Leakage, electrode noise, and estimation bounds (09/30/26)

TL;DR Parametric derivative removal by adiabatic gate (PDRAG)—a signed first- and second-derivative correction to a parametric frequency drive that cancels the two conjugate leakage channels of a fast exchange while keeping the target swap—cuts endpoint leakage by a geometric-mean factor of $5.27\times 10^5$ relative to the base pulse across $12.5$–$35\mathrm{ns}$ in Duffing simulations at coupling $g/2\pi =100\mathrm{MHz}$. For cQED hardware, the same derivative coefficients transfer to a charge Hamiltonian with an $893$-fold mean leakage reduction after amplitude and carrier recalibration, so programmable exchange gates and simulations can stay in the computational manifold at few-ten-nanosecond durations.

• Problem: Fast programmable exchange in weakly anharmonic transmons opens two conjugate leakage pathways that spoil gates and eject simulated many-body dynamics from the encoded subspace.
• Method: PDRAG (parametric DRAG) builds first- and second-derivative corrections from that conjugate structure and implements both through one real frequency command via Bessel inversion of a smooth envelope.
• Main result: At $g/2\pi =100\mathrm{MHz}$, calibrated PDRAG reaches geometric-mean leakage reduction $5.27\times 10^5$ versus the base pulse over $12.5$–$35\mathrm{ns}$; at $13\mathrm{ns}$ the full-exchange endpoint leakage is $1.98\times 10^{-7}$.
• Transfer: Moving the Duffing-calibrated derivative coefficients onto a charge Hamiltonian yields a mean $893$-fold leakage cut over $12.5$–$22\mathrm{ns}$ after amplitude and carrier recalibration.
• Mechanism: Floquet return interference (phase-coherent reassembly of leakage amplitude over a finite pulse) and charge-induced gap shifts account for the calibration gains and for why the controls survive the model transfer.

TL;DR A microscopic BCS calculation of evanescent-wave Johnson noise (EWJN)—near-surface electromagnetic fluctuations from thermally driven currents—maps how superconducting electrodes set the relaxation time $T_1$ of nearby spin and charge qubits. Magnetic noise peaks just below the critical temperature $T_c$ via a Hebel–Slichter coherence peak (a transient enhancement of dissipative conductivity), then falls exponentially, while magnetic impurities leave a zero-temperature floor that bounds how quiet a gapped electrode can be.

• Framework: The transverse current-response kernel $Q(q,\omega )$ of a BCS half-space, with non-magnetic and magnetic impurities, plus nonlocal surface impedances, yields magnetic and electric field noise for qubit height $z\gg k_F^{-1}$ (Fermi wavelength).
• Magnetic vs electric: Just below $T_c$, magnetic EWJN is enhanced relative to the normal state by the Hebel–Slichter peak and drops exponentially at lower $T$; electric noise shows no coherence peak.
• Impurity floor: Magnetic impurities induce a $T=0$ noise floor; in the gapless (pair-broken) regime the subgap density of states $\nu (0)$ sets a temperature-independent spectrum with $T_1^{-1}(T)\le [\nu (0)/{\nu }_F{]}^2{T}_{1,N}^{-1}(T)$ for $T\ll T_c$, where ${\nu }_F$ is the normal Fermi-level DOS and $T_{1,N}$ is the same electrode’s normal-state $T_1$.
• Hardware takeaway: For cQED and hybrid devices with qubits nanometers from superconducting metal, residual pair-breaking—not the clean BCS gap alone—can dominate the EWJN-limited $T_1$ floor.

TL;DR A nearly optimal quantum algorithm estimates the Chern number—the integer topological invariant of a gapped ground-state bundle over a two-dimensional parameter torus—by transporting two ground-state copies from one reference point and coherently accumulating Berry phases via generalized quantum signal processing (phase-polynomial synthesis of Hamiltonian evolutions). Hamiltonian-oracle evolution time $\tilde{O}(L_x{L}_y/{\Delta }_{\min }^3)$ matches a worst-case lower bound up to polylog factors, where $L_x,L_y$ bound parameter derivatives of the Hamiltonian and ${\Delta }_{\min }$ is a known spectral-gap lower bound, and guided local instances make even the binary decision $\mathsf{BQP}$-complete.

• Main result: The algorithm reuses two ground states prepared at a single reference point on the parameter torus and accumulates geometric phases with generalized quantum signal processing, estimating the Chern number of any smooth, uniquely gapped Hamiltonian family—including interacting many-body systems.
• Complexity: Total Hamiltonian-oracle evolution time is $\tilde{O}(L_x{L}_y/{\Delta }_{\min }^3)$, with $L_x,L_y$ Lipschitz-type bounds on ${\partial }_{x}H$ and ${\partial }_{y}H$ and ${\Delta }_{\min }$ a known gap lower bound.
• Optimality: A matching worst-case oracle lower bound holds even when the Chern number is promised to be $0$ or $1$, so the algorithm is optimal up to polylogarithmic factors.
• Complexity class: For local Hamiltonian families with an inverse-polynomial gap and a supplied guiding state, exact Chern-number computation lies in $\mathsf{FBQP}$ (function problems solvable by bounded-error quantum polynomial time) and is $\mathsf{BQP}$-hard.
• Hardness: Already deciding whether the Chern number is zero or one is $\mathsf{BQP}$-complete, giving formal evidence for quantum advantage in topological phase characterization.

TL;DR A three-parameter rank-two quantum model shows that the Holevo Cramér–Rao bound—the asymptotic multiparameter precision limit that accounts for incompatible measurements—can be unattainable with one copy yet attained exactly by a two-copy collective measurement, so finite-copy gap persistence is not universal beyond two parameters. Superconducting-qubit experiments confirm a two-copy estimation error below single-copy and separate-measurement bounds, with the advantage surviving moderate depolarization.

• Main result: An explicit three-parameter, rank-two model on a four-dimensional Hilbert space has a Holevo bound that one copy cannot attain, but a collective measurement on two copies attains exactly.
• Theory contrast: For any full-rank multiparameter model, the gap between the attainable estimation cost and the Holevo bound persists at every finite copy number, so rank deficiency is necessary for finite-copy closure.
• Related bounds: The same model also closes a strict gap between the Nagaoka–Hayashi bound (the optimal single-copy multiparameter cost) and the Holevo bound, answering the higher-parameter persistence question for those two limits.
• Experiment: On superconducting qubits, a two-copy collective measurement yields estimation error below single-copy and separate-measurement lower bounds inferred from state tomography.
• Noise robustness: Controlled depolarization removes exact Holevo attainability but leaves a two-copy advantage over separate measurements across a finite noise window.