50\, \mathrm{ns}$ with a low error of $2.5(1)\cdot 10^{-3}$ on the computational subspace, thereby reaching durations and fidelities comparable to those of single-qubit gates. We demonstrate that using the leakage reduction unit in repeated weight-two stabilizer measurements reduces the total number of detected errors in a scalable fashion to close to what can be achieved using leakage-rejection methods which do not scale. Our approach does neither require additional control electronics nor on-chip components and is applicable to both auxiliary and data qubits. These benefits make our method particularly attractive for mitigating leakage in large-scale quantum error correction circuits, a crucial requirement for the practical implementation of fault-tolerant quantum computation.

quant-ph↗

arXiv2023

Inhomogeneous Quantum Quenches of Conformal Field Theory with Boundaries

We develop a method to calculate generic time-dependent correlation functions for inhomogeneous quantum quenches in (1+1)-dimensional conformal field theory (CFT) induced by sudden Hamiltonian deformations that modulate the energy density inhomogeneously. Our work particularly focuses on the effects of spatial boundaries, which have remained unresolved by previous analytical methods. For generic post-quench Hamiltonian, we develop a generic method to calculate the correlations by mirroring the system, which otherwise are Euclidean path integrals in complicated spacetime geometries difficult to calculate. On the other hand, for a special class of inhomogeneous post-quench Hamiltonians, including the M\"obius and sine-square-deformation Hamiltonians, we show that the quantum quenches exhibit simple boundary effects calculable from Euclidean path integrals in a straightforward strip spacetime geometry. Applying our method to the time evolution of entanglement entropy, we find that for generic cases, the entanglement entropy shows discontinuities (shockwave fronts) propagating from the boundaries.In contrast, such discontinuities are absent in cases with simple boundary effects. We verify that our generic CFT formula matches well with numerical calculations from free fermion tight-binding models for various quench scenarios.

cond-mat.stat-mech↗

arXiv2023

Anomalously large relaxation times in dissipative lattice models beyond the non-Hermitian skin effect

We show for generic quantum non-Hermitian tight-binding models that relaxation timescales of local observables are not controlled by the localization length $ξ_{\rm loc}$ associated with the non-Hermitian skin effect, contrary to popular belief. Instead, interference between eigenvectors effectively makes the extreme localization of modes largely irrelevant to relaxation; this is ultimately a consequence of causality and locality. Focusing on the paradigmatic Hatano-Nelson model, we demonstrate that there exists instead a much larger length scale $ξ_{\rm prop}$ which controls the rate of decay towards the steady state. Further, varying $ξ_{\rm prop}$ can lead to anomalously large relaxation times that scale with system size, or to the expected behavior where the dissipative gap correctly predicts the rate of decay. Our work highlights an important aspect of the non-Hermitian skin effect: the exceptional sensitivity to boundary conditions here necessarily takes a finite amount of time to manifest itself.

quant-ph↗

arXiv2023

Entanglement phase transition due to reciprocity breaking without measurement or post-selection

Despite its fully unitary dynamics, the bosonic Kitaev chain (BKC) displays key hallmarks of non-Hermitian physics including non-reciprocal transport and the non-Hermitian skin effect. Here we demonstrate another remarkable phenomena: the existence of an entanglement phase transition (EPT) in a variant of the BKC that occurs as a function of a Hamiltonian parameter g, and which coincides with a transition from a reciprocal to a non-reciprocal phase. As g is reduced below a critical value, the post-quench entanglement entropy of a subsystem of size l goes from a volume-law phase where it scales as l to a super-volume law phase where it scales like lN with N the total system size. This EPT occurs for a system undergoing purely unitary evolution and does not involve measurements, post-selection, disorder or dissipation. We derive analytically the entanglement entropy out of and at the critical point for the $l=1$ and $l/N \ll 1$ case.

quant-ph↗

arXiv2023

Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations

The connections between standard theoretical tools used to study open quantum systems can sometimes seem opaque. Whether it is a Lindblad master equation, the equation of motion for the Wigner function or a dissipative Keldysh action, features evident in one formalism are often masked in another. Here, we reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. This symmetry can then be used to easily diagonalize these models, and provides a intuitive way to demonstrate the separation of dissipation and fluctations in linear systems. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix in the eigenbasis of the third-quantized superoperators we introduce. The field-theory representation of the time-evolution operator in this basis is then the Keldysh path integral. To highlight the utility of our approach, we apply our version of third quantization to a dissipative non-linear oscillator, and use it to obtain new exact results.

