One of the most fundamental problems in quantum many-body physics is the characterization of correlations among thermal states. Of particular relevance is the thermal area law, which justifies the tensor network approximations to thermal states with a bond dimension growing polynomially with the system size. In the regime of sufficiently low temperatures, which is particularly important for practical applications, the existing techniques do not yield optimal bounds. Here, we propose a new thermal area law that holds for generic many-body systems on lattices. We improve the temperature dependence from the original O(β) to O~(β2/3), thereby suggesting diffusive propagation of entanglement by imaginary time evolution. This qualitatively differs from the real-time evolution which usually induces linear growth of entanglement. We also prove analogous bounds for the Rényi entanglement of purification and the entanglement of formation. Our analysis is based on a polynomial approximation to the exponential function which provides a relationship between the imaginary-time evolution and random walks. Moreover, for one-dimensional (1D) systems with n spins, we prove that the Gibbs state is well-approximated by a matrix product operator with a sublinear bond dimension of eO~(βlog(n))√. This allows us to rigorously establish, for the first time, a quasi-linear time classical algorithm for constructing an MPS representation of 1D quantum Gibbs states at arbitrary temperatures of β=o(log(n)). Our new technical ingredient is a block decomposition of the Gibbs state, that bears resemblance to the decomposition of real-time evolution given by Haah et al., FOCS'18.
On 19 September, Ignacio Cirac, Director of the Theory Department at the Max Planck Institute of Quantum Optics, received the first La Vanguardia Prize in the category "Innovation", which the Spanish daily by the same name awarded for the first time on the occasion of its 142nd anniversary in 2023. The prize was ceremoniously presented to him by Spain's King Felipe VI, who graced the event together with his wife, Queen Letizia.
Focusing on so-called symmetry-protected topological (SPT) phases, the theorist uncovered some essential but previously unknown properties. Her findings further our understanding of STP phases in open systems.
The simulation of quantum chemical processes promises a lot of progress, such as the discovery of new chains of reactions, new synthetic materials or pharmaceuticals. But it is an enormous task, which known methods have failed to date. For classical supercomputers, the molecules are too complex, and for quantum simulations with cold atoms, the technological hurdles are still too high. In a new paper, theorists have now developed...
In his thesis, he studied and applied methods from quantum information to, among other things, find the ground state in complex quantum systems. As a next career step, he will start working as a Quantum Application Engineer at a Munich start-up company.
NISQ computers need quantum entanglement as a key resource to perform computations. But the presence of entanglement can also in some cases be a threat to their accuracy, like a recently published paper shows.