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.
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/\ensuremathω2 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.
This dissertation is a study of the decoherence of a solid-state spin qubit, either that of a localized electron spin or a donor nucleus, caused by a nuclear spin bath relevant to semiconductor quantum computer architectures. In the presence of an external magnetic field and at low temperatures, the dominant decoherence mechanism is the spectral diffusion of the qubit spin resonance frequency due to the temporally fluctuating random magnetic field associated with the dipolar interaction induced flip-flops of nuclear spin pairs. The qubit spin dephasing due to this random magnetic field depends intricately on the quantum dynamics of the nuclear spin bath, making the coupled decoherence problem difficult to solve. We provide a formally exact solution of this non-Markovian quantum decoherence problem which numerically calculates accurate spin decoherence at short times, of particular relevance in solid-state spin quantum computer architectures. A quantum cluster expansion method is motivated, developed, and tested for the spectral diffusion problem. The method is applicable to any ideal pulse sequence applied to the qubit. Dynamical decoupling sequences, which aim to prolong qubit coherence, are analyzed. In particular, concatenated dynamical decoupling sequences are shown to prolong not only the coherence time over the entire sequence but also the length of time between pulses necessary to maintain coherence. This is shown to result from successive low-order cancellations in applicable perturbative expansions with each level of concatenation. Each cancellation, however, will require the inclusion, in the cluster expansion, of increasingly large clusters to obtain the lowest-order results. These larger clusters in the lowest order often dominate decoherence and therefore invalidate, as being overly optimistic, the pair approximation as a means to study the effect of concatenated dynamical decoupling. We present numerical results from our cluster expansion technique for echoes of single (Hahn), concatenated, and periodic pulse sequences using realistic models of a localized electron in phosphorus doped Si and in a GaAs quantum dot and of a P donor nucleus in Si or GaAs. In the Si:P electron spin decoherence problem, we consider, along with spectral diffusion, the effects of anisotropic hyperfine (AHF) interactions and suggest a technique to suppress electron spin echo envelope modulations (ESEEM), an additional source of decoherence resulting from the AHF interactions. Our calculations for the Si:P Hahn echoes, including the effects of both anisotropic hyperfine interactions and spectral diffusion, are in excellent agreement with experimental results. Our calculations of concatenated pulse sequence echoes offer important predictions for the effectiveness of a promising strategy to preserve qubit coherence in semiconductor quantum computer architectures.
Avoiding the loss of coherence of quantum mechanical states is an important prerequisite for quantum information processing. Dynamical decoupling (DD) is one of the most effective experimental methods for maintaining coherence, especially when one can access only the qubit system and not its environment (bath). It involves the application of pulses to the system whose net effect is a reversal of the system-environment interaction. In any real system, however, the environment is not static, and therefore the reversal of the system-environment interaction becomes imperfect if the spacing between refocusing pulses becomes comparable to or longer than the correlation time of the environment. The efficiency of the refocusing improves therefore if the spacing between the pulses is reduced. Here, we quantify the efficiency of different DD sequences in preserving different quantum states. We use 13C nuclear spins as qubits and an environment of 1H nuclear spins as the environment, which couples to the qubit via magnetic dipole-dipole couplings. Strong dipole-dipole couplings between the proton spins result in a rapidly fluctuating environment with a correlation time of the order of 100 $\ensuremath{\mu}$s. Our experimental results show that short delays between the pulses yield better performance if they are compared with the bath correlation time. However, as the pulse spacing becomes shorter than the bath correlation time, an optimum is reached. For even shorter delays, the pulse imperfections dominate over the decoherence losses and cause the quantum state to decay.
With the power of chemistry for inexpensive synthesis of tailored systems, molecular qubits are attractive candidates for quantum computing. Here decoherence persists as a major obstacle; for its effective suppression, the properties of environmental noise must be elucidated. Traditional noise spectroscopy with spurious harmonics leads to false identification of nuclear spins. The authors demonstrate a protocol for noise-spectrum analysis without spurious harmonics, through dynamical decoupling. This result enables enhanced coherence for molecular qubits, and could be quite significant for quantum information processing based on such systems.