quant-ph↗

arXiv2022

Non-equilibrium stationary states of quantum non-Hermitian lattice models

We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner by constructing an appropriate open quantum system. We focus on the quantum steady states of such models for both fermionic and bosonic systems. Surprisingly, key features and spatial structures in the steady state cannot be simply understood from the non-Hermitian Hamiltonian alone. Using the 1D Hatano-Nelson model as a paradigmatic example, we show that the steady state has a marked sensitivity to boundary conditions. This dependence however is qualitatively and quantitatively distinct from the non-Hermitian skin effect, and has no simple connection to non-Hermitian topology. Further, particle statistics play an unexpected role: the steady-state density profile is dramatically different for fermions versus bosons. Our work highlights the key role of fluctuations in quantum realizations of non-Hermitian dynamics, and provides a starting point for future work on engineered steady states of open quantum systems.

quant-ph↗

arXiv2021

Intrinsic mechanisms for drive-dependent Purcell decay in superconducting quantum circuits

We develop a new approach to understanding intrinsic mechanisms that cause the $T_1$-decay rate of a multi-level superconducting qubit to depend on the photonic population of a coupled, detuned cavity. Our method yields simple analytic expressions for both the coherently driven or thermally excited cases which are in good agreement with full master equation numerics, and also facilitates direct physical intuition. It also predicts several new phenomena. In particular, we find that in a wide range of settings, the cavity-qubit detuning controls whether a non-zero photonic population increases or decreases qubit Purcell decay. Our method combines insights from a Keldysh treatment of the system, and Lindblad perturbation theory.

quant-ph↗

arXiv2021

A low-loss ferrite circulator as a tunable chiral quantum system

Ferrite microwave circulators allow one to control the directional flow of microwave signals and noise, and thus play a crucial role in present-day superconducting quantum technology. They are typically viewed as a black-box, and their internal structure is not specified, let alone used as a resource. In this work, we demonstrate a low-loss waveguide circulator constructed with single-crystalline yttrium iron garnet (YIG) in a 3D cavity, and analyze it as a multi-mode hybrid quantum system with coupled photonic and magnonic excitations. We show the coherent coupling of its chiral internal modes with integrated superconducting niobium cavities, and how this enables tunable non-reciprocal interactions between the intra-cavity photons. We also probe experimentally the effective non-Hermitian dynamics of this system and its effective non-reciprocal eigenmodes. The device platform provides a test bed for implementing non-reciprocal interactions in open-system circuit QED.

quant-ph↗

arXiv2021

Exact solutions of interacting dissipative systems via weak symmetries

We demonstrate how the presence of continuous weak symmetry can be used to analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method can be viewed as implementing an exact, sector-dependent mean-field decoupling, or alternatively, as a kind of quantum-to-classical mapping. We focus on two canonical examples: a nonlinear bosonic mode subject to incoherent loss and pumping, and an inhomogeneous quantum Ising model with arbitrary connectivity and local dissipation. In both cases, we calculate and analyze the full dissipation spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.

quant-ph↗

arXiv2020

Exponentially-enhanced quantum sensing with non-Hermitian lattice dynamics

We study how unique features of non-Hermitian lattice systems can be harnessed to improve Hamiltonian parameter estimation in a fully quantum setting. While the so-called non-Hermitian skin effect does not provide any distinct advantage, alternate effects yield dramatic enhancements. We show that certain asymmetric non-Hermitian tight-binding models with a $\mathbb{Z}_2$ symmetry yield a pronounced sensing advantage: the quantum Fisher information per photon increases exponentially with system size. We find that these advantages persist in regimes where non-Markovian and non-perturbative effects become important. Our setup is directly compatible with a variety of quantum optical and superconducting circuit platforms, and already yields strong enhancements with as few as three lattice sites.

quant-ph↗

arXiv2018

Phase-dependent chiral transport and effective non-Hermitian dynamics in a bosonic Kitaev-Majorana chain

We study a 1D chain of non-interacting bosonic cavities which are subject to nearest-neighbour parametric driving. With a suitable choice of drive phases, this model is strongly analogous to the celebrated Kitaev chain model of a 1D p-wave superconductor. The system exhibits phase-dependent chirality: photons propagate and are amplified in a direction that is determined by the phase of the initial drive or excitation. Further, we find a drastic sensitivity to boundary conditions: for a range of parameters, the boundary-less system has only delocalized, dynamically unstable modes, while a finite open chain is described by localized, dynamically stable modes. While our model is described by a Hermitian Hamiltonian, we show that it has a surprising connection to non-Hermitian asymmetric-hopping models.

cond-mat.mes-hall↗