Near-GV QLDPC codes and modular RF control (10/05/26)

TL;DR The QICK Box (Quantum Instrumentation Control Kit RF front-end) is a modular open-source analog chain—up to 16 RF outputs, 8 inputs, and eight 20-bit DC biases, with daughtercards for DC-coupled or ≤10 GHz RF paths—built around an AMD ZCU216 RFSoC. On a six-transmon device at Fermilab’s QUIET testbed it delivers $(91.7\pm 0.4)\%$ single-shot readout fidelity (limited by $T_1$ decay during the readout window) and SNR $4.4\pm 0.1$ with no quantum amplifier, so room-temperature QICK hardware alone can already support high-fidelity cQED control and measurement.

• Hardware: The QICK Box mates a ZCU216 companion board to modular output/input daughtercards, adding software-controlled step attenuation, bandpass filtering, and eight 20-bit DC bias channels for flux or gate lines.
• Signal chain: Users swap DC-coupled cards for baseband control against RF cards spanning up to 10 GHz, matching typical superconducting drive and readout bands without a custom rack of discrete amplifiers and mixers.
• Main result: Single-shot readout of a six-transmon chip at QUIET reached $(91.7\pm 0.4)\%$ assignment fidelity, with the residual error attributed to $T_1$ decay during the integration window rather than electronics SNR.
• SNR: Clean-side Gaussian-core fitting gives a single-shot SNR of $4.4\pm 0.1$ without a quantum-limited amplifier, confirming the room-temperature front-end is not the fidelity bottleneck.
• Scope: This white paper covers the analog box and cryogenic demo; firmware/software advances are deferred to a companion paper.

TL;DR An infinite family of $p$-ary quantum low-density parity-check (QLDPC) codes—stabilizer codes whose checks have bounded weight—achieves any rate $R$ with normalized distance within $ϵ$ of the quantum Gilbert–Varshamov bound ${\delta }_{\mathrm{GV}}(p,R)$, the random-coding distance benchmark for $p$-ary stabilizers. The construction quantitatively controls degeneracy (many low-weight stabilizers) via Alon–Edmonds–Luby (AEL) expander amplification, then random concatenation, and a random draw matches random stabilizers on erasure and Pauli channels.

• Main result: For any rate $R$, any $ϵ>0$, and any prime alphabet size $p\ge 2$, there is an infinite family of $p$-ary QLDPC codes with check weight $O_{ϵ}(1)$ and normalized distance at least ${\delta }_{\mathrm{GV}}(p,R)-ϵ$.
• Ensemble: A random code from the constructed ensemble lies near the Gilbert–Varshamov bound with high probability, rather than only existentially.
• Channels: The same ensemble approaches the quantum capacity of the erasure channel and the hashing bound (the random-stabilizer achievable rate) for memoryless Pauli channels, including depolarizing noise.
• Degeneracy control: Starting from asymptotically good QLDPC codes near the quantum Singleton bound, AEL distance amplification yields low-degeneracy outer codes, then each coordinate is concatenated with a random inner code (a quantum Thommesen-type construction).

TL;DR Sparse Hermitian evolution can be simulated with only square-root query dependence on sparsity $s$: for row/column Euclidean norms bounded by $\eta$, time $t$, and error $ϵ$, the cost is $\mathcal{O}(\sqrt{s}\tau +\sqrt{s\tau \log (1/ϵ)}+\log (1/ϵ))$ with $\tau =\eta |t|$. The same root-sparsity idea extends to dissipative ODEs and linear systems via an exact entrywise encoding plus Cayley transducers (unitaries that realize the Cayley transform of a sparse block), with lower bounds nearly matching the joint scaling.

• Main result: For an $s$-sparse Hermitian Hamiltonian with row and column Euclidean norms $\le \eta$, simulating evolution for time $t$ to error $ϵ$ costs $\mathcal{O}(\sqrt{s}\tau +\sqrt{s\tau \log (1/ϵ)}+\log (1/ϵ))$ queries with $\tau =\eta |t|$, including time-dependent cases under coherent sparse access.
• Method: An exact entrywise sparse representation is composed with Cayley transducers and a boundary-resolvent filter so that each physical time step queries the matrix only $\sim \sqrt{s}$ times rather than linearly in $s$.
• ODEs: Dissipative linear differential equations inherit root-sparsity scaling $\mathcal{O}(\bar{g}[\sqrt{s}(\tau +\sqrt{\tau })+1]\log (C\bar{g}/ϵ))$, where $\bar{g}$ is the ratio of combined input/source norms to the final-solution norm and $C$ is an absolute constant.
• Linear systems: A Cayley walk with a Chebyshev filter solves $Ax=b$ in $\mathcal{O}(\kappa \sqrt{s}\log (1/ϵ))$ queries when $\Vert A\Vert \le 1$ and $\Vert A^{-1}\Vert \le \kappa$, matching a joint lower bound.
• Hardness: A joint lower bound nearly matches the time–sparsity–precision dependence and rules out a uniformly additive cost in $\sqrt{s}\tau$ and $\log (1/ϵ)$ alone.