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arXiv:1706.08364 · Physical review. B./Physical review. B

Relaxation and decoherence of qubits encoded in collective states of engineered magnetic structures

Alexey M. Shakirov, Alexey N. Rubtsov, Alexander I. Lichtenstein, Pedro Ribeiro

Published Sep 11, 2017• 9 citations
arXivHTMLPDF

Abstract

The quantum nature of a microscopic system can only be revealed when it is sufficiently decoupled from surroundings. Interactions with the environment induce relaxation and decoherence that turn the quantum state into a classical mixture. Here, we study the timescales of these processes for a qubit encoded in the collective state of a set of magnetic atoms deposited on a metallic surface. For that, we provide a generalization of the commonly used definitions of ${T}_{1}$ and ${T}_{2}$ characterizing relaxation and decoherence rates. We calculate these quantities for several atomic structures, including a collective spin, a setup implementing a decoherence-free subspace, and two examples of spin chains. Our work contributes to the comprehensive understanding of the relaxation and decoherence processes and shows the advantages of the implementation of a decoherence free subspace in these setups.

DOI
10.1103/physrevb.96.094410

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The quantum nature of a microscopic system can only be revealed when it is sufficiently decoupled from surroundings. Interactions with the environment induce relaxation and decoherence that turn the quantum state into a classical mixture. Here, we study the timescales of these processes for a qubit encoded in the collective state of a set of magnetic atoms deposited on a metallic surface. For that, we provide a generalization of the commonly used definitions of T1{T}_{1}T1​ and T2{T}_{2}T2​ characterizing relaxation and decoherence rates. We calculate these quantities for several atomic structures, including a collective spin, a setup implementing a decoherence-free subspace, and two examples of spin chains. Our work contributes to the comprehensive understanding of the relaxation and decoherence processes and shows the advantages of the implementation of a decoherence free subspace in these setups.
Decoherence-free subspaces protect quantum information from the effects of noise that is correlated across the physical qubits used to implement them. Given the ability to impose suitable Hamiltonians upon such a multi-qubit system, one can also implement a set of logical gates which enables universal computation on this information without compromising this protection. Real physical systems, however, seldom come with the correct Hamiltonians built-in, let alone the ability to turn them off and on at will. In the course of our development of quantum information processing devices based on liquid-state NMR, we have found the task of operating on quantum information encoded in decoherence-free subspaces rather more challenging than is commonly assumed. This contribution presents an overview of these challenges and the methods we have developed for overcoming them in practice. These methods promise to be broadly applicable to many of the physical systems proposed for the implementation of quantum information processing devices.
In a two-qubit system the coupling with an environment considerably affects the entanglement dynamics, usually leads to the loss of entanglement within a finite time. Since entanglement is a key feature in the application of such systems to quantum information processing, it is highly desirable to find a way to prolonging its lifetime. We present a simple model of an interacting two-qubit system in the presence of a thermal Markovian environment. The qubits are modeled as interacting spin-1∕21∕21∕2 particles in a magnetic field and the environment is limited to inducing single spin-flip events. A simple scheme allows us to calculate the relaxation rates for all processes. We show that the relaxation dynamics of the most entangled state exhibit critical slowing down as a function of the magnetic field, where the relaxation rate changes from exponentially small values to finite values in the zero-temperature limit. We study the effect of temperature and magnetic field on all the other relaxation rates and find that they exhibit unusual properties, such as nonmonotonic dependence on temperature and a discontinuity as a function of magnetic field. In addition, a simple scheme to include non-Markovian effects is presented and applied to the two-qubit model. We find that the relaxation rates exhibit a sharp, cusplike resonant structure as a function of the environment memory time, and that for long memory times all the different relaxation rates merge into a single one.
Due to omnipresent environmental interferences, quantum coherences inevitably undergo irreversible transformations over certain time scales, thus leading to the loss of encoded information. This process, known as decoherence, has been a major obstacle in realizing efficient quantum information processors. Understanding the mechanism of decoherence is crucial in developing tools to inhibit it. Here we utilize a method proposed by Teklemariam et al. [Phys. Rev. A 67, 062316 (2003)] to engineer artificial decoherence in the system qubits by randomly perturbing their surrounding ancilla qubits. Using a two-qubit nuclear magnetic resonance quantum register, we characterize the artificial decoherence by noise spectroscopy and quantum process tomography. Further, we study the efficacy of dynamical decoupling sequences in suppressing the artificial decoherence. Here we describe the experimental results and their comparisons with theoretical simulations.
We report on the immersion of a spin-qubit encoded in a single trapped ion into a spin-polarized neutral atom environment, which possesses both continuous (motional) and discrete (spin) degrees of freedom. The environment offers the possibility of a precise microscopic description, which allows us to understand dynamics and decoherence from first principles. We observe the spin dynamics of the qubit and measure the decoherence times (T1 and T2), which are determined by the spin-exchange interaction as well as by an unexpectedly strong spin-nonconserving coupling mechanism.
We demonstrate storage and manipulation of one qubit encoded into a decoherence-free subspace (DFS) of two nuclear spins using liquid state nuclear magnetic resonance techniques. The DFS is spanned by states that are unaffected by arbitrary collective phase noise. Encoding and decoding procedures reversibly map an arbitrary qubit state from a single data spin to the DFS and back. The implementation demonstrates the robustness of the DFS memory against engineered dephasing with arbitrary strength as well as a substantial increase in the amount of quantum information retained, relative to an un-encoded qubit, under both engineered and natural noise processes. In addition, a universal set of logical manipulations over the encoded qubit is also realized. Although intrinsic limitations prevent maintenance of full noise tolerance during quantum gates, we show how the use of dynamical control methods at the encoded level can ensure that computation is protected with finite distance. We demonstrate noise-tolerant control over a DFS qubit in the presence of engineered phase noise significantly stronger than observed from natural noise sources.
We present a theoretical discussion of various aspects of the dynamics of information in quantum systems of qubits. We begin by reviewing ideas about entanglement and information in systems of qubits, different models for realistic qubits coupled to an external environment, how this causes the loss of information stored in qubits, and some practical designs for qubits that have been created. Then we study how the state of many-body systems can be decomposed in terms of its different subsystems and derived a hierarchy of equations describing the motion of these different parts. We show that in a qubit system, the central objects in this hierarchy are correlators between different components of different qubits. Systems where the environment coupled to a central qubit is a "spin bath'' of environmental qubits are then considered in detail and we find that information lost by the central qubit is transferred via a cascade to higher and higher order correlations with the environment. We discuses this process in the realistic example of an "Fe₈'' magnetic molecule qubit. Finally we discuss simple models of the dynamics of many entangled qubits.