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Quantum System Identification by Local Measurements

May 16, 2019 - 10:30am
Akira Sone
Harvard University

Quantum information processing, including quantum computation, quantum communication, and
quantum metrology, is expected to be the next-generation information technology capable of
outperforming classical devices. The physical platform for quantum information devices requires many-
body quantum systems with many interacting qubits (two-level systems), and several experimental
systems have been actively studied in recent years for realizing such scalable quantum information
processors. Reliable quantum information processing essentially requires robust initialization of the
quantum system, robust control protocols and precise measurement. As these indispensable tasks strongly
depend on the physical properties and dynamics of the quantum system, the precise characterization of the
experimental system, namely quantum system identification, is a crucial prerequisite.

In a closed quantum system, the Hamiltonian includes the information about the properties of the
system, such as the number of qubits, single-body energy of qubits, topology of qubit network graph and
coupling types between qubits. For thermal equilibrium state, the temperature also becomes an important
parameter characterizing the thermal properties of the system. Quantum system identification aims at
extracting these elements from measurements of the system dynamics or state. However, performing
measurement over the whole many-qubit system is typically a demanding task in the laboratory.
Furthermore, given the lack of knowledge about the system, one cannot control or measure the system
with high accuracy before characterizing it. Thanks to recent advances in quantum metrology with a
single qubit sensor, a well-characterized qubit system can play the role of a quantum probe, which is
coherently coupled to the target system, thus enabling practical schemes to identify the target many-body
quantum system indirectly through system-probe correlations. More broadly, this quantum probe strategy
is an example of system identification performed via local measurements.

This presentation focuses on the role of quantum correlations in quantum system identification assisted
by local measurements in two different regimes: (1) dynamical and (2) equilibrium regime.
In the dynamical regime, we introduce the mathematical concept of quantum system identifiability
with respect to Hamiltonian parameter identification and Hilbert space dimension identification.
Exploiting the linearity of the dynamics, we employ linear system realization theory, algebraic geometry
and graph-theory to analyze the identifiability of an unknown Hamiltonian or the dimensions of the
Hilbert space of the target many-body quantum system. Based on the formalism, we propose practical
algorithms for both identifiability problems. We further find that propagation of correlations between the
quantum probe and the whole system is a necessary condition to fully identify the parameters and
dimensions of the target system through local measurements on the quantum probe.

In the equilibrium regime, the thesis discusses the problem of estimating either the temperature or
Hamiltonian parameters, which can in general be extracted by characterizing the thermal equilibrium
state. We discuss a general local measurement scheme, which we call “greedy local measurement
scheme", where one performs sequential optimal measurement on a complete set of subsystems. We
introduce a practical measure of nonclassical correlations, called discord for local metrology, to measure
the nonclassical correlations induced by local optimal measurements. By comparing the greedy local
measurement scheme and global measurement scheme, we explicitly demonstrate that in the high-
temperature limit discord for local metrology quantifies the ultimate precision limit loss in local
metrology. Conversely, this shows that nonclassical correlations could contribute to sensitivity
enhancement in parameter estimation even at thermal equilibrium.

These results can be expected to contribute to the characterization of near-term quantum information
processors, such as Noisy Intermediate-Scale Quantum (NISQ) devices, and to find applications in
quantum sensing, e.g. in room-temperature nanoscale magnetic resonance sensing of nuclear spins in
molecules or imaging of biological complex systems.

PSC 2136