We study dynamical decoupling in a multi-qubit setting, where it is combined with quantum logic gates. This is illustrated in terms of computation using Heisenberg interactions only, where global decoupling pulses commute with the computation. We derive a rigorous error bound on the trace distance or fidelity between the desired computational state and the actual time-evolved state, for a system subject to coupling to a bounded-strength bath. The bound is expressed in terms of the operator norm of the effective Hamiltonian generating the evolution in the presence of decoupling and logic operations. We apply the bound to the case of periodic pulse sequences and find that in order maintain a constant trace distance or fidelity, the number of cycles -- at fixed pulse interval and width -- scales in inverse proportion to the square of the number of qubits. This sets a scalability limit on the protection of quantum computation using periodic dynamical decoupling.
We present rigorous performance bounds for the optimal dynamical decoupling pulse sequence protecting a quantum bit (qubit) against pure dephasing. Our bounds apply under the assumption of instantaneous pulses and of bounded perturbing environment and qubit-environment Hamiltonians. We show that if the total sequence time is fixed the optimal sequence can be used to make the distance between the protected and unperturbed qubit states arbitrarily small in the number of applied pulses. If, on the other hand, the minimum pulse interval is fixed and the total sequence time is allowed to scale with…
We present rigorous performance bounds for the quadratic dynamical decoupling (QDD) pulse sequence which protects a qubit from general decoherence, and for its nested generalization to an arbitrary number of qubits. Our bounds apply under the assumption of instantaneous pulses and of bounded perturbing environment and qubit-environment Hamiltonians such as those realized by baths of nuclear spins in quantum dots. We prove that if the total sequence time is fixed then the trace-norm distance between the unperturbed and protected system states can be made arbitrarily small by increasing the numb…
The need for strategies able to accurately manipulate quantum dynamics is ubiquitous in quantum control and quantum information processing. We investigate two scenarios where randomized dynamical decoupling techniques become more advantageous with respect to standard deterministic methods in switching off unwanted dynamical evolution in a closed quantum system: when dealing with decoupling cycles which involve a large number of control actions and/or when seeking long-time quantum information storage. Highly effective hybrid decoupling schemes, which combine deterministic and stochastic featur…
Color centers in solids, such as the nitrogen-vacancy center in diamond, offer well-protected and well-controlled localized electron spins that can be employed in various quantum technologies. Moreover, the long coherence time of the surrounding spinful nuclei can enable a robust quantum register controlled through the color center. We design pulse sequence protocols that drive the electron spin to generate robust entangling gates with these nuclear memory qubits. We find that compared to using Carr-Purcell-Meiboom-Gill (CPMG) alone, Uhrig decoupling sequence and hybrid protocols composed of C…
We study the parametric interaction between a single Nitrogen-Vacancy electronic spin and a diamond mechanical resonator in which the spin is embedded. Coupling between spin and oscillator is achieved by crystal strain, which is generated upon actuation of the oscillator and which parametrically modulates the spins' energy splitting. Under coherent microwave driving of the spin, this parametric drive leads to a locking of the spin Rabi frequency to the oscillator mode in the megahertz range. Both the Rabi oscillation decay time and the inhomogeneous spin dephasing time increase by two orders o…
Quantum Error Correction and Dynamical Decoupling: Better Together or Apart?
University of Southern California（南加州大学）；Center for Quantum Information Science & Technology, University of Southern California（南加州大学量子信息科学与技术中心）；Quantum Elements, Inc.（量子元素公司）；Department of Physics & Astronomy, University of Southern California（南加州大学物理与天文学系）；Department of Chemistry, University of Southern California（南加州大学化学系）
We show how dynamical decoupling (DD) and quantum error correction (QEC) can be optimally combined in the setting of fault tolerant quantum computing. To this end we identify the optimal generator set of DD sequences designed to protect quantum information encoded into stabilizer subspace or subsystem codes. This generator set, comprising the stabilizers and logical operators of the code, minimizes a natural cost function associated with the length of DD sequences. We prove that with the optimal generator set the restrictive local-bath assumption used in earlier work on hybrid DD-QEC schemes, …
Hybrid systems consisting of different types of qubits are promising for building quantum computers if they combine useful properties of their constituent qubits. However, they also pose additional challenges if one type of qubits is more susceptible to environmental noise than the others. Dynamical decoupling can help to protect such systems by reducing the decoherence due to the environmental noise, but the protection must be designed such that it does not interfere with the control fields driving the logical operations. Here, we test such a protection scheme on a quantum register consisting…
Protecting the dynamics of coupled quantum systems from decoherence by the environment is a key challenge for solid-state quantum information processing. An idle qubit can be efficiently insulated from the outside world via dynamical decoupling, as has recently been demonstrated for individual solid-state qubits. However, protection of qubit coherence during a multi-qubit gate poses a non-trivial problem: in general the decoupling disrupts the inter-qubit dynamics, and hence conflicts with gate operation. This problem is particularly salient for hybrid systems, wherein different types of qubit…
Beam-splitter operations are widely used to process information encoded in bosonic modes. In hybrid quantum systems, however, it might be challenging to implement a reliable beam-splitter operation between two distinct bosonic modes. Without beam-splitters, some basic operations such as decoupling modes and swapping states between modes can become highly non-trivial or not feasible at all. In this work, we develop novel interference-based protocols for decoupling and swapping selected modes of a multimode bosonic system without requiring beam-splitters. Specifically, for a given generic couple…
We derive rigorous upper bounds on the distance between quantum states in an open system setting, in terms of the operator norm between the Hamiltonians describing their evolution. We illustrate our results with an example taken from protection against decoherence using dynamical decoupling.
