Process Tomography of Ion Trap Quantum Gates

Abstract

A crucial building block for quantum information processing with trapped ions is a controlled-NOT quantum gate. In this paper, two different sequences of laser pulses implementing such a gate operation are analyzed using quantum process tomography. Fidelities of up to 92.6(6) % are achieved for single gate operations and up to 83.4(8) % for two concatenated gate operations. By process tomography we assess the performance of the gates for different experimental realizations and demonstrate the advantage of amplitude-shaped laser pulses over simple square pulses. We also investigate whether the performance of concatenated gates can be inferred from the analysis of the single gates.PACS numbers: 03.65. Wj, 03.67.Lx, 32.80.Qk Processing information with well-controlled quantum systems has the fascinating perspective of being much more powerful than classical computers for certain applications. A promising candidate for the experimental realization of quantum computing are strings of ions stored in linear Paul traps [1] as recently demonstrated by various key experiments, including the preparation of multi-particle entangled states [2,3], quantum teleportation [4,5] and quantum error correction [6]. Quantum information processing depends on the ability to implement single qubit rotations and most importantly an entangling two-qubit quantum gate [7,8,9,10]. Proper characterization and understanding of the action of gate operations and their imperfections is of vital importance in order to successfully apply them in complex computations.Generally, the implementations of quantum gates are imperfect due to decoherence and various systematic error sources present in experimental setups. A proper description of such an operation which accounts for the possibly non-unitary evolution of the qubits is provided by quantum process tomography [11,12]. Process tomography has already been applied for characterizing quantum gates in NMR and linear-optics quantum computing [13,14,15]. Here, we show that process tomography is a valuable tool for comparing different ion trap quantum gate implementations and optimizing the experimental parameters. This way, we were able to improve our controlled-NOT (CNOT) gate fidelity from 71 % [7] to almost 93 %. Moreover, the action of two successively applied gate operations is investigated and compared to the predictions from the single gate tomography result.We realize entangling gates between 40 Ca + ions held in a linear trap [16]. Quantum information is stored in superpositions of the |S ≡ S 1/2 (m = −1/2) ground state and the metastable |D ≡ D 5/2 (m = −1/2) state and is manipulated by laser pulses at a wavelength of 729 nm exciting the electric quadrupole transition between those states. A focus size smaller than the inter-ion distance and precise control of the focus position allows us to address single qubits. Detection of the qubit's quantum state is achieved by scattering light on the S 1/2 ↔ P 1/2 dipole transition and detecting the presence or absence of resonance fluorescence of t...

Fidelity of a Rydberg-blockade quantum gate from simulated quantum process tomography

“…In order to characterize more completely the fidelity and usefulness of Rydberg blockade for quantum computing applications we need to perform Quantum Process Tomography (QPT) [2,29] of the Rydberg blockade mediated quantum blackbox process. QPT has been demonstrated with several different physical systems including linear optics [30], trapped ions [31], and superconducting circuits [32]. Here, we perform numerical simulations of QPT with maximum likelihood estimation of tomographically reconstructed density matrices [30] for the Rydberg-blockade C Z gate.…”

Dynamics of axialized laser-cooled ions in a Penning trap

“…Equation 17 implies that there are two frequency components in the rotating frame. Recall that in the laboratory frame, the motional frequencies are ω = ω r ± (ω 1 + δ 0 ).…”

“…with δ 0 taking the two values given by Equation (17). We can vary M by changing the cooling laser beam position and detuning from resonance.…”

“…Thus, the effect on the trapped particles of patch potentials on the surface of the electrodes should be smaller. A final advantage of Penning traps is the shielding from external magnetic-field fluctuations through the Meissner effect when a superconducting magnet is employed; magnetic field stability has been found to be a limiting factor in some other experiments [17].…”

Experimental quantum verification in the presence of temporally correlated noise

“…9,10 Each protocol has relative strengths and weaknesses; for instance, RB has low experimental overhead but only provides average information about gate performance, while process tomography provides more information at the cost of unfavourable scaling in measurement overhead. 11 Despite their differences, these protocols share the common theme that they were originally developed and mathematically formalised assuming that error processes are statistically independent and do not exhibit strong correlations in time. 1,2,10 Even in highly controlled laboratory environments there are a range of noise sources that, when applied to a qubit concurrent with logical gate operations, produce effective error models that diverge significantly from the assumptions underlying most QCVV protocols.…”