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  1. Free, publicly-accessible full text available December 1, 2024
  2. Wave function ansatze based on the backflow transformation are widely used to parametrize anti-symmetric multivariable functions for many-body quantum problems. We study the geometric aspects of such ansatze, in particular we show that in general totally antisymmetric polyno- mials cannot be efficiently represented by backflow transformation ansatze at least in the category of polynomials. In fact, if there are $N$ particles in the system, one needs a linear combination of at least $O(N^{3N−3})$ determinants to represent a generic totally antisymmetric polynomial. Our proof is based on bounding the dimension of the source of the ansatze from above and bounding the dimension of the target from below. 
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    Free, publicly-accessible full text available October 1, 2024
  3. In cloud-native environments, containers are often deployed within lightweight virtual machines (VMs) to ensure strong security isolation and privacy protection. With the growing demand for customized cloud services, third-party vendors are turning to infrastructure-as-a-service (IaaS) cloud providers to build their own cloud-native platforms, necessitating the need to run a VM or a guest that hosts containers inside another VM instance leased from an IaaS cloud. State-of-the-art nested virtualization in the x86 architecture relies heavily on the host hypervisor to expose hardware virtualization support to the guest hypervisor, not only complicating cloud management but also raising concerns about an increased attack surface at the host hypervisor. This paper presents the design and implementation of PVM, a high-performance guest hypervisor for KVM that is transparent to the host hypervisor and assumes no hardware virtualization support. PVM leverages two key designs: 1) a minimal shared memory region between the guest and guest hypervisor to facilitate state transition between different privilege levels and 2) an efficient shadow page table design to reduce the cost of memory virtualization. PVM has been adopted by a major IaaS cloud provider for hosting tens of thousands of secure containers on a daily basis. Our experiments demonstrate that PVM significantly outperforms current nested virtualization in KVM for memory virtualization, particularly for concurrent workloads, while maintaining comparable performance in CPU and I/O virtualization. 
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