Cloud RCS advantage and purification nonadditivity (09/25/26)

TL;DR On IBM's 120-qubit Nighthawk r2 chip (`ibm_phoenix`), 61-qubit forward random-circuit sampling—drawing bitstrings from unstructured deep circuits with native CZ gates—reaches patched cross-entropy fidelity $F_{\mathrm{XEB}}(36)=2.3\times 10^{-3}$ at 36 cycles under ordinary cloud execution, with no benchmark-specific calibration. At that depth the classical tensor-network cost saturates, so matching a $10^6$-shot ensemble is estimated at $\sim 10^{27}$ operations (more than a century on Frontier) versus 19 s on the device—the first reported vanilla RCS advantage on a broadly accessible commercial processor.

• Hardware: Experiments use a square-lattice subset of Nighthawk r2 with native CZ entangling gates and the standard IBM cloud stack, deliberately avoiding special calibration that would inflate fidelities.
• Fidelity cross-check: Mirror benchmarking (run the circuit then its inverse and score return to $|0{⟩}^{\otimes n}$) from 4–40 cycles and three-/four-patch XEB (score output probabilities on classically tractable connected patches) from 20–40 cycles track each other over more than two decades of fidelity decay.
• Generation leap: At fixed depth the r2 fidelities sit more than an order of magnitude above first-generation Nighthawk r1, showing that the new device generation—not a softer task—drives the gain.
• Classical hardness: A contraction-cost estimator validated on published Sycamore and Zuchongzhi networks puts single-amplitude cost at $\sim 10^{22}$ complex operations at 36 cycles; under bounded-fidelity rejection sampling that maps to $1.2\times 10^{27}$ machine operations for $10^6$ samples.
• cQED takeaway: Replicable RCS advantage on a cloud CZ square lattice shifts the bar from one-off lab demos toward what users can actually submit and time against classical cost models.

TL;DR A bus-based reconfigurable quantum router—flux-tunable SQUID couplers that selectively link interface qubits to two shared buses—supports two disjoint controlled-$Z$ (CZ) gates in parallel while destructive interference suppresses idle crosstalk, with simulated parallel-gate errors at the $10^{-3}$ level. On 36-qubit benchmarks versus a matched 2D grid, hardware-aware compilation cuts median SWAP count by up to $34\%$ and native CZ count by up to $20\%$, but end-to-end depth gains are circuit-dependent, showing connectivity and schedulable parallelism as distinct compiler-visible resources for modular circuit QED (cQED).

• Architecture: Flux-tunable SQUID couplers selectively connect interface qubits to two shared buses, enabling non-local routing and two disjoint CZ gates in parallel while destructive interference parks unused links.
• Gate fidelity: Full-system Hamiltonian simulations give parallel CZ errors at the $10^{-3}$ level; open-system analysis maps the coherence needed for high-fidelity operation.
• Compilation gains: For 36-qubit quantum Fourier transform (QFT), QAOA-MaxCut, and random-pairing circuits, hardware-aware compilation and resource-constrained scheduling reduce median SWAP count by up to $34\%$ and native CZ count by up to $20\%$ versus a matched 2D grid.
• Depth caveat: End-to-end depth reduction reaches $20\%$ for QAOA-MaxCut but is negligible for QFT despite fewer gates—extra connectivity and schedulable parallelism do not always shorten the critical path.
• Hardware takeaway: The router is a compiler-visible modular interconnect: idle suppression via interference and dual-bus parallelism matter as much as raw non-local links for cQED scaling.

TL;DR A fluxonium–transmon–transmon (FTT) three-mode open-system model — target fluxonium, flux-tunable intermediate coupler, and lossy auxiliary transmon — shows that periodic flux modulation opens a temporary intermode transfer path so surplus occupation drains to the environment without raising the target’s intrinsic loss. The target then recovers its driven high-occupation condensate-like state (a continuously pumped Kerr-supported population that is not an equilibrium Bose–Einstein condensate), offering a circuit design handle for controllable dissipation and nonequilibrium recovery in cQED.

