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arXiv:2303.12655

Towards the coherent control of robust spin qubits in quantum algorithms

Luis Escalera‐Moreno

Published Mar 10, 2023• 1 citation
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Abstract

Many efforts have succeeded over the last decade at lengthening the timescale in which spin qubits loss quantum information under free evolution. With these design principles at a mature stage, it is now timely to widen the scope and take the whole picture: concerning applications that require user-driven coherent evolutions, qubits should be assessed operating within the desired algorithm. This means to test qubits under external control while relaxation and imperfections are active, and to maximize the algorithm fidelity as the actual figure of merit. Herein, we pose and analytically solve a master equation devised to run one-spin-qubit gate-based algorithms subject to relaxation. It is handled via a home-made code, QBithm, which inputs gate sequences and relaxation rates thus connecting with the longstanding work devoted to their $\textit{ab initio}$ computation. We evaluate the impact of relaxation and potential experimental imperfections in the calculated fidelities, and implement well-known pulse sequences quantitatively agreeing with experimental data. Hopefully, this work will stimulate the study of many-spin-qubit systems in quantum algorithms, and will serve as a help to design robust spin qubits against decoherence and to perform better-characterized experiments.

DOI
10.48550/arxiv.2303.12655

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Many efforts have succeeded over the last decade at lengthening the timescale in which spin qubits loss quantum information under free evolution. With these design principles at a mature stage, it is now timely to widen the scope and take the whole picture: concerning applications that require user-driven coherent evolutions, qubits should be assessed operating within the desired algorithm. This means to test qubits under external control while relaxation and imperfections are active, and to maximize the algorithm fidelity as the actual figure of merit. Herein, we pose and analytically solve a master equation devised to run one-spin-qubit gate-based algorithms subject to relaxation. It is handled via a home-made code, QBithm, which inputs gate sequences and relaxation rates thus connecting with the longstanding work devoted to their ab initio\textit{ab initio}ab initio computation. We evaluate the impact of relaxation and potential experimental imperfections in the calculated fidelities, and implement well-known pulse sequences quantitatively agreeing with experimental data. Hopefully, this work will stimulate the study of many-spin-qubit systems in quantum algorithms, and will serve as a help to design robust spin qubits against decoherence and to perform better-characterized experiments.
Many efforts have succeeded over the last decade at lengthening the timescale in which spin qubits loss quantum information under free evolution. With these design principles, it is now timely to zoom out and take the whole picture: concerning applications that require user-driven evolutions, qubits should be assessed within the desired algorithm. This means to test qubits under external control while relaxation is active, and to maximize the algorithm fidelity as the actual figure of merit. Herein, we pose and analytically solve a master equation devised to run one-spin-qubit algorithms subject to relaxation. It is handled via a code, QBithm, which inputs gate sequences and relaxation rates thus connecting with the longstanding work devoted to their ab initio computation. We calculate fidelities against relaxation and imperfections, and implement well-known pulse sequences quantitatively agreeing with experimental data. Hopefully, this work will stimulate the study of many-qubit systems driven under relaxation and imperfections in quantum algorithms.
Many efforts have succeeded over the last decade at lengthening the timescale in which spin qubits loss quantum information under free evolution. With these design principles, it is now timely to zoom out and take the whole picture: concerning applications that require user-driven evolutions, qubits should be assessed within the desired algorithm. This means to test qubits under external control while relaxation is active, and to maximize the algorithm fidelity as the actual figure of merit. Herein, we pose and analytically solve a master equation devised to run one-spin-qubit algorithms subject to relaxation. It is handled via a code, QBithm, which inputs gate sequences and relaxation rates thus connecting with the longstanding work devoted to their ab initio computation. We calculate fidelities against relaxation and imperfections, and implement well-known pulse sequences quantitatively agreeing with experimental data. Hopefully, this work will stimulate the study of many-qubit systems driven under relaxation and imperfections in quantum algorithms.
This paper presents a novel dynamic quantum decoherence correction algorithm designed to mitigate the detrimental effects of decoherence on quantum information processing. Decoherence, the loss of quantum coherence due to interactions with the environment, remains a significant obstacle to the reliable implementation of quantum technologies. Our algorithm leverages real-time monitoring and adaptive control strategies to actively counteract decoherence, aiming to preserve quantum information fidelity. The core principle involves precisely modulating the state of individual quantum bits (qubits) using quantum control techniques, effectively reducing the decoherence rate. We detail the mathematical framework underpinning the algorithm, including the relevant equations governing decoherence and the control pulses employed. The algorithm's dynamic nature allows it to respond to changes in the decoherence environment, offering a more robust solution compared to static correction methods. Simulation results (presented within) demonstrate the algorithm's efficacy in maintaining coherence for extended periods, highlighting its potential for applications in quantum communication, quantum computation, and quantum sensing. Finally, we outline potential future research directions and challenges associated with the broader implementation of this dynamic decoherence correction approach.
