By: Chi-Fang Chen, András Gilyén
We present a general protocol for estimating $M$ observables from only $\mathcal{O}(\log (M)/\varepsilon^2)$ copies of a Gibbs state whose Hamiltonian is accessible. The protocol uses single-copy, nonadaptive measurements and uses a total Hamiltonian simulation time of $\widetilde{\mathcal{O}}(βM/\varepsilon^2)$; we show that the sample complexity is optimal in a black-box setting where exponential time Hamiltonian simulation is prohibited. T... more
We present a general protocol for estimating $M$ observables from only $\mathcal{O}(\log (M)/\varepsilon^2)$ copies of a Gibbs state whose Hamiltonian is accessible. The protocol uses single-copy, nonadaptive measurements and uses a total Hamiltonian simulation time of $\widetilde{\mathcal{O}}(βM/\varepsilon^2)$; we show that the sample complexity is optimal in a black-box setting where exponential time Hamiltonian simulation is prohibited. The key idea is a new interpretation of quantum Gibbs samplers as \textit{detailed-balance measurement channels}: measurements that preserve the Gibbs state when outcomes are marginalized. Consequently, shadow tomography of thermal states admits a general efficient algorithm when the Hamiltonian is known, substantially lowering the readout cost in quantum thermal simulation. less
By: Charlotte Franke, Dorian A. Gangloff
Quantum error correction (QEC) is indispensable for scalable quantum computing, but implementing it with minimal hardware overhead remains a central challenge. Large spin systems with collective degrees of freedom offer a promising route to reducing the control complexity of qubit architectures while retaining a large Hilbert space for fault-tolerant encoding. However, existing proposals for logical gates and QEC in spin ensembles generally r... more
Quantum error correction (QEC) is indispensable for scalable quantum computing, but implementing it with minimal hardware overhead remains a central challenge. Large spin systems with collective degrees of freedom offer a promising route to reducing the control complexity of qubit architectures while retaining a large Hilbert space for fault-tolerant encoding. However, existing proposals for logical gates and QEC in spin ensembles generally rely on inefficient higher-order interactions. Here we introduce spin-N-Cat codes, which encode logical qubits in superpositions of spin-coherent states and generalize bosonic Cat codes to the modular subspaces of permutationally symmetric spin ensembles. The code corrects collective and individual dephasing, excitation, and decay errors. We also present an efficient physical realization in central-spin systems, such as a quantum dot, where encoding, decoding, and a universal, fault-tolerant, and bias-preserving gate set are implemented using only first-order interactions. Numerical simulations demonstrate high logical fidelity under dephasing and excitation-decay noise, independent of noise bias, and that full QEC cycles are feasible with realistic microscopic parameters. For the large collective spins available in quantum dots, this translates into a substantial extension of coherence time. Our results establish spin-N-Cat codes as a scalable, hardware-efficient approach to QEC in spin-based quantum architectures. less
By: Gengzhi Yang, Jiaqi Leng, Xiaodi Wu, Lin Lin
Non-Hermitian many-body systems can be spectrally unstable, so small perturbations may induce large eigenvalue shifts. The pseudospectrum quantifies this instability and provides a perturbation-robust diagnostic. For inverse-polynomially small $ε$, we show that deciding whether a point $z\in\mathbb{C}$ is $ε$-close to the spectrum is PSPACE-hard for $5$-local operators, whereas deciding whether $z$ lies in the $ε$-pseudospectrum is QMA-comple... more
Non-Hermitian many-body systems can be spectrally unstable, so small perturbations may induce large eigenvalue shifts. The pseudospectrum quantifies this instability and provides a perturbation-robust diagnostic. For inverse-polynomially small $ε$, we show that deciding whether a point $z\in\mathbb{C}$ is $ε$-close to the spectrum is PSPACE-hard for $5$-local operators, whereas deciding whether $z$ lies in the $ε$-pseudospectrum is QMA-complete for $4$-local operators. This identifies pseudospectrum membership as a natural computational target. We then present a concrete end-to-end quantum framework for deciding pseudospectrum membership, which combines a singular-value estimation step with a dissipative state preparation algorithm. Our Quantum Singular-value Gaussian-filtered Search (QSIGS) combines quantum singular value transformation (QSVT) with classical post-processing to achieve Heisenberg-limited query scaling for singular-value estimation. To prepare suitable input states, we introduce an algorithmic Lindbladian protocol for approximate ground right singular vectors and prove its effectiveness for the Hatano--Nelson model. Finally, we demonstrate the full pipeline on a trapped-ion quantum computer and distinguish points inside and outside the target pseudospectrum near the exceptional point of a minimal non-Hermitian qubit model. less
8 SciCasts by .