Speaker
Description
In the first work of this joint submission (Ref. 18), we introduce a general framework for quantum simulation in the Heisenberg picture using quantum computers. Central to our approach are the vectorization and transfer matrix formalisms, which we exploit to encode Heisenberg operators $O(t)= e^{iHt} O e^{-iHt}$ as quantum states $|{O(t)}\rangle\!\rangle$ in a structure-preserving manner. As a consequence, any task naturally defined in the Heisenberg picture -- including sampling from the Pauli distribution of an operator, the computation of OTOCs (Out-of-Time-Order Correlators), two-point correlators, operator stabilizer entropies, local operator entanglement, and more -- can be mapped to tasks in the Schrodinger picture, yielding novel algorithms for their computation.
In the second work of this submission, Ref. 19, we focus on the task of simultaneously learning many correlators at once. Introducing the notion of the shadow of a Heisenberg operator, we show how it can be obtained efficiently via randomized measurements with either local or global Clifford measurements. This enables, respectively, the efficient simultaneous estimation of all low-weight OTOCs and all possible two-point correlators. Moreover, treating this as a novel information-theoretic framework to model OTOC-learning protocols, we prove fundamental information-theoretic lower bounds for the task of simultaneously estimating many OTOCs. Considering general OTOC learning protocols with various capabilities such as access to ancillas, adaptivity, and quantum memory (i.e. the ability to entangle multiple copies of the state), we prove lower bounds on certain OTOC learning tasks, which imply both the optimality of our algorithms, and exponential learning separations in several situations.
| Topic | Quantum state and process tomography with learning-based approaches |
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| Additional Topic | Theoretical foundations of quantum learning |