There are several important solid-state systems, such as defects in solids, superconducting circuits and molecular qubits, for attractive candidates of quantum computations. Molecular qubits, which benefit from the power of chemistry for the tailored and inexpensive synthesis of new systems, face the challenge from decoherence effect. The decoherence effect is due to the molecular qubits' inevitable interactions to their environment. Strategies to overcome decoherence effect have been developed, such as designing a nuclear spin free environment and working at atomic clock transitions. These chemical approaches, however, have some fundamental limitations. For example, chemical approach restricts the ligand selection and design to ligands with zero nuclear magnetic dipole moment, such as carbon, oxygen, and sulfur. Herein, a physical approach, named Dynamical decoupling (DD), is utilized to combat decoherence, while the limitations of the chemical approaches can be avoided. The phase memory time
T2 for a transition metal complex has been prolonged to exceed one millisecond (
1.4 ms) by employing DD. The single qubit figure of merit $Q_M $ reaches $ 1.4\times 10^5$, which is
40 times better than that previously reported value for such system. Our results show that molecular qubits, with milliseconds
T2, are promising candidates for quantum information processing.
Molecular qubits are promising as they can benefit from tailoring and versatile design of chemistry. It is essential to reduce the decoherence of molecular qubits caused by their interactions with the environment. Herein the dynamical decoupling (DD) technique is utilized to combat such decoherence. The coherence time for a transition-metal complex (PPh4)2[Cu(mnt)2] is prolonged from 6.8 μs to 1.4 ms. The ratio of the coherence time and the length of π/2 pulse, defined as the single qubit figure of merit (Q M), reaches 1.4 × 105, which is 40 times greater than what previously reported for this molecule. Our results show that molecular qubits, with milliseconds coherence time, are promising candidates for quantum information processing.
Decoherence is one of the most important obstacles that must be overcome in quantum information processing. It depends on the qubit-environment coupling strength, but also on the spectral composition of the noise generated by the environment. If the spectral density is known, fighting the effect of decoherence can be made more effective. Applying sequences of inversion pulses to the qubit system, we developed a method for dynamical decoupling noise spectroscopy. We generate effective filter functions that probe the environmental spectral density without requiring assumptions about its shape. Comparing different pulse sequences, we recover the complete spectral density function and distinguish different contributions to the overall decoherence.
A qubit subjected to pure dephasing due to classical Gaussian noise can be turned into a spectrometer of this noise by utilizing its readout under properly chosen dynamical decoupling (DD) sequences to reconstruct the power spectral density of the noise. We review the theory behind this DD-based noise spectroscopy technique, paying special attention to issues that arise when the environmental noise is non-Gaussian and/or it has truly quantum properties. While we focus on the theoretical basis of the method, we connect the discussed concepts with specific experiments, and provide an overview of environmental noise models relevant for solid-state based qubits, including quantum-dot based spin qubits, superconducting qubits, and NV centers in diamond.
We present a study of the prospects for coherence preservation in solid-state spin qubits using dynamical decoupling protocols. Recent experiments have provided the first demonstrations of multipulse dynamical decoupling sequences in this qubit system, but quantitative analyses of potential coherence improvements have been hampered by a lack of concrete knowledge of the relevant noise processes. We present calculations of qubit coherence under the application of arbitrary dynamical decoupling pulse sequences based on an experimentally validated semiclassical model. This phenomenological approach bundles the details of underlying noise processes into a single experimentally relevant noise power spectral density. Our results show that the dominant features of experimental measurements in a two-electron singlet-triplet spin qubit can be replicated using a $1/{\ensuremath{\omega}}^{2}$ noise power spectrum associated with nuclear spin flips in the host material. Beginning with this validation, we address the effects of nuclear programming, high-frequency nuclear spin dynamics, and other high-frequency classical noise sources, with conjectures supported by physical arguments and microscopic calculations where relevant. Our results provide expected performance bounds and identify diagnostic metrics that can be measured experimentally in order to better elucidate the underlying nuclear spin dynamics.
I present a theory of environmental noise spectroscopy via dynamical decoupling of a qubit at an optimal working point. Considering a sequence of
n pulses and pure dephasing due to quadratic coupling to Gaussian distributed noise $\ensuremath{\xi}(t)$, I use the linked-cluster (cumulant) expansion to calculate the coherence decay. Solutions allowing for reconstruction of spectral density of noise are given. For noise with correlation time shorter than the time scale on which coherence decays, the noise filtered by the dynamical decoupling procedure can be treated as effectively Gaussian at large
n, and well-established methods of noise spectroscopy can be used to reconstruct the spectrum of ${\ensuremath{\xi}}^{2}(t)$ noise. On the other hand, for noise of dominant low-frequency character $(1/{f}^{\ensuremath{\beta}}$ noise with $\ensuremath{\beta}>1)$, an infinite-order resummation of the cumulant expansion is necessary, and it leads to an analytical formula for coherence decay having a power-law tail at long times. In this case, the coherence at time
t depends both on spectral density of $\ensuremath{\xi}(t)$ noise at $\ensuremath{\omega}=n\ensuremath{\pi}/t$, and on the effective low-frequency cutoff of the noise spectrum, which is typically given by the inverse of the data acquisition time. Simulations of decoherence due to purely transverse noise show that the analytical formulas derived in this paper apply in this often encountered case of an optimal working point, provided that the number of pulses is not very large, and that the longitudinal qubit splitting is much larger than the transverse noise amplitude.