More Like this

1. Quantum State Combinatorics

   https://doi.org/10.3390/e26090764  

   Scholes, Gregory D (September 2024, Entropy)

   This paper concerns the analysis of large quantum states. It is a notoriously difficult problem to quantify separability of quantum states, and for large quantum states, it is unfeasible. Here we posit that when quantum states are large, we can deduce reasonable expectations for the complex structure of non-classical multipartite correlations with surprisingly little information about the state. We show, with pegagogical examples, how known results from combinatorics can be used to reveal the expected structure of various correlations hidden in the ensemble described by a state. 

   more » « less
2. Topological quantum photonics

   https://doi.org/10.1063/5.0239265  

   Hashemi, Amin; Zakeri, M_Javad; Jung, Pawel_S; Blanco-Redondo, Andrea (January 2025, APL Photonics)

   Topological quantum photonics explores the interaction of the topology of the dispersion relation of photonic materials with the quantum properties of light. The main focus of this field is to create robust photonic quantum information systems by leveraging topological protection to produce and manipulate quantum states of light that are resilient to fabrication imperfections and other defects. In this perspective, we provide a theoretical background on topological protection of photonic quantum information and highlight the key state-of-the-art experimental demonstrations in the field, categorizing them based on the quantum features they address. An analysis of the key challenges and limitations concerning topological protection of quantum states is presented. Importantly, this paper takes a thorough perspective look into what future research in this area may bring. 

   more » « less
3. Quantum Curved Tetrahedron, Quantum Group Intertwiner Space, and Coherent States

   https://doi.org/10.1088/1361-6382/adb533  

   Hsiao, Chen-Hung; Pan, Qiaoyin (February 2025, Classical and Quantum Gravity)

   Abstract In this paper, we construct the phase space of a constantly curved tetrahedron with fixed triangle areas in terms of a pair of Darboux coordinates called the length and twist coordinates, which are in analogy to the Fenchel-Nielsen coordinates for flat connections, and their quantization. The curvature is identified to the value of the cosmological constant, either positive or negative. The physical Hilbert space is given by the $$\mathcal{U}_q(\mathfrak{su}(2))$$ intertwiner space. We show that the quantum trace of quantum monodromies, defining the quantum length operators, form a fusion algebra and describe their representation theory. We also construct the coherent states in the physical Hilbert space labeled by the length and twist coordinates. These coherent states describe quantum curved tetrahedra and peak at points of the tetrahedron phase space. This work is closely related to 3+1 dimensional Loop Quantum Gravity with a non-vanishing cosmological constant. The coherent states constructed herein serve as good candidates for the application to the spinfoam model with a cosmological constant. 

   more » « less
4. Quantum mixed state compiling

   https://doi.org/10.1088/2058-9565/acc4e3  

   Ezzell, Nic; Ball, Elliott M.; Siddiqui, Aliza U.; Wilde, Mark M.; Sornborger, Andrew T.; Coles, Patrick J.; Holmes, Zoë (April 2023, Quantum Science and Technology)

   Abstract The task of learning a quantum circuit to prepare a given mixed state is a fundamental quantum subroutine. We present a variational quantum algorithm (VQA) to learn mixed states which is suitable for near-term hardware. Our algorithm represents a generalization of previous VQAs that aimed at learning preparation circuits for pure states. We consider two different ansätze for compiling the target state; the first is based on learning a purification of the state and the second on representing it as a convex combination of pure states. In both cases, the resources required to store and manipulate the compiled state grow with the rank of the approximation. Thus, by learning a lower rank approximation of the target state, our algorithm provides a means of compressing a state for more efficient processing. As a byproduct of our algorithm, one effectively learns the principal components of the target state, and hence our algorithm further provides a new method for principal component analysis. We investigate the efficacy of our algorithm through extensive numerical implementations, showing that typical random states and thermal states of many body systems may be learnt this way. Additionally, we demonstrate on quantum hardware how our algorithm can be used to study hardware noise-induced states. 

   more » « less
5. A molecular perspective on quantum information

   https://doi.org/10.1098/rspa.2023.0599  

   Scholes, Gregory D. (November 2023, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   Some of the fundamentals of quantum information science are described, including the concepts of quantum resources, quantum states and mixedness of states. The explanations are detailed and include a combination of basic facts with fully worked examples, and some more advanced topics. The principles of quantum information are illustrated with chemical examples drawn from singlet fission, photophysics of radicals, molecular excitons, electron transfer and so on. Suggestions for prospects and challenges for the field are discussed. 

   more » « less