Drive-hardened qubits and Tsirelson gaps (10/08/26)

TL;DR Sub-GHz charge driving of superconducting Kerr oscillators (KOs)—nonlinear resonators operated as transmons—activates fast parametric gates while suppressing $1/f$ charge-noise sensitivity, because the drive-induced frequency shift grows quadratically with drive frequency and amplitude. On this platform the authors cool a KO below its thermal occupation in 82 ns, encode a dual-rail erasure qubit (logical states in single-photon occupation of one of two modes) with nearly fourfold erasure bias, and reach a 25 ns Clifford error of $5.6\times 10^{-4}$ ($1.5\times 10^{-4}$ after post-selection).

• Mechanism: Using the AC Stark shift (drive-induced qubit-frequency pull) as a probe, KO charge sensitivity grows quadratically with drive frequency and amplitude, so the oscillator couples weakly to low-frequency $1/f$ charge noise yet strongly to ~1 GHz drives.
• Reset: Sub-GHz charge driving cools and resets a KO in 82 ns to residual excited-state population below $0.7\%$, below its $2.5\%$ steady-state thermal population.
• Encoding: Two KOs implement logical control and dynamical protection of a dual-rail qubit—logical information carried by which mode holds the photon—with nearly fourfold erasure bias (erasure errors dominate Pauli errors by ~$4\times$).
• Gates: A single end-of-circuit erasure check yields an error per Clifford of $5.6\times 10^{-4}$ with 25 ns gates, falling to $1.5\times 10^{-4}$ after post-selection on no erasure.
• Hardware takeaway: Low-frequency charge driving sidesteps the usual trade-off in which strong dynamical decoupling drives also cause dephasing and leakage, enabling protected parametric control on imperfect cQED hardware.

TL;DR Sub-Riemannian geodesic search—finding shortest allowed paths in the unitary group under hardware control limits—yields microwave pulses that outperform Gaussian and DRAG (derivative removal by adiabatic gate) for short $R_x(\pi /2)$ gates on leakage-aware superconducting qubits, cutting both average-gate infidelity and leakage. For the two-qubit $i$SWAP, the same method raises fidelity at roughly fixed leakage, at the price of a slightly longer gate.

• Method: The authors adapt sub-Riemannian geodesic search on the unitary group to a two-transmon model that keeps higher levels, so the optimizer can trade control effort against leakage out of the computational subspace.
• Single-qubit result: Optimized $R_x(\pi /2)$ pulses beat standard Gaussian and DRAG envelopes in average gate fidelity and leakage, with the largest gains at short gate durations where spectral content otherwise drives $|2⟩$ strongly.
• Two-qubit result: For $i$SWAP, leakage stays roughly unchanged while fidelity rises substantially, requiring only a modestly longer evolution than the comparison pulse.
• Hardware takeaway: For cQED pulse design, geodesic control is most compelling when short single-qubit gates dominate the leakage budget; two-qubit gains come mainly as fidelity, not as further leakage suppression.

TL;DR In waveguide QED, scattering a single-photon exponential pulse from an already excited ladder three-level emitter—the continuum analogue of stimulated emission—is strongly altered by the third level at transmon-like anharmonicity: when the relative anharmonicity (fractional shift of the $|1⟩\leftrightarrow |2⟩$ vs. $|0⟩\leftrightarrow |1⟩$ spacing) satisfies $|{\alpha }_r|<4\%$, that extra level largely suppresses the stimulated-emission signature. The same ladder, however, can produce photon bunching in reflection that incident-pulse tuning can switch off—so few-level waveguide models of cQED artificial atoms must retain $|2⟩$ when anharmonicity is weak.

• Main result: An exact real-space wavefunction for an excited ladder three-level emitter coupled to a 1D open waveguide shows that a third level with relative anharmonicity $|{\alpha }_r|<4\%$ largely suppresses the stimulated-emission response that a two-level atom would give under single-photon exponential-pulse scattering.
• Hardware implication: Typical transmon anharmonicity sits in that weak-$|{\alpha }_r|$ regime, so waveguide-QED predictions for on-chip microwave photon scattering and amplification that truncate to two levels misrepresent the emitted-field dynamics.
• Correlation control: The ladder system can imprint photon bunching on the reflected field—an excess of coincident two-photon detections versus a coherent state—yet that bunching can be switched off by retuning the incident photon’s spectral parameters.
• Method: The real-space waveguide-QED formalism yields closed-form probability amplitudes for the joint emitter–field state, enabling direct comparison of two- versus three-level scattering without a Markovian master-equation truncation.

TL;DR An explicit binary linear system game—a nonlocal game whose winning conditions are the equations of a sparse system over $\mathrm{GF}(2)$—admits a perfect commuting-operator strategy yet every correlation in $C_{qa}$, the closure of finite-dimensional quantum correlations, wins with probability strictly less than $1$. That separates $C_{qa}$ from $C_{qc}$, the set of commuting-operator correlations, and gives a concrete counterexample to Tsirelson's problem in its approximation form (whether those two sets coincide).

• Main result: The constructed game has quantum value $<1$ on all of $C_{qa}$ while a commuting-operator strategy wins with probability $1$, so $C_{qa}\ne C_{qc}$.
• Game size: The defining binary system has $1,417,152$ equations in $1,889,684$ variables, three nonzero coefficients per equation, and a single nonzero right-hand-side entry.
• Classical value: The authors compute the classical winning probability of the game exactly (besides the quantum/commuting separation).
• Mechanism: The proof routes through a Kazhdan group (a discrete group with property (T), which forces approximate unitary representations to be close to genuine ones) and an amalgamated-product construction that produces a central involution obstructing finite-dimensional approximate representations while still allowing a perfect commuting strategy.
• Formalization: The full linear system is specified in Lean 4, and Mathlib formalizes both the $C_{qa}$–$C_{qc}$ separation and the exact classical value.

TL;DR Projective-geometry $X$-stabilizers that are $8$-divisible (every $X$-check support has weight a multiple of $8$), plus a SAT search for compatible $X$-logicals, yield CSS codes (separate $X$/$Z$ stabilizers) with $k=3$ logical qubits whose logical CCZ (controlled-controlled-$Z$) is exactly transversal physical $T/T^{†}$ ($\pi /8$ phase gates), at thirteen lengths $n=48$–$496$ with $Z$-distance $d_Z=3$ or $4$. No such CSS code with $d_Z\ge 3$ and a quasi-transversal CCZ (transversal $T$ plus a diagonal Clifford correction) exists for $n<39$, so the open window sits between that lower bound and the known $[[47,3,3]]$ example.

• Main result: CSS codes with three logical qubits implement logical CCZ by transversal physical $T/T^{†}$ alone, with distance at least $3$, at thirteen block lengths from $n=48$ to $n=496$ and $d_Z=3$ or $4$.
• Construction: $8$-divisible $X$-stabilizers from projective geometry enforce $d_Z\ge 3$; a SAT solver then finds three $X$-logical operators compatible with the transversal CCZ phase pattern.
• Example: The method produces the $[[48,3,3]]$ code $Q_{48}$ as the smallest constructed instance in this family.
• Lower bound: No CSS code with $k=3$, $d_Z\ge 3$, and a quasi-transversal CCZ exists below $n=39$; Jacinto et al.'s $[[47,3,3]]$ leaves $39\le n\le 46$ open.