arXiv subjects

Taiki Tanimae

Publications and source records attributed to Taiki Tanimae.

5 recordsLinked to original sources

arXiv2026

The $\gamma_c$-Peak: Covariant Recovery on Four Organic Qubit Platforms

We characterize where, in the noise parameter space of the uniform dephasing--depolarizing channel $\mathcal N_\gamma^\delta=\mathcal E_\delta\!\circ\!\mathcal D_\gamma$, a deterministic, \emph{nonlinear, target-informed} denoising heuristic yields its largest fidelity gain. The procedure pulls the off-diagonal magnitudes of the noisy state toward those of a known target, with efficiency set by a SWAP-test-purified catalyst; it is not a quantum channel, and target access is an explicit classical resource, so the results describe a benchmark procedure, not blind error correction. Our main tool is the covariant purification map $\mathcal P_\mathrm{cov}(\rho)=(\rho+\rho^2)/(1+\mathrm{Tr}\,\rho^2)$, an exact closed form for one SWAP-test purification round (a rederivation of symmetrization purification: Barenco \emph{et al.}, Cirac--Ekert--Macchiavello) that reduces the catalyst to a scalar eigenvalue iteration. With it we derive the $d\to\infty$ fidelity-gain peak location on Haar-random pure states (Theorem~3): $\gamma_{\rm peak}(d)\to\gamma^\star(r,\delta)$, with $\gamma^\star(2,0.1)=0.4725$ and limiting magnitude $0.2262$. Bootstrap-quantified sweeps to $d=256$ are consistent with both limits. The peak is resource- and protocol-dependent: a catalyst-only reference moves it from $\approx0.50$ to $\approx0.34$, and one purification round instead of two to $\approx0.39$. Bell and uniform $d=4$ states admit unique-peak theorems for the $r=0$, $\delta=0$ protocol member. All results are reproducible from the open-source \texttt{organic-qc-bench} package with seed~42.

q-bio.NC↗

arXiv2026

Markovian dephasing has no entanglement-breaking threshold, and a fixed tolerance will report one anyway

When modelling decoherence in a biological spin system it is tempting to seek a critical rate beyond which the channel is entanglement-breaking (EB) and quantum resources are gone. We show that for the two channel families in which such a model would be posed, no critical rate exists. For uniform dephasing at rate $\gamma$ the partial transpose of the Choi state has eigenvalue $-e^{-\gamma}/d$, so the channel is non-PPT -- hence not EB -- at every finite $\gamma$. Adding amplitude damping changes nothing: the qubit map's partial transpose stays negative at all finite rates. What does vanish at a finite rate is the coherent information, exactly where the qubit map turns antidegradable: the root of $c^{2}=p$, $\gamma_{\Ic}=0.668$ at $\kappa=0.1$. Antidegradability survives tensor products, so the single-letter and regularised thresholds coincide: of the three properties usually conflated here, two share one finite boundary and the third has none. Our main object is the numerical mechanism that manufactures a threshold where there is none. A quantity that decays exponentially to zero without reaching it, tested against a fixed absolute cutoff, yields a "threshold" set by the cutoff: the PPT test gives $\gamma=5.49$ at $\epsilon=10^{-10}$ and $6.58$ at $10^{-12}$, sliding by $0.55$ per decade. We reported the first number in three now-retracted preprints. Preparing this paper we made the same error three more times -- most seriously in $\gamma_{\Ic}$ itself, which a bisection against a $10^{-7}$ cutoff placed at $0.62$ -- and we document all four instances, with the closed forms and code that avoid them.

q-bio.NC↗

arXiv2026

Catalytic Quantum Error Correction: Theory, Efficient Catalyst Preparation, and Numerical Benchmarks

