Welcome & Introductory Remarks

Truncation-Free Quantum Simulation of Lattice QED using Josephson Arrays

• Guy Pardo (Hebrew University)

Quantum simulation is one of the methods that have been proposed and used in practice to bypass computational challenges in the investigation of lattice gauge theories. While most of the proposals rely on truncating the infinite dimensional Hilbert spaces that these models feature, we propose a truncation-free method based on the exact analogy between the local Hilbert space of lattice QED and that of a Josephson junction. We provide several proposals, mostly semi-analog, arranged according to experimental difficulty. Our method can simulate a quasi-2D system of up to 2×N plaquettes, and we present an approximate method that can simulate the fully-2D theory, but is more demanding experimentally and not immediately feasible. This sets the ground for analog quantum simulation of lattice gauge theories with superconducting circuits, in a completely Hilbert space truncation-free procedure, for continuous gauge groups.

Hubbard Model Emulation with Superconducting Qubit Arrays: Entanglement, Vector Potentials, and Flat Bands

• Ilan Rosen (MIT)

Arrays of coupled superconducting qubits are a compelling platform for analog quantum simulations of solid-state matter as they natively emulate the Bose-Hubbard model while offering a high degree of control, fast operation rates, and site-resolved readout. Here, we discuss three recent experiments using a two-dimensional array of superconducting qubits. First, we prepare highly entangled many-body states with tunable energy. By increasing the energy of the states, we observe a transition from area-law to volume-law entanglement scaling. Second, we adopt a parametric coupling scheme to emulate an adjustable synthetic magnetic vector potential. We verify that spatial gradients of the vector potential create a synthetic magnetic field, and time variation creates a synthetic electric field. Third, we emulate a lattice with adjustable bandwidth and study localization dynamics in the transition from a dispersive to a flat band structure. We conclude by discussing opportunities and limitations for future simulators based on superconducting qubit arrays.

Designing a superconducting quantum circuit that realizes a symmetry protected topological phase

• Parmesh Pasnoori (University of Maryland)

Superconducting quantum circuits based on Josephson junction arrays have a strong potential in simulating many-body physics. Refined experimental control that has been achieved over superconducting quantum circuits may provide a promising path towards probing exotic phases arising from many-body effects. Among these, Symmetry Protected Topological (SPT) phases are of particular interest since they host protected zero energy modes (ZEM) localized at the edges of an open system. These modes may in turn possibly provide for protected qubits, i.e. immune to external disorder or circuitry, suitable for quantum computing. A prototypical example is the quantum sine-Gordon (QSG) model which exhibits two SPT phases which are dual to each other and are characterized by a doubly degenerate ground state which host exponentially localized phase accumulation at the edges. In this talk I will discuss the design of a superconducting quantum circuit whose low energy degrees of freedom are described by the QSG model. I will demonstrate that by tuning various parameters in the circuit one can probe the QSG model in both the semi-classical regime and the quantum regime. In the quantum regime, the phase accumulations in the two degenerate ground states give rise to super-currents that flow across the circuit elements localized at the two edges. These super-currents are associated with Majorana zero modes (MZM) which are protected by the symmetries of the system, indicating an intriguing possibility of realizing MZM in superconducting quantum circuits.

Discussion

Fluxonium readout prevented by coherent destruction of tunneling

• Alexandru Petrescu (Mines Paris)

Dispersive readout facilitates the quantum non-demolition measurement of the state of a superconducting qubit. It is expected that, as the drive amplitude is increased, readout fidelity increases. However, with increasing readout power qubit coherence can diminish, and unwanted measurement-induced transitions can occur. In this talk, we consider the sensitivity of readout to drive power in the fluxonium qubit. We observe that close to, but not at, half flux quantum, the measurement rate vanishes for a range of drive amplitudes. We attribute this disabling of the readout to a competition between the measurement and a coherent destruction of tunneling between the wells of the energy potential resulting in a localization of the computational manifold wavefunctions into the wells. We present experimental results and a theoretical model in quantitative agreement. Beyond the disabling of readout close to half flux quantum, our model captures the rate of the transitions between the first energy levels that is induced by the readout drive at half flux quantum. This research was supported by the ARO HiPS (contract No. W911-NF18-1-0146) and GASP (contract No. W911-NF23-10093) programs. Theory-experiment collaboration with: Joachim Cohen (Alice & Bob), Alexis Jouan, Réouven Assouly, Denis Bénâtre, Rémy Dassonneville, Antoine Essig, Jeremy Stevens, Audrey Bienfait, Benjamin Huard (ENS Lyon).

Hybrid Oscillator-Qubit Quantum Processors: Simulating Fermions, Bosons, and Gauge Fields

• Ella Crane (MIT)

We develop a hybrid oscillator-qubit processor framework for quantum simulation of strongly correlated fermions and bosons that avoids the boson-to-qubit mapping overhead encountered in qubit hardware. This framework gives exact decompositions of particle interactions such as density- density terms and gauge-invariant hopping, as well as approximate methods based on the Baker- Campbell Hausdorff formulas including the magnetic field term for the U(1) quantum link model in (2 + 1)D. We use this framework to show how to simulate dynamics using Trotterisation, perform ancilla-free partial error detection using Gauss’s law, measure non-local observables, estimate ground state energies using a oscillator-qubit variational quantum eigensolver as well as quantum signal processing, and we numerically study the influence of hardware errors in circuit QED experiments. To show the advantages over all-qubit hardware, we perform an end-to-end comparison of the gate complexity for the gauge-invariant hopping term and find an improvement of the asymptotic scaling with the boson number cutoff S from O(log(S)2) to O(1) in our framework as well as, for bosonic matter, a constant factor improvement of better than 104. We also find an improvement from O(log(S)) to O(1) for the U(1) magnetic field term. While our work focusses on an implementation in superconducting hardware, our framework can also be used in trapped ion, and neutral atom hardware. This work establishes digital quantum simulation with hybrid oscillator-qubit hardware as a viable and advantageous method for the study of qubit-boson models in materials science, chemistry, and high-energy physics.