The optimization of dynamical decoupling and quantum error correction for a particular qubit realization is based on a detailed knowledge of the noise properties. Spectroscopy of single-axis noise using dynamical decoupling pulse sequences has garnered much recent attention. Here we consider noise spectroscopy based on a spin-locking type pulse sequence, i.e. a continuous-wave (CW) on-resonance driving field. We show that a heuristic filter function approach produces a qualitatively correct (but quantitatively incorrect) result, whereas a 0th-order average Hamiltonian calculation is shown to agree with the result predicted by the generalized Bloch equations. We further calculate up to 2nd-order average Hamiltonian corrections and show the deviation from the generalized Bloch equation result. This shows that noise spectroscopy using continuous fields, in some cases simpler to implement and more robust to errors than pulsed schemes, can be rigorously analyzed and criteria for reliable measurements can be established. Finally, a solid-state nuclear magnetic resonance experiment is presented which demonstrates that the CW and pulsed methods agree within experimental error. The noise, due to magnetization fluctuations in a dipolar coupled proton spin bath, is found to obey a roughly 1/ω power law decay in the range of frequencies ω investigated.
The dynamics of a nuclear spin bath generates magnetic noise that is a key contributor to the decoherence of electron spin qubits in electrostatically-defined quantum dots. In this paper, we extend the cluster correlation expansion (CCE) technique, which has proven useful for predicting solid-state qubit coherence times across various settings but is limited to shorter time scales, to incorporate stochastic treatments of cluster dynamics in order to efficiently predict slow drifting Overhauser fields over longer time scales. This approach combines quantum evolution with classical rate matrices to enable simulation across a wide range of temporal regimes required to simulate, for example, the long-time convergence of the ergodic T2∗ from Ramsey experiments. Our methodology is validated against experimental data from various silicon spin qubit systems, demonstrating a strong agreement between simulation and measurement of Ramsey experiments presented in the form of T2∗ versus averaging time, autocorrelation functions, as well as power spectral densities. Furthermore, we demonstrate significant back-action effects through modeling and experiment; specifically, the dynamics of the nuclear spin bath depends upon the electron spin occupation schedule. Finally, our modeling quantitatively predicts the benefits from compensating for the slow drift of Overhauser fields in qubit operations. Our findings indicate that compensating for an Overhauser rotation measured Δt in the past results in an effective T2∗, which we denote T~2∗(Δt) for clarity, under certain scenarios of interest, can be one or two orders of magnitude larger than the ergodic T2∗ if the Overhauser rotation is re-characterized every 100 milliseconds; that is, T~2∗(Δt=100ms) can be 10 to 100 times larger than T2∗.
Maintaining quantum coherence is a crucial requirement for quantum computation; hence protecting quantum systems against their irreversible corruption due to environmental noise is an important open problem. Dynamical decoupling (DD) is an effective method for reducing decoherence with a low control overhead. It also plays an important role in quantum metrology, where, for instance, it is employed in multiparameter estimation. While a sequence of equidistant control pulses [the Carr-Purcell-Meiboom-Gill (CPMG) sequence] has been ubiquitously used for decoupling, Uhrig recently proposed that a nonequidistant pulse sequence [the Uhrig dynamic decoupling (UDD) sequence] may enhance DD performance, especially for systems where the spectral density of the environment has a sharp frequency cutoff. On the other hand, equidistant sequences outperform UDD for soft cutoffs. The relative advantage provided by UDD for intermediate regimes is not clear. In this paper, we analyze the relative DD performance in this regime experimentally, using solid-state nuclear magnetic resonance. Our system qubits are 13C nuclear spins and the environment consists of a 1H nuclear spin bath whose spectral density is close to a normal (Gaussian) distribution. We find that in the presence of such a bath, the CPMG sequence outperforms the UDD sequence. An analogy between dynamical decoupling and interference effects in optics provides an intuitive explanation as to why the CPMG sequence performs better than any nonequidistant DD sequence in the presence of this kind of environmental noise.