Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · quant-ph/0606194

Adiabatic Computation - A Toy Model

P. Ribeiro·R. Mosseri
View original source ↗Read source document ↗Export metadata ↓

Abstract

We discuss a toy model for adiabatic quantum computation which displays some phenomenological properties expected in more realistic implementations. This model has two free parameters: the adiabatic evolution parameter $s$ and the $α$ parameter which emulates many-variables constrains in the classical computational problem. The proposed model presents, in the $s-α$ plane, a line of first order quantum phase transition that ends at a second order point. The relation between computation complexity and the occurrence of quantum phase transitions is discussed. We analyze the behavior of the ground and first excited states near the quantum phase transition, the gap and the entanglement content of the ground state.

Explore related subjects

quant-phcond-mat.other

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

P. Ribeiro, R. Mosseri. 2006-06-23. Adiabatic Computation - A Toy Model. https://doi.org/10.1103/physreva.74.042333

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Entanglement-based quantum communication may prevent tracking the message sender

The possibility of attaining current position of the message sender without person's consent seriously compromises the secrecy of correspondence. Classical communication systems cannot guarantee the security of communication against unwanted location tracking, because the sender must broadcast a signal at the moment of sending the message. The source of the signal could be always located, at least in principle. We show that quantum communication enables sending the message with pre-distributed entangled quantum systems, local weak measurements, time synchronization between the sender and the receiver and classical communication by the message receiver alone, therefore, physically securing the sender's location.

quant-ph↗
arXiv2026

Fully Passive Quantum Conference Key Agreement

Quantum Conference Key Agreement (CKA) provides a secure method for multi-party communication. A recently developed interference-based prepare-and-measure quantum CKA possesses the advantages of measurement-device-independence, namely, being immune to side-channels from the detector side. Besides, it achieves good key rate performance, especially for high-loss channels, due to the use of single photon interference. Meanwhile, several fully passive QKD schemes have been proposed, which eliminate all side channels from the source modulation side. We extend the fully passive idea to an interference-based CKA, which has a high level of implementation security for many-user communication.

quant-ph↗
arXiv2026

Fast simulations of X-ray absorption spectroscopy for battery materials on a quantum computer

X-ray absorption spectroscopy (XAS) is a leading technique for understanding structural changes in advanced battery materials such as lithium-excess cathodes. However, extracting critical information like oxidation states from the experimental spectra requires expensive and time-consuming simulations. Building upon a recent proposal to simulate XAS using quantum computers, this work proposes a highly-optimized implementation of the time-domain algorithm for X-ray absorption. Among a host of improvements to Hamiltonian representation, circuit implementation, and measurement strategies, three optimizations are key to the efficiency of the algorithm. The first is the use of product formulas with the compressed double factorized form of the Hamiltonian. The second is recognizing that for spectroscopy applications, it is sufficient to control the error in the eigenvalues of the (approximate) Hamiltonian being implemented by the product formula, rather than the generic error on the full time evolution operator. Using perturbation theory to estimate this eigenvalue error, we find that significantly fewer Trotter steps are needed than expected from the time evolution error bound. The third is the choice of an optimized distribution of samples that takes advantage of the exponentially decaying Lorentzian kernel. Through constant factor resource estimates, we show that a challenging model Li$_4$Mn$_2$O cluster system with 18 spatial orbitals and 22 electrons in the active space can be simulated with 100 logical qubits and less than $4 \times 10^8$ Toffoli gates per circuit. Finally, the algorithm is implemented on a simulator, and the reconstructed spectrum is verified against a classical computational reference. The low cost of our algorithm makes it attractive to use on fault-tolerant quantum devices to accelerate the development and commercialization of high-capacity battery cathodes.

quant-ph↗