Heisenberg-limited metrology in the presence of non-Markovian noise with finite control rates
Center for Quantum Information and Control, University of New Mexico（新墨西哥大学量子信息与控制中心）；Department of Physics and Astronomy, University of New Mexico（新墨西哥大学物理与天文学系）
A rigorous hybridization of variational quantum eigensolver with classical neural network
Seoul National University（首尔大学）；NextQuantum, Seoul National University（NextQuantum，首尔大学）；Automation and Systems Research Institute, Seoul National University（自动化与系统研究所，首尔大学）；Institute for Convergence Research and Education in Advanced Technology, Yonsei University（先进技术研究融合教育与研究所，延世大学）；Department of Quantum Information, Yonsei University（量子信息系，延世大学）
The hierarchical equations of motion (HEOM) for a generalized quantum dissipative system is rigorously constructed in the frameworks of two different stochastic dynamical descriptions, i.e., the non-Markovian quantum state diffusion approach as well as the stochastic decoupling scheme. We demonstrated that the HEOMs obtained by these two different stochastic dynamical methods are identical. Moreover, we present some numerical examples to verify the feasibility of our formalism.
We revisit the problem of switching off unwanted phase evolution and decoherence in a single two-state quantum system in the light of recent results on random dynamical decoupling methods [L. Viola and E. Knill, Phys. Rev. Lett. {\bf 94}, 060502 (2005)]. A systematic comparison with standard cyclic decoupling is effected for a variety of dynamical regimes, including the case of both semiclassical and fully quantum decoherence models. In particular, exact analytical expressions are derived for randomized control of decoherence from a bosonic environment. We investigate quantitatively control pr…
I show how to protect adiabatic quantum computation (AQC) against decoherence and certain control errors, using a hybrid methodology involving dynamical decoupling, subsystem and stabilizer codes, and energy gaps. Corresponding error bounds are derived. As an example I show how to perform decoherence-protected AQC against local noise using at most two-body interactions.
Hybrid quantum systems aim at combining the advantages of different physical systems and to produce novel quantum devices. In particular, the hybrid combination of superconducting circuits and spins in solid-state crystals is a versatile platform to explore many quantum electrodynamics problems. Recently, the remote coupling of nitrogen-vacancy center spins in diamond via a superconducting bus was demonstrated. However, a rigorous experimental test of the quantum nature of this hybrid system and in particular entanglement is still missing. We review the theoretical ideas to generate and detect…
Quantum communication over long distances relies on the ability to create entanglement between two remote quantum nodes. Recent proposals aiming at experimental realization propose a hybrid quantum repeater setup where two distant material qubits are entangled by light-matter interaction. Motivated by these developments, we investigate possible decoherence effects originating from the centre- of-mass motion of the spatially well separated trapped qubits. Within the Lamb-Dicke regime we use photon exchange involving coherent states of the radiation field to entangle the two material qubits. Opt…
A calculation of the photonic Green's tensor of a structure is at the heart of many photonic problems, but for non-trivial nanostructures, it is typically a prohibitively time-consuming task. Recently, a general normal mode expansion (GENOME) was implemented to construct the Green's tensor from eigenpermittivity modes. Here, we employ GENOME to the study the response of a cluster of nanoparticles. To this end, we use the rigorous mode hybridization theory derived earlier by D. J. Bergman [Phys. Rev. B 19, 2359 (1979)], which constructs the Green's tensor of a cluster of nanoparticles from the …
Fault-tolerant hyper-Ramsey spectroscopy of optical clock transitions with dynamical decoupling
Centre for Quantum Technologies, Department of Physics, Sofia University（索非亚大学量子技术中心物理系）；Sorbonne Université CNRS, MONARIS, UMR 8233（索邦大学CNRS，MONARIS实验室）；MajuLab, International Research Laboratory IRL 3654, Université Côte d’Azur, Sorbonne Université, National University of Singapore, Nanyang Technological University（新加坡国立大学-索邦大学-尼斯蔚蓝海岸大学南洋理工大学联合研究实验室）；Center for Quantum Technologies, Nanyang Technological University（南洋理工大学量子技术中心）；Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University（南洋理工大学理学院南洋量子枢纽）；Laboratoire de Physique des Lasers, CNRS, Université Sorbonne Paris Nord（巴黎北索邦大学CNRS激光物理实验室）
Helicity decoupling ultrastrong Rabi splitting from quantum vacuum dressing
College of Physical Sciences and Engineering, University Mohammed VI Polytechnic（物理科学与工程学院，穆罕默德六世polytechnic大学）；Institut für Theoretische Physik, Universität Tübingen（理论物理研究所，蒂宾根大学）；Jülich Supercomputing Centre, Forschungszentrum Jülich（于利希超级计算中心，于利希研究中心）；Department of Chemistry, Princeton University（化学系，普林斯顿大学）
A general strategy to maintain the coherence of a quantum bit is proposed. The analytical result is derived rigorously including all memory and back-action effects. It is based on an optimized $π$-pulse sequence for dynamic decoupling extending the Carr-Purcell-Meiboom-Gill (CPMG) cycle. The optimized sequence is very efficient, in particular for strong couplings to the environment.
