In this paper, we propose a concept to use a quantum speed limit (QSL) as a measure of robustness of states, defining that a state with bigger QSL is more robust. In this perspective, it is important to have an explicitly-computable QSL, because then we can formulate an engineering problem of Hamiltonian that makes a target state robust against decoherence. Hence we derive a new explicitly-computable QSL that is applicable to general Markovian open quantum systems. This QSL is tighter than another explicitly-computable QSL, in an important setup such that decoherence is small. Also the Hamiltonian engineering problem with this QSL is a quadratic convex optimization problem, and thus it is efficiently solvable. The idea of robust state characterization and the Hamiltonian engineering, in terms of QSL, is demonstrated with several examples.
Quantum speed limits for two time-evolved states are introduced and applied to overlap between true dynamics and approximate dynamics. In particular, we point out that the present idea is suitable for invariant-based inverse engineering, i.e., the worst case performance of invariant-based inverse engineering can be evaluated by using a designed time-evolved state. As demonstrations, we apply the present method to stimulated Raman adiabatic passage and quantum annealing, and then we find that the present idea brings valuable insight to control scheduling.
Engineering Precise and Robust Effective Hamiltonians
Institute for Quantum Computing（量子计算研究所）；Department of Physics, University of Waterloo（滑铁卢大学物理系）；Department of Chemistry, University of Waterloo（滑铁卢大学化学系）
Since 2005 there has been a huge growth in the use of engineered control pulses to perform desired quantum operations in systems such as NMR quantum information processors. These approaches, which build on the original gradient ascent pulse engineering (GRAPE) algorithm, remain computationally intensive because of the need to calculate matrix exponentials for each time step in the control pulse. Here we discuss how the propagators for each time step can be approximated using the Trotter--Suzuki formula, and a further speed up achieved by avoiding unnecessary operations. The resulting procedure…
A protocol is proposed to generate singlet states of three logical qubits constructed by pairs of spins. Single and multiple operations of logical qubits are studied for the construction of an effective Hamiltonian, with which robust control fields are derived with invariant-based reverse engineering and optimal control. Moreover, systematic errors are further compensated by periodic modulation for better robustness. Furthermore, resistance to decoherence of the protocol is also shown with numerical simulations. Therefore, the protocol may provide useful perspectives for generations of logical…
Adiabatic operations are powerful tools for robust quantum control in numerous fields of physics, chemistry and quantum information science. The inherent robustness due to adiabaticity can, however, be impaired in applications requiring short evolution times. We present a single versatile gradient-based optimization protocol that combines adiabatic control with effective Hamiltonian engineering in order to design adiabatic operations tailored to the specific imperfections and resources of an experimental setup. The practicality of the protocol is demonstrated by engineering a fast, 2.3 Rabi cy…
Robust Preparation of Bell States by Time Boundary Effect
School of Physics, Beijing Institute of Technology（北京理工大学物理学院）；School of Physics Science and Technology, Kunming University（昆明大学物理科学与技术学院）；National Laboratory of Solid State Microstructures, Department of Physics, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学固体微结构物理国家重点实验室、物理系和先进微结构协同创新中心）
We theoretically investigate the escape rate occurring via quantum tunneling in a system affected by tailored dissipation. Specifically, we study the environmental assisted quantum tunneling of the superconducting phase in a current-biased Josephson junction. We consider Ohmic resistors inducing dissipation both in the phase and in the charge of the quantum circuit. We find that the charge dissipation leads to an enhancement of the quantum escape rate. This effect appears already in the low Ohmic regime and also occurs in the presence of phase dissipation that favors localization. Inserting re…
The development of efficient algorithms that generate robust quantum controls is crucial for the realization of quantum technologies. The commonly used gradient-based optimization algorithms are limited by their sensitivity to the initial guess, which affects their performance. Here we propose combining the gradient method with the simulated annealing technique to formulate a hybrid algorithm. Our numerical analysis confirms its superior convergence rate. Using the hybrid algorithm, we generate spin-selective $π$ pulses and employ them for experimental measurement of local noise-spectra in a t…
We address the performance of a coin-biased quantum walk as a generator for non-classical position states of the walker. We exploit a phenomenon of coherent localisation in the position space --- resulting from the choice of small values of the coin parameter and assisted by post-selection --- to engineer large-size coherent superpositions of distinguishable position states of the walker. The protocol that we design appears to be remarkably robust against both the actual value taken by the coin parameter and strong dephasing-like noise acting on the spatial degree of freedom. We finally illust…
