Junction harmonics, hBN stacks, and coset codes (10/12/26)

TL;DR A Hilbert-space Josephson junction—charged particle on a loop with self-adjoint boundary conditions of coupling $\lambda$ (junction transparency) and phase jump $\delta$ (superconducting phase difference)—yields supercurrent $⟨{\hat{p}}_0⟩=I_c(\delta ,\lambda )\sin \delta$ and recovers $V\propto \dot{\delta }$ from a gauge transform. For transparent junctions, $I_c$ depends on $\delta$ already at $O({\lambda }^{-2})$, giving a first-principles route to the higher Josephson harmonics needed in cQED spectroscopy.

• Model: The junction is a point on a 1D loop where the wave function obeys self-adjoint boundary conditions labelled by transparency coupling $\lambda$ and phase jump $\delta$.
• Main result: Ground-state momentum expectation—identified with the supercurrent—factorises exactly as $⟨{\hat{p}}_0⟩=I_c(\delta ,\lambda )\sin \delta$.
• Opaque / attractive limits: Opaque junctions make $I_c$ independent of $\delta$, recovering $I=I_c\sin \delta$; strongly attractive coupling recovers the same law with an exponentially suppressed amplitude.
• Transparent corrections: For more transparent contacts, $I_c$ acquires $\delta$ dependence at $O({\lambda }^{-2})$, matching the higher Josephson harmonics used in qubit spectra; a fully transparent contact gives current linear in $\delta$.
• Second relation: A time-dependent $\delta$ implies a voltage drop $\propto \dot{\delta }$ via gauge transformation, so both Josephson relations emerge without being imposed.

TL;DR Niobium coplanar resonators on few-layer epitaxial hexagonal boron nitride (hBN; a 2D wide-gap dielectric) grown by molecular beam epitaxy on sapphire keep a low-power internal loss tangent of order $10^{-6}$, so hBN can enter the conventional superconducting qubit stack with only modest quality-factor cost. The materials bet is that the 2D layer’s thermal mismatch can block athermal phonons (nonequilibrium substrate phonons) from crossing the metal–substrate interface and seeding phonon-mediated correlated errors.

• Main result: Nb resonators atop few-layer epitaxial hBN on sapphire match the control stack’s low dielectric loss, with a low-power internal loss tangent of order $10^{-6}$ and only minimal degradation of the internal quality factor.
• Device stack: Molecular-beam-epitaxy hBN is inserted under the Nb film on sapphire and compared against an otherwise identical no-hBN control, with radiofrequency sweeps in power and temperature plus temporal tracking of two-level systems (TLS; electric-field-coupled defects that set millikelvin dielectric loss).
• cQED implication: Epitaxial hBN can be added as a phonon-interface layer in the standard resonator/qubit materials stack without spoiling the TLS-limited loss floor that already constrains coherent cQED hardware.
• Stated motivation: The work frames hBN as a first materials step toward stopping athermal phonons from transmitting into the superconductor—aimed at correlated quasiparticle errors in qubits, or at steering phonons into active sensors rather than passive metal films.

TL;DR Coset lifted product (CLP) codes—quantum LDPC codes built by letting two protographs act from the left and right on cosets $G/H$ of a possibly non-normal subgroup—push the record figure of merit $Q=k{d}^2/n$ at check weights $w=6,7,9$, including $[[360,20,20]]$ and $[[360,24,20]]$. The construction widens the algebraic search space beyond normal subgroups while still yielding certified CSS parameters in the $120\le n\le 400$ window.

• Construction: CLP codes take a finite group $G$, a subgroup $H\le G$ that need not be normal, a protograph $A$ over the group algebra ${\mathbb{F}}_2[G]$, and a protograph $B$ over ${\mathbb{F}}_2[N_G(H)]$ (the normalizer of $H$ in $G$); left and right coset actions on $G/H$ produce a quantum CSS code.
• Dimension formula: For groups of odd order, the logical dimension equals a sum over irreducible representations $\rho$ of $G$ of ordinary hypergraph-product dimensions built from the Fourier images $A_{\rho }$ and $B_{\rho }$.
• Record figure of merit: A certified search over $14,843$ pairs $(G,H)$ with non-normal $H$ and $120\le n\le 400$ beats the best published $Q=k{d}^2/n$ at $w=6,7,9$, highlighted by $[[360,20,20]]$ ($w=6$), $[[360,24,20]]$ ($w=7$), and $[[252,16,18]]$, $[[288,16,20]]$ ($w=9$).
• High distance: The same search yields strong-distance examples $[[168,10,14]]$ and $[[240,8,20]]$ at $w=6$, plus $[[216,8,18]]$ at $w=7$.

TL;DR On ibm_boston, a doublon–holon collision (a doubly occupied site scattering off an empty site) in a 21-site half-filled Fermi–Hubbard chain on 42 qubits yields a transmission probability that matches the Bethe-ansatz S-matrix with no free parameters. The same collision superposes transmitted and reflected channels and generates number entanglement, witnessed by particle-number fluctuations—unlike a doublon–doublon control that shows neither interaction dependence nor fluctuations.

• Main result: A programmable doublon–holon collider on a digital processor measures Hubbard quasiparticle transmission in quantitative agreement with the integrable Bethe-ansatz scattering matrix.
• Setup: A half-filled Fermi–Hubbard chain of 21 sites is encoded on 42 qubits of ibm_boston, with on-demand quasiparticle creation, directed motion, and controlled collisions.
• Entanglement: The collision superposes transmission and reflection; particle-number fluctuations infer the resulting number entanglement between the outgoing channels.
• Control: A collision of two indistinguishable doublons shows neither interaction-dependent transmission nor number fluctuation, isolating the doublon–holon effect.
• Significance: Flavor-selective quasiparticle preparation and scattering turns a digital quantum processor into an experimental tool for probing entanglement generated by correlated scattering.