Quantum state tomography of large nuclear spins in a semiconductor quantum well: Optimal robustness against errors as quantified by condition numbers

Abstract

We discuss methods of quantum state tomography for solid-state systems with a large nuclear spin I = 3/2 in nanometer-scale semiconductors devices based on a quantum well. Due to quadrupolar interactions, the Zeeman levels of these nuclear-spin devices become nonequidistant, forming a controllable four-level quantum system (known as quartit or ququart). The occupation of these levels can be selectively and coherently manipulated by multiphoton transitions using the techniques of nuclear magnetic resonance (NMR) [Yusa et al., Nature (London) 434, 101 (2005)]. These methods are based on an unconventional approach to NMR, where the longitudinal magnetization Mz is directly measured. This is in contrast to the standard NMR experiments and tomographic methods, where the transverse magnetization Mxy is detected. The robustness against errors in the measured data is analyzed by using the condition number based on the spectral norm. We propose several methods with optimized sets of rotations yielding the highest robustness against errors, as described by the condition number equal to 1, assuming an ideal experimental detection. This robustness is only slightly deteriorated, as given by the condition number equal to 1.05, for a more realistic "noisy" Mz detection based on the standard cyclically-ordered phase sequence (CYCLOPS) method.

Landauer-Büttiker approach for hyperfine mediated electronic transport in the integer quantum Hall regime

“…Materials with four nuclear spin levels (GaAs) and nine nuclear spin levels (InAs) offer attractive options since multi-bits of information can be stored and manipulated. An attractive method to manipulate the individual spin levels is introducing quadrupolar splitting which creates a slight difference in the splitting energy of consecutive nuclear spin levels [17,[42][43][44].…”

Optimal choice of state tomography quorum formed by projection operators

“…However, in this paper, we will restrict the discussion to projective measurements. Further note that if loss in the measurement * violeta@math.bas.bg † niklas.rohling@ntnu.no process has to be taken into account, which effectively refers to Trρ < 1, the optimal choice of the measurement set is different from MUBs [21][22][23]. In that situation n 2 parameters have to be determined.…”

Protocol of a quantum walk in circuit QED

“…In [40], a 1D DTQW scheme is proposed, in which a pair of superconducting qubits are used as a node and nearest-neighbor qubits are coupled In recent years, quantum information processing with qudits ( d-level systems), including qutrits (i.e., d = 3), has been attracting increasing interest, since qudits (with d > 2) can be used to encode more information. For example, quantum information processing and tomography of nanoscale semiconductor devices were studied [41,42]. In [43,44], schemes for quantum state transfer of a qutrit in circuit QED were proposed.…”