Demonstrating Quadratic Monte Carlo Speedup via Quantum Amplitude Estimation: Nuclear Engineering Examples
Ken and Mary Alice Lindquist Department of Nuclear Engineering, Pennsylvania State University（宾夕法尼亚州立大学核工程系）；Department of Physics, University of Massachusetts Boston（马萨诸塞大学波士顿分校物理系）
Engineering dissipation and control pulses for high-fidelity fault-tolerance quantum computing
Fujian Key Laboratory of Quantum Information and Quantum Optics, Fuzhou University（福州大学）；Department of Physics, Fuzhou University（福州大学）；Quantum Information Physics Theory Research Team, Center for Quantum Computing, RIKEN（理化学研究所）；Institute of Quantum Science and Technology, Yanbian University（延边大学）
Starting from a geometric perspective, we derive a quantum speed limit for arbitrary open quantum evolution, which could be Markovian or non-Markovian, providing a fundamental bound on the time taken for the most general quantum dynamics. Our methods rely on measuring angles and distances between (mixed) states represented as generalized Bloch vectors. We study the properties of our bound and present its form for closed and open evolution, with the latter in both Lindblad form and in terms of a memory kernel. Our speed limit is provably robust under composition and mixing, features that largel…
Framework for robust quantum speedups in practical correlated electronic structure and dynamics
California Institute of Technology（加州理工学院）；Institute for Quantum Information and Matter（量子信息物质研究所）；Division of Physics, Mathematics, and Astronomy, California Institute of Technology（加州理工学院物理、数学与天文学部）；Division of Chemistry and Chemical Engineering, California Institute of Technology（加州理工学院化学与化学工程系）；Marcus Center for Theoretical Chemistry（马库斯理论化学中心）
We propose a scheme to implement the phase-robust topological router based on a one-dimensional dimerized superconducting circuit lattice with long-range hopping. We show that the proposed dimerized superconducting circuit lattice can be mapped into an extended chiral-symmetric Su-Schrieffer-Heeger (SSH) model with long-range hopping, in which the existence of long-range hopping induces a special zero-energy mode. The peculiar distribution of the zero-energy mode enables us to engineer a phase-robust topological router, which can achieve quantum state transfer (QST) from one site (input port) …
We develop new protocols for high-fidelity single qubit gates that exploit and extend theoretical ideas for accelerated adiabatic evolution. Our protocols are compatible with qubit architectures with highly isolated logical states, where traditional approaches are problematic; a prime example are superconducting fluxonium qubits. By using an accelerated adiabatic protocol we can enforce the desired adiabatic evolution while having gate times that are comparable to the inverse adiabatic energy gap (a scale that is ultimately set by the amount of power used in the control pulses). By modelling t…
We proposed a method to engineer the light matter interaction while initializing a qubit in presence of physical constraints utilizing the inverse engineering. Combining the multiple degrees of freedom in the pulse parameters with the perturbation theory, we developed pulses to initialize the qubit within a tightly packed frequency interval to an arbitrary superposition state with high fidelity. Importantly, the initialization induces low off-resonant excitations to the neighboring qubits, and it is robust against the spatial inhomogeneity in the laser intensity. We applied the method to the e…
We propose an analytical method to achieve complete energy conversion in sum frequency generation based on Lewis-Riesenfeld invariants theory. This technique, derived from a two-level atom transition in quantum mechanics, is more efficient and robust than conventional methods. In our scheme, the quasi-adiabatic single control parameter model is established, and the value of single control parameter is selected to make the initial eigenstate perfectly converted to the final eigenstate we need. Corresponds to the nonlinear frequency conversion process, the nonlinear crystal structure is designed…
We study the decoherence speed limit (DSL) of a single impurity atom immersed in a Bose-Einsteincondensed (BEC) reservoir when the impurity atom is in a double-well potential. We demonstrate how the DSL of the impurity atom can be manipulated by engineering the BEC reservoir and the impurity potential within experimentally realistic limits. We show that the DSL can be controlled by changing key parameters such as the condensate scattering length, the effective dimension of the BEC reservoir, and the spatial configuration of the double-well potential imposed on the impurity. We uncover the phys…
Quantum Fanout Gates in Constant Depth via Resonance Engineering
ETH Zürich（苏黎世联邦理工学院）；Institute for Quantum Electronics, ETH Zürich（苏黎世联邦理工学院量子电子学研究所）；Fraunhofer Institute for Applied Solid State Physics IAF（弗劳恩霍夫应用固态物理研究所）
We propose a fast mixed-state control scheme to transfer the quantum state along designable trajectories in Hilbert space, which is robust to multiple decoherence noises. Starting with the dynamical invariants of open quantum systems, we present the shortcuts to adiabaticity (STAs) of open quantum systems at first, then apply the STAs to speed up the adiabatic steady process. Our scheme drives open systems from a initial steady state to a target steady state by a controlled Liouvillian that possesses the same form as the reference (original) one which is accessible in present-day experiments. …
