Concatenated dynamical decoupling (CDD) pulse sequences hold much promise as a strategy to mitigate decoherence in quantum information processing. It is important to investigate the actual performance of these dynamical decoupling strategies in real systems that are promising qubit candidates. In this Rapid Communication, we compute the echo decay of concatenations of the Hahn echo sequence for a solid-state electronic spin qubit in a nuclear spin bath using a cluster expansion technique. We find that each level of concatenation reverses the effect of successive levels of intrabath fluctuations. On the one hand, this advances CDD as a versatile and realistic decoupling strategy. On the other hand, this invalidates, as overly optimistic, results of the simple pair approximation used previously to study restoration, through CDD, of coherence lost to a mesoscopic spin bath.
Concatenated dynamical decoupling (CDD) pulse sequences hold much promise as a strategy to mitigate decoherence in quantum information processing. It is important to investigate the actual performance of these dynamical decoupling strategies in real systems that are promising qubit candidates. In this Rapid Communication, we compute the echo decay of concatenations of the Hahn echo sequence for a solid-state electronic spin qubit in a nuclear spin bath using a cluster expansion technique. We find that each level of concatenation reverses the effect of successive levels of intrabath fluctuations. On the one hand, this advances CDD as a versatile and realistic decoupling strategy. On the other hand, this invalidates, as overly optimistic, results of the simple pair approximation used previously to study restoration, through CDD, of coherence lost to a mesoscopic spin bath.
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.
One of the fundamental problems of chemistry is the difficulty in determining full quantum mechanical descriptions of molecules. Molecules contain many degrees of freedom and as a result the classical description scales factorially with the number of electrons. One way to overcome this mismatch between quantum and classical pictures is to use one quantum system, a quantum computer, to simulate another. Quantum computation is based upon a two-level system, a qubit, which is analogous to a bit in classical computation. Unlike a classical bit, a qubit can exist in a superposition of quantum states. The interaction between a quantum system and its environment results in the decay of the superposition state of the system into a probability density of classical states [1]. This is known as decoherence. A realistic quantum computer requires qubits with long coherence times; with respect to the achievable gating times, for a formal relation refer to section 1.2.2. The spin echo effect in nuclear magnetic resonance (NMR) offers a way to increase the coherence time of a qubit and has been studied as a way to mitigate decoherence in quantum computation[2][3]. By applying an appropriate Π pulse to a system under the influence of a large external field, as in NMR, the interaction term of the Hamiltonian between the qubit and environment can be eliminated[3][4]. Periodic implementation of such pulses is known as periodic dynamic decoupling (PDD). Similar to PDD, concatenated dynamic decoupling (CDD) is a periodic pulse sequence which removes the interaction term of the Hamiltonian, however in CDD pulse sequences are recursively embedded within the overall pulse train. Such pulse sequences have been shown theoretically to work for model quantum systems such as GaAs quantum dots, and theoretically such pulse sequences vastly improve the coherence time of a qubit [5]. There have been many calculations showing that by progressively increasing the number of concatenated pulse sequences increasingly longer coherence times can be achieved [6][7]. These techniques have not been tested in the laboratory and experimental implementation of these promising techniques motivates current research. There also continues to be extensive work on developing novel pulse sequences which may improve coherence times even further. The goal of this research is to experimentally determine the coherence times which can be achieved with a trapped calcium atom by applying these pulse sequences.
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.
Dynamical decoupling pulse sequences have been used to extend coherence times in quantum systems ever since the discovery of the spin-echo effect. Here we introduce a method of recursively concatenated dynamical decoupling pulses, designed to overcome both decoherence and operational errors. This is important for coherent control of quantum systems such as quantum computers. For bounded-strength, non-Markovian environments, such as for the spin-bath that arises in electron- and nuclear-spin based solid-state quantum computer proposals, we show that it is strictly advantageous to use concatenated pulses, as opposed to standard periodic dynamical decoupling pulse sequences. Namely, the concatenated scheme is both fault tolerant and superpolynomially more efficient, at equal cost. We derive a condition on the pulse noise level below which concatenation is guaranteed to reduce decoherence.
Quantum information processing requires overcoming decoherence—the loss of ‘quantumness’ due to the inevitable interaction between the quantum system and its environment. One approach towards a solution is quantum dynamical decoupling—a method employing strong and frequent pulses applied to the qubits. Here we report on the first experimental test of the concatenated dynamical decoupling (CDD) scheme, which invokes recursively constructed pulse sequences. Using nuclear magnetic resonance, we demonstrate a near order of magnitude improvement in the decay time of stored quantum states. In conjunction with recent results on high fidelity quantum gates using CDD, our results suggest that quantum dynamical decoupling should be used as a first layer of defense against decoherence in quantum information processing implementations, and can be a stand-alone solution in the right parameter regime.
We experimentally demonstrate coherence recovery of singlet-triplet superpositions by interlacing qubit rotations between Carr-Purcell (CP) echo sequences. We then compare the performance of Hahn, CP, concatenated dynamical decoupling (CDD), and Uhrig dynamical decoupling for singlet recovery. In the present case, where gate noise and drift combined with spatially varying hyperfine coupling contribute significantly to dephasing, and pulses have limited bandwidth, CP and CDD yield comparable results, with T(2)∼80 μs.