Quantum algorithms for problems such as integer factorization and database search have spurred great interest in quantum computation. However, the construction of scalable quantum computers has proved to be extremely difficult. Among the challenging requirements that must be fulfilled in the “standard model” of quantum computation, one must be able to initialize qubits into known pure states. In addition, quantum computers must be protected from noise due to unwanted interactions with their environment. This work is concerned with two theoretical issues motivated by these difficulties. First, I analyze the efficiency of an algorithm for an alternate model for quantum computation that is motivated by bulk nuclear magnetic resonance. In such ensemble systems, the initial state is not a fiducial pure state, but is instead a maximally-mixed density operator. The algorithm that I consider allows one to estimate the free energy of arbitrary spin-1/2 lattice models. To determine the efficiency of this algorithm, I calculate the computation time required to estimate the free energy to bounded error as a function of the lattice size. In the absence of stochastic fluctuations in the measurement output, it is found that the algorithm is efficient. However, evidence is presented that suggests that the algorithm becomes exponentially sensitive to fluctuations as the lattice size increases. While techniques such as quantum error-correcting codes and decoherence-free subsystem encodings have been devised to mitigate errors due to unwanted environmental couplings, these methods require many additional qubits or complicated encodings. Here, I investigate a simple approach to reduce errors in the quantum search algorithm due to a collective decoherence model. This method takes advantage of the freedom inherent in compiling the search algorithm into fundamental gates. Transition rate calculations and more rigorous quantum master equation simulations are carried out for small-qubit instances to contrast the performance of the original and modified algorithm. It is shown that the expected computational effort can be reduced by 22% for selected five-bit instances of the quantum search algorithm. While this approach does not constitute a general strategy for quantum error-correction, it illustrates the importance of judicious gate design in mitigating decoherence.
Abstract The coherent dynamics and control of spin qubits are fundamental requirements for the development and implementation of quantum technology. However, controlling a single spin qubit within a set of qubits is challenging due to the spatial extent of the applied magnetic field, which can negatively impact the coherent dynamics of neighboring qubits. In this study, a scheme is proposed for characterizing and controlling the coherent dynamics of spin qubits. The proposed scheme comprises a resonator that encloses the desired quantum system and a modulated electron beam that passes through the resonator in close proximity to the qubit of interest. The scheme involves solving the quantum master equation with Lindblad terms to obtain the system's dynamics. Reliability of the proposed model is validated by testing it on a potassium atom, 41 K, and an NV ‐ center in diamond. The results demonstrate that by controlling the parameters of the resonator and electron beam, the coherence and decoherence rates of these quantum systems can be enhanced. The proposed scheme has the potential to characterize various types of spin‐based quantum systems and implement quantum logic gates for quantum computation .
An exquisite control over the dynamics of a quantum system is essential for realizing any quantum technology. This thesis presents some practical and efficient strategies for coherent quantum control: a paradigm for controlling quantum dynamics using electromagnetic fields. Coherent control is a common framework for describing the physical implementation of quantum logic gates in several quantum information processing platforms including superconducting qubits and trapped ions. For the purpose of demonstration, however, liquid-state Nuclear Magnetic Resonance (NMR) is used in this thesis as it is an ideal test-bed for developing, testing and benchmarking coherent control tools and techniques. Coherent control was revitalised in 2005 by the development of Gradient Ascent Pulse Engineering (GRAPE), a powerful optimal control technique that is widely used for designing shaped pulses for a variety of tasks. GRAPE, like any other closed-loop optimal control algorithm, requires multiple evaluations of the computationally expensive matrix exponential and the full time-evolution propagator. To this end, I present strategies to sidestep the explicit evaluation of matrix exponentials, thereby offering substantial speed-ups over conventional implementations of the GRAPE algorithm. The results are demonstrated experimentally in NMR, but also in simulations of ultracold molecules and superconducting qubits. Beyond GRAPE, this thesis also considers methods for designing spin-echo sequences for implementing any arbitrary network of controlled-Z gates in a system of qubits with zz-couplings. First, a method based on linear-programming provides near time-optimal sequences in fully-coupled systems having up to a few hundred qubits. Further, an analytic method based on graph colouring finds near time-optimal spin echo sequences in engineered systems with any number of qubits having only nearest and next-nearest neighbour-couplings.