QMA equality meets parametric drive ceilings (09/14/26)

TL;DR Across 14 transmons spanning a wide anharmonicity range, the critical sub-resonant drive strength where Floquet hybridization (drive-induced mixing of quasienergy branches) sets in collapses onto a simple function of $\gamma ={\omega }_q/\alpha$, the ratio of qubit frequency to anharmonicity. That scaling bounds how hard you can pump a transmon coupler before leakage dominates, and therefore how large a parametric interaction rate a circuit can safely target.

• Main result: Experiment plus Floquet branch analysis and semiclassical simulations establish a direct map from $\gamma$ to ${\eta }_{\max }$, the largest usable effective drive amplitude before strong hybridization appears.
• Device physics: Sub-resonant microwave drives—tones well below the qubit frequency ${\omega }_q$ used for parametric control—eventually hybridize the driven spectrum; that threshold, not just heating or filtering, sets the practical amplitude ceiling.
• Hardware implication: When the transmon is a parametrically driven coupler, ${\eta }_{\max }(\gamma )$ converts into an estimate of the maximum parametric interaction rate, giving a design rule for gate speed versus fidelity.
• Design takeaway: Choosing ${\omega }_q$ and $\alpha$ is no longer only about coherence and selectivity; the ratio $\gamma$ also sets how far into the nonlinear drive regime a coupler can be pushed.

TL;DR Every $\mathsf{QMA}$ protocol—Merlin sends a quantum witness, Arthur runs a quantum verifier with completeness $c$ and soundness $s<c$—can be rewritten as a perfectly complete ${\mathsf{QMA}}_1$ protocol with $c=1$, so $\mathsf{QMA}={\mathsf{QMA}}_1$. The equality settles Bravyi’s open question and upgrades quantum $3$-SAT from ${\mathsf{QMA}}_1$-hard to $\mathsf{QMA}$-complete.

• Main result: The authors prove $\mathsf{QMA}={\mathsf{QMA}}_1$: every quantum Merlin–Arthur system can be compiled so YES instances admit a witness that Arthur accepts with certainty, while soundness stays inverse-polynomially below $1$.
• Gate set: The compilation uses only Hadamard, Toffoli, and $X$, which therefore form a universal gate set for ${\mathsf{QMA}}_1$ verifiers.
• Complexity payoff: Quantum $3$-SAT—decide whether given $3$-local projectors share a common zero-energy state, or every state has inverse-polynomial energy—becomes $\mathsf{QMA}$-complete.
• Oracle transfer: The construction relativizes to classical oracles, so known classical-oracle separations of $\mathsf{QMA}$ from $\mathsf{QCMA}$ (classical witnesses, quantum verifier) carry over to ${\mathsf{QMA}}_1$.

TL;DR A correctness-preserving parallelization of sparse blossom—the practical minimum-weight perfect matching (MWPM) decoder that matches detectors on a sparse syndrome graph—makes average decoding time per round vanish as $o(1)$ for the rotated surface code below threshold. Larger code distance need not lengthen the classical decoding bottleneck relative to syndrome extraction.

• Main result: Parallel sparse blossom is proved to return the same correction as serial sparse blossom, so the MWPM error-suppression guarantees are unchanged.
• Runtime bound: For the rotated surface code of distance $d$ below a finite physical-error threshold, the average parallel runtime over $O(d)$ syndrome-extraction rounds is at most quasi-polylogarithmic in $d$.
• Per-round scaling: Over a $d$-round decoding window, that bound implies average parallel runtime per round is $o(1)$—asymptotically shorter than one round of syndrome extraction.
• Numerical evidence: Simulations identify regimes where the parallel runtime per round decreases as $d$ grows, rather than increasing with problem size.
• Why it matters: Matching-based decoding (including MWPM confidence metrics used in magic-state protocols) can stay synchronized with the quantum pipeline as codes scale.

TL;DR A hot-vapour ${}^{129}\mathrm{Xe}$–$\mathrm{Cs}$ co-magnetometer is run as a non-Markovian spin oscillator—magnetization whose update depends on delayed feedback, not only the present state—with programmable delay and gain. Tuning those knobs maps a shared memory-induced instability into time-crystalline response, nonlinear bifurcations, and frequency-comb spectra, unifying several non-equilibrium phases on one spin platform.

• Platform: Feedback delay and gain close a programmable loop on a hot-vapour ${}^{129}\mathrm{Xe}$–$\mathrm{Cs}$ co-magnetometer (dual-species magnetometer that reads one spin ensemble against the other).
• Phase hierarchy: Delay–gain tuning yields continuous time-crystalline response (persistent oscillation that spontaneously breaks continuous time-translation symmetry), nonlinear bifurcations, and frequency-comb formation (discrete spectral lines at commensurate spacings).
• Mechanism: Linear stability analysis of delayed Bloch equations—Bloch spin dynamics with a finite-history feedback term—reproduces the measured spectra and phase boundaries as branches of one memory-induced instability.
• Implication: Time-delayed feedback becomes a control dial for non-equilibrium order, aiming quantum sensing, frequency referencing, and synchronization from the same spin hardware.