Symmetry-protected sign problem and magic in quantum phases of matter

We introduce the concepts of a symmetry-protected sign problem and symmetry-protected magic to study the complexity of symmetry-protected topological (SPT) phases of matter. In particular, we say a state has a symmetry-protected sign problem or symmetry-protected magic, if finite-depth quantum circuits composed of symmetric gates are unable to transform the state into a non-negative real wave function or stabilizer state, respectively. We prove that states belonging to certain SPT phases have these properties, as a result of their anomalous symmetry action at a boundary. For example, we find that one-dimensional Z2×Z2 SPT states (e.g. cluster state) have a symmetry-protected sign problem, and two-dimensional Z2 SPT states (e.g. Levin-Gu state) have symmetry-protected magic. Furthermore, we comment on the relation between a symmetry-protected sign problem and the computational wire property of one-dimensional SPT states. In an appendix, we also introduce explicit decorated domain wall models of SPT phases, which may be of independent interest.

A simple polymerization control method for the air conditioning cluster

Taking the air conditioner cluster as the object, under the condition of individual perception and controllable state of the air conditioner, the cluster state is given a considerable and controllable function. In the analysis of the load model of a single air conditioner, considering the comfort of indoor temperature, the characteristics of on and off are given, that is, the cycle of on time and off time; on this basis, the air conditioning clusters are divided according to the same or similar switching cycles, thereby forming a switching strategy of series and parallel groups to achieve load balance. In the on state, if the adjustment of the power of the air conditioner itself is not considered, a simple aggregation control method is given. The analysis of numerical examples shows that this method is simple and reliable.

Multidimensional cluster states using a single spin-photon interface coupled strongly to an intrinsic nuclear register

Photonic cluster states are a powerful resource for measurement-based quantum computing and loss-tolerant quantum communication. Proposals to generate multi-dimensional lattice cluster states have identified coupled spin-photon interfaces, spin-ancilla systems, and optical feedback mechanisms as potential schemes. Following these, we propose the generation of multi-dimensional lattice cluster states using a single, efficient spin-photon interface coupled strongly to a nuclear register. Our scheme makes use of the contact hyperfine interaction to enable universal quantum gates between the interface spin and a local nuclear register and funnels the resulting entanglement to photons via the spin-photon interface. Among several quantum emitters, we identify the silicon-29 vacancy centre in diamond, coupled to a nanophotonic structure, as possessing the right combination of optical quality and spin coherence for this scheme. We show numerically that using this system a 2×5-sized cluster state with a lower-bound fidelity of 0.5 and repetition rate of 65 kHz is achievable under currently realised experimental performances and with feasible technical overhead. Realistic gate improvements put 100-photon cluster states within experimental reach.

Correspondence between isoscalar monopole strengths and α inelastic cross sections on 24Mg

The correspondence between the isoscalar monopole (IS0) transition strengths and α inelastic cross sections, the B(IS0)-(α,α′) correspondence, is investigated for 24Mg(α,α′) at 130 and 386 MeV. We adopt a microscopic coupled-channel reaction framework to link structural inputs, diagonal and transition densities, for 24Mg obtained with antisymmetrized molecular dynamics to the (α,α′) cross sections. We aim at clarifying how the B(IS0)-(α,α′) correspondence is affected by the nuclear distortion, the in-medium modification to the nucleon-nucleon effective interaction in the scattering process, and the coupled-channels effect. It is found that these effects are significant and the explanation of the B(IS0)-(α,α′) correspondence in the plane wave limit with the long-wavelength approximation, which is often used, makes no sense. Nevertheless, the B(IS0)-(α,α′) correspondence tends to remain because of a strong constraint on the transition densities between the ground state and the 0+ excited states. The correspondence is found to hold at 386 MeV with an error of about 20%–30%, while it is seriously stained at 130 MeV mainly by the strong nuclear distortion. It is also found that when a 0+ state that has a different structure from a simple α cluster state is considered, the B(IS0)-(α,α′) correspondence becomes less valid. For a quantitative discussion on the α clustering in 0+ excited states of nuclei, a microscopic description of both the structure and reaction parts will be necessary.