arXiv subjects

Larissa Kroell

Publications and source records attributed to Larissa Kroell.

5 recordsLinked to original sources

arXiv2026

Quantum Resource Estimation for Simulating the SYK Model with Trotterization, qDRIFT, and Asymmetric Qubitization

The Sachdev-Ye-Kitaev (SYK) model has been identified as a promising candidate to run on early fault-tolerant quantum computers due to the relatively modest resources required to probe non-trivial physics (namely holographic duality and AdS/CFT correspondence). As such, it is crucial that the details of how to run such a simulation are well understood. Using PsiQuantum's Construct platform, we implement and analyze three different approaches to simulate the SYK model: Trotterization, qDRIFT, and asymmetric qubitization with Quantum Signal Processing. We provide an open-source library containing implementations for SYK simulation using all three methods, which we use to obtain quantum resource estimates for qubit and T gate count as functions of the number of Majorana modes and precision. We find that while qDRIFT and Trotterization benefit from a lower qubit count, the large number of T gates required lead to asymmetric qubitization being advantageous in most cases. This reinforces previous theoretical considerations. We intend both the implementations and the estimates to be useful for researchers to continue to study the SYK model and understand how the techniques and resources vary.

quant-ph↗

arXiv2026

Injective envelopes of partial C*-dynamical systems

We extend Hamana's theory of injective envelopes, along with several key features of the theory, to the realm of partial C*-dynamical systems. In particular, we show that a partial C*-dynamical system has the ideal intersection property if and only if its injective envelope does. A key ingredient in our arguments is a new kind of unitization of a partial action on a unital C*-algebra $A$ arising from the C*-algebra generated by the orbits of $A$ in its injective envelope~$I(A)$. For an arbitrary unital partial C*-dynamical system, which is known to have an enveloping action, we establish a natural relationship between the injective envelope of the system and the injective envelope of its enveloping action. For an abelian partial C*-dynamical system, we show that our construction coincides with the algebra of continuous functions on the Furstenberg boundary of the corresponding transformation groupoid. It is crucial in our work to consider a notion of generalized unital partial C*-dynamical systems, in which the unital ideals are replaced by unital hereditary subalgebras.

math.OA↗

arXiv2026

Approximate factorization properties for operator systems

We show that many of the standard nuclearity properties considered in the literature for the hierarchy of operator system tensor products can be expressed as approximate factorization properties, generalizing the well-known Completely Positive Approximation Property for nuclear C*-algebras due to Choi and Effros and its generalization to nuclear operator systems due to Han and Paulsen.

math.OA↗

arXiv2025

The NPA hierarchy does not always attain the commuting operator value

We show that it is undecidable to determine whether the commuting operator value of a nonlocal game is strictly greater than 1/2. Specifically, there is a computable mapping from Turing machines to /boolean constraint system (BCS) nonlocal games in which the halting property of the machine is encoded as a decision problem for the commuting operator value of the game. As a corollary, there is a BCS game for which the value of the Navascués-Pironio-Acín (NPA) hierarchy does not attain the commuting operator value at any finite level.

quant-ph↗

arXiv2025

Primality and the ideal intersection property for reduced crossed products

We consider the ideal structure of reduced crossed products over discrete groups. First, we completely characterize primality for reduced crossed products. Second, we characterize the ideal intersection property for reduced crossed products over FC-hypercentral groups. Both of these characterizations are intrinsic, in terms of conditions on the underlying dynamics. A key intermediate result is a complete characterization of the regular ideal intersection property for reduced crossed products. For C*-dynamical systems over groups with restrictive subgroup structure, these characterizations simplify even further, which we demonstrate with a number of examples.

math.OA↗