32 research outputs found
Experimentally efficient methods for estimating the performance of quantum measurements
Efficient methods for characterizing the performance of quantum measurements
are important in the experimental quantum sciences. Ideally, one requires both
a physically relevant distinguishability measure between measurement operations
and a well-defined experimental procedure for estimating the distinguishability
measure. Here, we propose the average measurement fidelity and error between
quantum measurements as distinguishability measures. We present protocols for
obtaining bounds on these quantities that are both estimable using
experimentally accessible quantities and scalable in the size of the quantum
system. We explain why the bounds should be valid in large generality and
illustrate the method via numerical examples.Comment: 20 pages, 1 figure. Expanded details and typos corrected. Accepted
versio
Gaining Information About a Quantum Channel Via Twirling
Finding correctable encoding that protects against a quantum process is in general a difficult task. Two main obstacles are that an exponential number of experiments are needed to gain complete information about the quantum process, and known algorithmic methods for finding correctable encodings involve operations on exponentially large matrices.
In this thesis we discuss how useful partial information of a quantum channel can be systematically extracted by averaging the channel under the action of a set of unitaries in a process known as twirling. We show that in some cases it is possible to find correctable encodings for the channel using the partial information obtained via twirling.
We investigate the particular case of twirling over the set of Pauli operators and qubit permutations, and show that the resulting quantum operation can be characterized experimentally in a scalable
manner. A post-processing scheme for finding
unitarily correctable codes for these twirled channels is presented which does
not involve exponentially large matrices. A test for non-Markovian noise using such a twirling process is also discussed
Characterizing Noise in Quantum Systems
In practice, quantum systems are not completely isolated from their environment and the resulting system-environment interaction can lead to information leakage from the system. As a result, if a quantum system is to be used for storing or manipulating information, one would like to characterize these environmental noise effects. Such a characterization affords one the ability to design robust methods for preserving the information contained in the system. Unfortunately, completely characterizing the noise in a realistic amount of time is impossible for even moderately large systems.
In this thesis we discuss methods and diagnostics for partially characterizing quantum noise processes that are especially useful in quantum information and computation. We present a randomized benchmarking protocol that provides a scalable method for determining important properties of the noise affecting the set of gates used on a quantum information processor. We also prove various properties of the quantum gate fidelity, which is a useful state-dependent measure of the distance between two quantum operations, and an important diagnostic of the noise affecting a quantum process. Some non-intuitive generic features of quantum operations acting on large-dimensional quantum systems are also presented
Time-resolved magnetic sensing with electronic spins in diamond
Quantum probes can measure time-varying fields with high sensitivity and
spatial resolution, enabling the study of biological, material, and physical
phenomena at the nanometer scale. In particular, nitrogen-vacancy centers in
diamond have recently emerged as promising sensors of magnetic and electric
fields. Although coherent control techniques have measured the amplitude of
constant or oscillating fields, these techniques are not suitable for measuring
time-varying fields with unknown dynamics. Here we introduce a coherent
acquisition method to accurately reconstruct the temporal profile of
time-varying fields using Walsh sequences. These decoupling sequences act as
digital filters that efficiently extract spectral coefficients while
suppressing decoherence, thus providing improved sensitivity over existing
strategies. We experimentally reconstruct the magnetic field radiated by a
physical model of a neuron using a single electronic spin in diamond and
discuss practical applications. These results will be useful to implement
time-resolved magnetic sensing with quantum probes at the nanometer scale.Comment: 8+12 page
Time-dependent Schrieffer-Wolff-Lindblad Perturbation Theory: measurement-induced dephasing and second-order Stark shift in dispersive readout
We develop a time-dependent Schrieffer-Wolff-Lindblad perturbation theory to
study effective interactions for driven open quantum systems. The starting
point of our analysis is a given Lindblad equation, based on which we obtain an
effective (averaged) map that describes the renormalization of both the
Hamiltonian and collapse operators due to the drive. As a case study, we apply
this method to the dispersive readout of a transmon qubit and derive an
effective disperive map that describes measurement-induced dephasing and Stark
shift for the transmon. The effective map we derive is completely positive and
trace-preserving under adiabatic resonator response. To benchmark our method,
we demonstrate good agreement with a numerical computation of the effective
rates via the Lindbladian spectrum. Our results are also in agreement with, and
extend upon, an earlier derivation of such effects by Gambetta et al. (Phys.
Rev. A 74, 042318 (2006)) using the positive P-representation for the resonator
field.Comment: 19 pages, 7 figures, 1 table, 7 appendice