``Leakage'' errors are particularly serious errors which couple states within a code subspace to states outside of that subspace thus destroying the error protection benefit afforded by an encoded state. We generalize an earlier method for producing leakage elimination decoupling operations and examine the effects of the leakage eliminating operations on decoherence-free or noiseless subsystems which encode one logical, or protected qubit into three or four qubits. We find that by eliminating the large class of leakage errors, under some circumstances, we can create the conditions for a decoherence free evolution. In other cases we identify a combination decoherence-free and quantum error correcting code which could eliminate errors in solid-state qubits with anisotropic exchange interaction Hamiltonians and enable universal quantum computing with only these interactions.
Decoherence-induced leakage errors can potentially damage physical or logical qubits by coupling them to other system levels. Here we report the first experimental implementation of Leakage Elimination Operators (LEOs) that aims to reduce this undermining, and that can be applied alongside universal quantum computing. Using IBM's cloud quantum computer, we have studied three potentially applicable examples of subspaces in two- and three-qubit Hilbert spaces and found that the LEOs significantly suppress leakage.
Adiabatic evolution is used in a variety of quantum information processing tasks. However, the elimination of errors is not as well-developed as it is for circuit model processing. Here, we present a strategy to accelerate a reliable quantum adiabatic process by adding Leakage Elimination Operators (LEO) to the evolution which are a sequence of pulse controls acting in an adiabatic subspace. Using the Feshbach $PQ$ partitioning technique, we obtain an analytical solution which traces the footprint of the target eigenstate. The effectiveness of the LEO is independent of the specific form of the…
Dynamical decoupling operations have been shown to reduce errors in quantum information processing. Leakage from an encoded subspace to the rest of the system space is a particularly serious problem for which leakage elimination operators (LEO) were introduced. These are a particular type of decoupling which are designed to eliminate such leakage errors. Here, we provide an analysis of non-ideal pulses, rather than the well-understood ideal pulses or bang-bang controls. We show that under realistic conditions for experiments these controls will provide protection from errors. Furthermore, we f…
In all lossy communication channels realized to date, information is inevitably leaked to a potential eavesdropper. Here we present a communication protocol that does not allow for any information leakage to a potential eavesdropper in a purely lossy channel. By encoding information into a restricted Gaussian alphabet of squeezed states we show, both theoretically and experimentally, that the Holevo information between the eavesdropper and the intended recipient can be exactly zero in a purely lossy channel while minimized in a noisy channel. This result is of fundamental interest, but might a…
Leakage errors damage a qubit by coupling it to other levels. Over the years, several theoretical approaches to dealing with such errors have been developed based on perturbation arguments. Here we propose a different strategy: we use a sequence of finite rotation gates to exactly eliminate leakage errors. The strategy is illustrated by the recently proposed charge quadrupole qubit in a triple quantum dot, where there are two logical states to support the qubit and one leakage state. We have found an su(2) subalgebra in the three-level system, and by using the subalgebra we show that ideal Pau…
Continuous-variable (CV) systems are attracting increasing attention in the realization of universal quantum computation. Several recent experiments have shown the feasibility of using CV systems to, e.g., encode a qubit into a trapped-ion mechanical oscillator and perform logic gates [Nature 566, 513-517 (2019)]. The essential next step is to protect the encoded qubit from quantum decoherence, e.g., the motional decoherence due to the interaction between a mechanical oscillator and its environment. Here we propose a scheme to suppress quantum decoherence of a single-mode harmonic oscillator u…
Realizing leakage elimination operator-based adiabatic speedup on a superconducting quantum processor
College of Physics and Optoelectronic Engineering, Ocean University of China（中国海洋大学物理与光电工程学院）；China Mobile (Suzhou) Software Technology Co., Ltd（中国移动（苏州）软件技术有限公司）；School of Sciences, Qingdao University of Technology（青岛理工大学理学院）
We derive an exact one-component equation of motion for the probability amplitude of a target time-dependent state, and use the equation to reformulate quantum dynamics and control for both closed and open systems. Using the one-component equation, we show that an unexpected time-dependent leakage-free path can be induced and we capture the essential quantity in determining the effect of decoherence suppression. Our control protocol based on the nonperturbative leakage elimination operator provides a unified perspective connecting some subtle, popular and important concepts of quantum control,…
Readout-Induced Leakage in Superconducting Circuits with Nonlinear Couplings
Yale University（耶鲁大学）；Yale Quantum Institute, Yale University（耶鲁量子研究所，耶鲁大学）；University of California Santa Barbara（加州大学圣塔芭芭拉分校）；Google Quantum AI（谷歌量子AI）
Photon-Number Conserved Universal Quantum Logic Employing Continuous-Time Quantum Walk on Dual-Rail Qubit Arrays
Southern University of Science and Technology（南方科技大学）；Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology（南方科技大学量子科学工程学院）；Lanzhou University（兰州大学）；Cuiying Honors College, Lanzhou University（兰州大学萃英学院）；International Quantum Academy, Shenzhen（深圳国际量子研究院）
We present an exact master equation for a central spin-$1/2$ system coupled to a spin-$1/2$ bath in terms of hyperfine interaction, which provides a unified formalism for both free evolution and controlled dynamics of the central spin. The equation enables us to study controllability of dynamics processes with various degrees of non-Markovianity. We investigate the Overhauser's effect on decoherence dynamics of the central spin under different bath spectra and the system-bath coupling strengths. Nonperturbative leakage elimination approach is applied to the system to suppress decoherence in so…
Randomized benchmarking (RB) is a powerful method for determining the error rate of experimental quantum gates. Traditional RB, however, is restricted to gatesets, such as the Clifford group, that form a unitary 2-design. The recently introduced character RB can benchmark more general gates using techniques from representation theory; up to now, however, this method has only been applied to "multiplicity-free" groups, a mathematical restriction on these groups. In this paper, we extend the original character RB derivation to explicitly treat non-multiplicity-free groups, and derive several app…
We numerically study the implementation of a universal two-qubit gate set, composed of CNOT, Hadamard, phase and $π/8$ gates, for transmon-based systems. The control signals to implement such gates are obtained using the Chopped Random Basis optimal control technique, with a target gate infidelity of $10^{-2}$. During the optimization processes we account for the leakage toward non-computational states, an important non-ideality affecting transmon qubits. We also test and benchmark the optimal control solutions against the introduction of Gaussian white noise and spectral distortion, two key n…
Emerging reinforcement learning techniques using deep neural networks have shown great promise in control optimization. They harness non-local regularities of noisy control trajectories and facilitate transfer learning between tasks. To leverage these powerful capabilities for quantum control optimization, we propose a new control framework to simultaneously optimize the speed and fidelity of quantum computation against both leakage and stochastic control errors. For a broad family of two-qubit unitary gates that are important for quantum simulation of many-electron systems, we improve the con…
Universal gates for a metastable qubit in strontium-88
Max-Planck-Institut für Quantenoptik（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Fakultät für Physik, Ludwig-Maximilians-Universität（慕尼黑大学物理学院）
