aiqbench analysis
This paper extends an existing fault-tolerant quantum computing framework to handle finite-temperature Gibbs states by decoupling energy filters from thermal response frequencies. The authors provide a rigorous block-encoding and QSP formulation that includes a compatibility analysis for four distinct simulation routes, highlighting the exponential scaling of preparation factors with system size at fixed temperature.
Finite-temperature transition-window weights on a fault-tolerant quantum computer: duplex filtering on a thermal purification
arXiv:2611.06809v1 Announce Type: new Abstract: The excite-filter-readout framework of Kharazi et al. computes zero-temperature response windows on a fault-tolerant quantum computer from a pure ground state. We extend it to Gibbs states, where the two objects decouple: filters act on absolute energies, a thermal response on transition frequencies. The extension rests on a Liouville-space/TFD identity, explicit in the block-encoding/QSP setting: the thermally weighted transition-window weight is a spectral projection of H_0 (x) I - I (x) H_0^T onto the Schmidt (thermofield-double) purification, instance of Rall's framework. Around it we assemble a routed-SELECT block encoding (one Hamiltonian query per filter query), a conjugate-pair readout, and a four-route (duplex, bin, Fourier-LCU, METTS) compatibility analysis. The cost is multiplicative and conditional: a per-window query bound M_"AE" * (2*sqrt(d/Z_"lb")*d_"vt" + 4*d_W), with a tight signal-adaptive count, the optimal sqrt(alpha beta) degree, and a window-edge term. The preparation factor sqrt(d/Z) grows exponentially with system size at fixed temperature in positive-entropy-density systems (2.08 -> 25.7, N = 8 to 14 at beta = 2), relieved only as beta -> 0. Zero temperature is recovered for beta G >= ln(2(d-1)||D||^2/epsilon). Identities are cross-checked between independent formula paths to 10^(-16)-10^(-12) and the readout assembly is validated at matrix level under a block-encoding promise.
Abstract:The excite-filter-readout framework of Kharazi et al. computes zero-temperature response windows on a fault-tolerant quantum computer from a pure ground state. We extend it to Gibbs states, where the two objects decouple: filters act on absolute energies, a thermal response on transition frequencies. The extension rests on a Liouville-space/TFD identity, explicit in the block-encoding/QSP setting: the thermally weighted transition-window weight is a spectral projection of H_0 (x) I - I (x) H_0^T onto the Schmidt (thermofield-double) purification, instance of Rall's framework. Around it we assemble a routed-SELECT block encoding (one Hamiltonian query per filter query), a conjugate-pair readout, and a four-route (duplex, bin, Fourier-LCU, METTS) compatibility analysis. The cost is multiplicative and conditional: a per-window query bound M_"AE" * (2*sqrt(d/Z_"lb")*d_"vt" + 4*d_W), with a tight signal-adaptive count, the optimal sqrt(alpha beta) degree, and a window-edge term. The preparation factor sqrt(d/Z) grows exponentially with system size at fixed temperature in positive-entropy-density systems (2.08 -> 25.7, N = 8 to 14 at beta = 2), relieved only as beta -> 0. Zero temperature is recovered for beta G >= ln(2(d-1)||D||^2/epsilon). Identities are cross-checked between independent formula paths to 10^(-16)-10^(-12) and the readout assembly is validated at matrix level under a block-encoding promise.
arXiv:2611.06809 [quant-ph]
(or arXiv:2611.06809v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2611.06809 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 291 words