Speeding up state preparation with adaptive quantum circuits

• Kevin Smith (IBM)

Adaptive quantum circuits, which combine local unitary gates, midcircuit measurements, and feedforward operations, have recently emerged as a promising avenue for efficient state preparation, particularly on near-term quantum devices limited to shallow-depth circuits. Matrix product states (MPS) comprise a significant class of many-body entangled states, efficiently describing the ground states of one-dimensional gapped local Hamiltonians and finding applications in a number of recent quantum algorithms. In this work, we demonstrate that a diverse class of MPS can be exactly prepared using constant-depth adaptive quantum circuits, outperforming theoretically optimal preparation with unitary circuits. We show that this class includes short- and long-ranged entangled MPS, symmetry-protected topological (SPT) and symmetry-broken states, MPS with finite Abelian, non-Abelian, and continuous symmetries, resource states for MBQC, and families of states with tunable correlation length. Moreover, we illustrate the utility of our framework for designing constant-depth sampling protocols, such as for random MPS or for generating MPS in a particular SPT phase. Altogether, this work demonstrates the immense promise of adaptive quantum circuits for efficiently preparing many-body entangled states on near-term devices while providing explicit algorithms that outperform known protocols to prepare an essential class of states.

Quantum electrodynamics of the Schmid-Bulgadaev dissipative quantum phase transition

• Roman Kuzmin (UW Madison)

Advances in circuit quantum electrodynamics (cQED) provide new ways to look at well-known condensed matter problems. I will present our results on the quantum phase transition between superconducting and insulating states of a single Josephson junction placed in an ohmic dissipative environment [1]. Employing the tools of cQED, we gain access to individual degrees of freedom of the dissipative environment, which we construct as a long section of a high-impedance transmission line. Such a setup allows us to study how a small Josephson junction scatters environmental photons as we tune the strength of the dissipation. The photon scattering rates and their scaling provide an unambiguous way to separate superconducting and insulating junction’s behavior, revealing the transition, observation of which has been a challenge. I will also briefly discuss other applications of high-impedance circuits for the simulation of quantum many-body physics. [1] R. Kuzmin, N. Mehta, N. Grabon, R. A. Mencia, A. Burshtein, M. Goldstein, V. E. Manucharyan. Observation of the Schmid-Bulgadaev dissipative quantum phase transition. Nature Physics 21, 132-136 (2025).

Discussion

Suppressing chaos with mixed superconducting qubit devices

• Gianluigi Catelani (Forschungszentrum Jülich & Technology Innovation Institute)

Suppressing chaos with mixed superconducting qubit devices In quantum information processing, a tension between two different tasks occurs: while qubits’ states can be preserved by isolating the qubits, quantum gates can be realized only through qubit-qubit interactions. In arrays of qubits, weak coupling leads to states being spatially localized and strong coupling to delocalized states [1]. We study the average energy level spacing and the relative entropy of the distribution of the level spacings (Kullback-Leibler divergence from Poisson and Gaussian Orthogonal Ensemble) to analyze the crossover between localized and delocalized (chaotic) regimes in linear arrays of superconducting qubits. We consider both transmons as well as capacitively shunted flux qubits, which enables us to tune the qubit anharmonicity. Arrays with uniform anharmonicity, comprising only transmons or flux qubits, display remarkably similar dependencies of level statistics on the coupling strength. In systems with alternating anharmonicity, so-called residual ZZ interactions can be suppressed [2]; at the same time, the localized regime is found to be more resilient to the increase in qubit-qubit coupling strength in comparison to arrays with a single qubit type. This result supports designing devices that incorporate different qubit types to achieve higher performances [3]. [1] C. Berke, E. Varvelis, S. Trebst, A. Altland, and D. P. DiVincenzo, Transmon platform for quantum computing challenged by chaotic fluctuations, Nat. Commun. 13, 2495 (2022). [2] J. Ku, X. Xu, M. Brink, D. C. McKay, J. B. Hertzberg, M. H. Ansari, and B. L. T. Plourde, Suppression of Unwanted ZZ Interactions in a Hybrid Two-Qubit System, Phys. Rev. Lett. 125, 200504 (2020). [3] B. Blain, G. Marchegiani, L. Amico, and G. Catelani, Suppressing chaos with mixed superconducting qubit devices, arXiv:2410.18543 (2024).

Low-frequency offset-charge-based control of the fluxonium qubit

• Agustin di Paolo (Google)

Because of the presence of an inductive shunt, the fluxonium qubit is insensitive to the dc value of the offset-charge bias, ng. However, a sensitivity to offset-charge fluctuations develops at nonzero frequency. In this talk, we derive a convenient form of the fluxonium Hamiltonian that makes it easier to characterize the effects of a time-dependent offset-charge bias, and discuss its implications for improved qubit coherence and control.

A lattice field theory of quantum circuits

• Neill Warrington (MIT)

I will present a lattice field theory formulation of the many-body dynamics of superconducting quantum circuits. This technique is adapted from an ab initio formulation of nuclear physics called "lattice QCD", and consists of writing quantum circuit problems as path integrals then numerically solving them. We apply the method to fluxonium, and examine the charge dispersion at high impedance and ground capacitance.

Discussion