Quantum computers promise transformative speedups, but environmental noise destroys their fragile states. Conventional quantum error correction (QEC) encodes information redundantly across physical qubits, yet fails above a threshold of about 1% and incurs polynomial qubit overhead. A recent theorem from the resource theory of coherence shows that catalytic covariant operations amplify coherence at an unbounded rate, but this result has never been cast as an operational protocol. The challenge is to turn an asymptotic theorem into a recovery scheme that works at any noise strength with realistic resources. Here we show that catalytic coherence amplification can be cast as an error-correction primitive, Catalytic Quantum Error Correction (CQEC), which recovers a known target state from noisy copies without any error magnitude threshold whenever the target's coherent modes are preserved. In an effective model of the recovery map, fidelity exceeds 0.99 across 200 noise configurations spanning d = 4-64; the catalyst cost drops from the constructive bound n* ~ d^4 e^(2 gamma) to 32 copies at matched fidelity (10^4- to 10^9-fold) via a pipeline of dynamical decoupling, Clifford twirling, and recursive swap-test purification. A first explicitly CPTP, exactly covariant joint-channel implementation validates genuine recovery under dephasing at small dimension (0.54 -> 0.77) while showing that shallow circuits consume the catalyst, quantifying the model-vs-channel gap. These results turn an abstract resource-theoretic statement into a concrete protocol candidate complementary to stabilizer- and purification-based QEC; an open-source package reproducing the benchmarks accompanies this work (arXiv:2603.25774, https://github.com/deeptell-inc/cqec).

quant-ph↗

arXiv2026

Evaluation artifacts in reversible quantum reservoir protocols: a withdrawal of our own claims, and an entangled channel that survives the controls

This replaces v1, which reported a ten-order shot-noise suppression from a quantum reservoir autoencoder and a two-phase protocol reconstructing unseen inputs at MSE ~ 10^-4. We withdraw both claims: under one consistent evaluation the suppression reverses sign (reset channels degrade reconstruction 144x), the two-phase target is invertible in closed form without training, and a polynomial using no quantum features matches the full model. We trace these to four evaluation artifacts; the fourth also invalidates the companion latent code, which never leaves its initialization. What survives the same controls is a joint scrambling channel: injected on one reservoir half, read out on the other, decoded by a readout calibrated once on training messages. Over 32 realizations the held-out error is below chance in 31-32 (permutation p<10^-4) with a shuffled control at chance. Scrambler T-doping is necessary for one-shot injection, while interleaved injection supplies its own non-Cliffordness; a matched classical scrambler decodes the task better, so the transport is not evidence of a quantum mechanism. The access threshold, recomputed on nested subsystems with right-censoring, gives interleaved medians f* = 0.25-0.33; one-shot injection reaches full detectability in only half the realizations at the largest settings. A trained variational ansatz loses to the fixed untrained circuit by 2.6-4.4x. Three extensions pass the same discipline: streaming requires dissipative reset of the accessible half; the decoder does not transfer across the eight keys tested; a receiver holding the key matches the supervised ceiling from self-simulated pairs. A first hardware run decodes at 0.23 with the shuffled control at chance, while coherent device errors partially open the t=0 control. We close with the controls that separate transport from interpolation.

quant-ph↗

arXiv2026

Quantum Reservoir Autoencoder: Conditions, Protocol, and Noise Resilience

Quantum reservoir computing exploits fixed quantum dynamics and a trainable linear readout to process temporal data, yet reversing the transformation -- reconstructing the input from the reservoir output -- has been considered intractable due to the recursive nonlinearity of sequential quantum state evolution. We introduce the quantum reservoir autoencoder, a four-equation encode--decode protocol with cross-key pairing, and constructively empirically demonstrate that satisfying reservoir--key combinations can be found using a full XYZ Hamiltonian reservoir (10~data qubits, feature dimension~76, 16~random Hamiltonian realizations). Under ideal conditions the mean-squared error (MSE) reaches ${\sim}10^{-17}$ for data lengths up to 30; under shot noise (1\,000~shots) and depolarizing noise ($p = 0.005$), the MSE degrades to $10^{-3}$--$10^{-1}$. Asymmetric resource allocation -- 10~shots for encoding, $10^5$ for decoding -- yields a 102-fold MSE improvement (16~seeds $\times$ 3~trials). Comparison of single-body features (dimension~31) with the full feature set and six baselines identifies the iterative protocol structure -- not the feature dimension -- as the dominant noise bottleneck: baselines solving the linear system in a single step retain machine precision under identical noise, whereas per-iteration noise inconsistency in the coupled solver limits the MSE to ${\sim}10^{-1}$. The current protocol requires plaintext access during decoder training, restricting practical deployment. These results establish a proof-of-concept for bidirectional information transformation within quantum reservoir computing and identify iterative noise mismatch and blind decryption as the principal open challenges.

quant-ph↗