Gradient ascent pulse engineering algorithm (GRAPE) is a typical method to solve quantum optimal control problems. However, it suffers from an exponential resource in computing the time evolution of quantum systems with the increasing number of qubits, which is a barrier for its application in large-qubit systems. To mitigate this issue, we propose an iterative GRAPE algorithm (iGRAPE) for preparing a desired quantum state, where the large-scale, resource-consuming optimization problem is decomposed into a set of lower-dimensional optimization subproblems by disentanglement operations. Consequ…
We introduce a new approach for the robust control of quantum dynamics of strongly interacting many-body systems. Our approach involves the design of periodic global control pulse sequences to engineer desired target Hamiltonians that are robust against disorder, unwanted interactions and pulse imperfections. It utilizes a matrix representation of the Hamiltonian engineering protocol based on time-domain transformations of the Pauli spin operator along the quantization axis. This representation allows us to derive a concise set of algebraic conditions on the sequence matrix to engineer robust …
A new class of atomic interferences using ultra-narrow optical transitions are pushing quantum engineering control to a very high level of precision for a next generation of sensors and quantum gate operations. In such context, we propose a new quantum engineering approach to Ramsey-Bordé interferometry introducing multiple composite laser pulses with tailored pulse duration, Rabi field amplitude, frequency detuning and laser phase-step. We explore quantum metrology with hyper-Ramsey and hyper-Hahn-Ramsey clocks below the $10^-18$ level of fractional accuracy by a fine tuning control of light …
Recent progress toward the fabrication of Majorana-based qubits has sparked the need for systematic approaches to optimize experimentally relevant parameters for the realization of robust Majorana bound states. Here, we introduce an efficient numerical method for the real-space optimization of tunable parameters, such as electrostatic potential profiles and magnetic field textures, in Majorana wires. Combining ideas from quantum control and quantum transport, our algorithm, applicable to any noninteracting tight-binding model, operates on a largely unexplored parameter space and opens new rout…
Global control strategies for arrays of qubits are a promising pathway to scalable quantum computing. A continuous-wave global field provides decoupling of the qubits from background noise. However, this approach is limited by variability in the parameters of individual qubits in the array. Here we show that by modulating a global field simultaneously applied to the entire array, we are able to encode qubits that are less sensitive to the statistical scatter in qubit resonance frequency and microwave amplitude fluctuations, which are problems expected in a large scale system. We name this appr…
We demonstrate how robust entanglement of quantum dot molecular system in a voltage controlled junction can be generated. To improve the quantum information characteristics of this system, we propose an applicable protocol which contains the implementation of asymmetric quantum dots as well as engineering reservoirs. Quantum dots with tunable energy barriers can provide asymmetric coupling coefficients which can be tuned by gap voltages. Also by engineering reservoirs, superconductors can be used as leads in a biased-voltage junction. The high-controllability characteristics of system supplies…
Reservoir engineering is a powerful tool for the robust generation of quantum states or transport properties. Using both a weak-coupling quantum master equation and the exact solution, we show that directional transport of electrons through a double quantum dot can be achieved through an appropriately designed electronic environment. Directionality is attained through the interference of coherent and dissipative coupling. The relative phase is tuned with an external magnetic field, such that directionality can be reversed, as well as turned on and off dynamically. Our work introduces fermionic…
University of California, Berkeley（加州大学伯克利分校）；IBM Quantum, T.J. Watson Research Center（IBM量子托马斯·J·沃森研究中心）
Over the past few years several quantum machine learning algorithms were proposed that promise quantum speed-ups over their classical counterparts. Most of these learning algorithms either assume quantum access to data -- making it unclear if quantum speed-ups still exist without making these strong assumptions, or are heuristic in nature with no provable advantage over classical algorithms. In this paper, we establish a rigorous quantum speed-up for supervised classification using a general-purpose quantum learning algorithm that only requires classical access to data. Our quantum classifier …
A robust cryogenic infrastructure in form of a wired, thermally optimized dilution refrigerator is essential for present and future solid-state based quantum processors. Here, we engineer an extensible cryogenic setup, which minimizes passive and active heat loads, while guaranteeing rapid qubit control and readout. We review design criteria for qubit drive lines, flux lines, and output lines used in typical experiments with superconducting circuits and describe each type of line in detail. The passive heat load of stainless steel and NbTi coaxial cables and the active load due to signal dissi…