• Motivation: Single-mode effective-decay models hide mode-resolved exchange and circuit-selective loss channels, so they cannot track how occupation leaves a driven target or briefly parks in auxiliaries.
• Circuit model: An FTT stack couples a Kerr-driven target fluxonium to a flux-tunable intermediate transmon that spectrally gates a dissipative transmon, so intermode coherent exchange and environmental release stay separately resolved in Lindblad dynamics.
• Main result: Periodic flux modulation temporarily opens the auxiliary pathway, transferring target occupation outward and driving the fluxonium from a high-occupation nonequilibrium condensate-like state into a low-occupation near-equilibrium Bose–Einstein condensation (BEC) regime.
• Hardware implication: Auxiliary-mode tuning engages an extra environmental drain without increasing the target mode’s intrinsic loss, then spectral suppression restores the original drive–Kerr–weak-loss balance so the high-occupation state re-forms after irreversible release.
• Robustness check: Three-mode simulations probe depletion and recovery under pure dephasing, finite temperature, and detuning fluctuations, framing controllable dissipation as a design axis for nonequilibrium-state recovery.

TL;DR A $20\mu \mathrm{m}$-wide tungsten silicide superconducting strip single-photon detector (SSPD; a wide-strip cousin of nanowire detectors) reaches slew-rate-corrected timing jitter of $13.2\mathrm{ps}$ at $532\mathrm{nm}$ and $20.5\mathrm{ps}$ at $1550\mathrm{nm}$ with saturated internal detection efficiency through telecom wavelengths. Focused optical scans show edge-vs-center absorption sets a spatially dependent pulse slew rate that dominates timing spread; parallel superconducting rails that actively redistribute supercurrent shrink that latency mismatch, suppress thermally activated dark counts, and open higher-temperature operation—physics that time-dependent Ginzburg–Landau (TDGL) modeling ties to the strip geometry.

• Main result: A $20\mu \mathrm{m}$ $\mathrm{WSi}$ SSPD delivers slew-rate-corrected jitter of $13.2\mathrm{ps}$ ($532\mathrm{nm}$) and $20.5\mathrm{ps}$ ($1550\mathrm{nm}$) while keeping internal detection efficiency saturated up to $1550\mathrm{nm}$.
• Position-dependent timing: Free-space focused scans show absorption near the strip edge versus center produces different pulse rise rates (slew rates), so arrival-time jitter tracks where the photon lands across the strip width.
• Active control: A parallel superconducting rail architecture redistributes bias supercurrent in situ, reducing edge–center latency mismatch and cutting thermally activated intrinsic dark counts so the device can run warmer.
• Mechanism: Time-dependent Ginzburg–Landau (TDGL) modeling of the nonequilibrium superconducting order-parameter dynamics reproduces the transverse photoresponse and points to rails or specialized readout electronics as practical jitter mitigations.
• Hardware takeaway: Wide-strip SSPDs trade fill factor and signal amplitude for a geometric timing channel; controlling transverse current density is the lever that recovers picosecond timing without shrinking back to nanowires.

TL;DR The entanglement of purification $E_P$—the minimal entanglement across a purifying cut of a bipartite state—is rigorously nonadditive: for the two-qubit Werner state $W$ at singlet fraction $f=1/200$, the regularized value $E_P^{\infty }(W)\le 0.9663\dots$ sits strictly below $E_P(W)$. This closes the 2012 Chen–Winter numerical conjecture with machine-checkable certificates and settles a question open since Terhal–Horodecki–Leung–DiVincenzo (2002).

• Main result: For that Werner state $W$, $E_P^{\infty }(W)\le 0.9663\dots <97/100<E_P(W)$, so $E_P$ fails additivity at some finite tensor power.
• Lower bound: Analytic reductions map every purification’s Schmidt spectrum into a 3D box; an exact-rational subdivision with 25,383 leaves either excludes nonphysical points or certifies the entropy bound.
• Upper bound: An exact symmetric-support endpoint, an explicit feasible isometry, and a convexity theorem for $E_P^{\infty }$ close the chain via two directed rational-logarithm certificates.
• Verification: Every computer-assisted step reduces to integer comparisons; a dependency-free program checks them all from the supplementary artifact.