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.
Decoherence-induced leakage errors can couple a physical or encoded qubit to other levels, thus potentially damaging the qubit. They can therefore be very detrimental in quantum computation and require special attention. Here we present a general method for removing such errors by using simple decoupling and recoupling pulse sequences. The proposed gates are experimentally accessible in a variety of promising quantum computing proposals.
``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 decohe…
Quantum error prevention strategies will be required to produce a scalable quantum computing device and are of central importance in this regard. Progress in this area has been quite rapid in the past few years. In order to provide an overview of the achievements in this area, we discuss the three major classes of error prevention strategies, the abilities of these methods and the shortcomings. We then discuss the combinations of these strategies which have recently been proposed in the literature. Finally we present recent results in reducing errors on encoded subspaces using decoupling contr…
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）
In realizations of quantum computing, a two-level system (qubit) is often singled out of the many levels of an anharmonic oscillator. In these cases, simple qubit control fails on short time scales because of coupling to leakage levels. We provide an easy to implement analytic formula that inhibits this leakage from any single-control analog or pixelated pulse. It is based on adding a second control that is proportional to the time-derivative of the first. For realistic parameters of superconducting qubits, this strategy reduces the error by an order of magnitude relative to the state of the a…
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,…
We experimentally demonstrate the manipulation of optical diffraction, utilizing the atomic thermal motion in a hot vapor medium of electromagnetically-induced transparency (EIT). By properly tuning the EIT parameters, the refraction induced by the atomic motion may completely counterbalance the paraxial free-space diffraction and by that eliminates the effect of diffraction for arbitrary images. By further manipulation, the diffraction can be doubled, biased asymmetrically to induced deflection, or even reversed. The latter allows an experimental implementation of an analogy to a negative-ind…
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）
In general, fault-tolerant quantum error correction (FTQEC) procedures are designed to detect, correct, and be fault-tolerant against errors occurring within the qubit subspace. But in some qubit implementations, additional "leakage" errors can occur in which the system leaves this subspace, and standard FTQEC procedures may not be fault-tolerant against such errors. Generic methods for achieving fault-tolerance against leakage are costly in terms of resources. In this paper we demonstrate that for a leakage model common to many photonic gate implementations, FTQEC can be implemented with far …
We use a gradient-based optimization scheme to find single-qubit rotations to be interwoven between timesteps of a noisy logical two-qubit entangling gate in order to suppress arbitrary logical and leakage errors in the two-qubit gate. We show how the sequence fidelity is affected by imperfections in the single-qubit operations, as well as by various relative strengths of the logical and leakage noise. Our approach is completely general and system-independent, allowing for application to any two-qubit system regardless of the experimental implementation details.
Leakage outside of the qubit computational subspace, present in many leading experimental platforms, constitutes a threatening error for quantum error correction (QEC) for qubits. We develop a leakage-detection scheme via Hidden Markov models (HMMs) for transmon-based implementations of the surface code. By performing realistic density-matrix simulations of the distance-3 surface code (Surface-17), we observe that leakage is sharply projected and leads to an increase in the surface-code defect probability of neighboring stabilizers. Together with the analog readout of the ancilla qubits, this …
Distributing cryptographic keys over public channels in a way that can provide information-theoretic security is the holy grail for secure communication. This can be achieved by exploiting quantum mechanical principles in so-called quantum key distribution (QKD). Continuous-variable (CV) QKD based on coherent states, in particular, is an attractive scheme for secure communication since it requires only standard telecommunication technology that can operate at room temperature. However, a recently discovered side-channel created in the process of state preparation leads to a leakage of informat…
Population leakage outside the qubit subspace presents a particularly harmful source of error that cannot be handled by standard error correction methods. Using a trapped $^{171}$Yb$+$ ion, we demonstrate an optical pumping scheme to suppress leakage errors in atomic hyperfine qubits. The selection rules and narrow linewidth of a quadrupole transition are used to selectively pump population out of leakage states and back into the qubit subspace. Each pumping cycle reduces the leakage population by a factor of $\sim3$, allowing for an exponential suppression in the number of cycles. We use inte…
Dark state as a consequence of interference between different quantum states has great importance in the fields of chip-scale atomic clock and quantum information. For the $Λ$-type three-level system, this dark state is generally regarded as being dissipation-free because it is a superposition of two lowest states without dipole transition between them. However, previous studies are based on the rotating-wave approximation (RWA) by neglecting the counter-rotating terms in the system-environment interaction. In this work, we study non-Markovian quantum dynamics of the dark state in a $Λ$-type t…
Physical implementations of cryptographic algorithms leak information, which makes them vulnerable to so-called side-channel attacks. The problem of secure computation in the presence of leakage is generally known as leakage resilience. In this work, we establish a connection between leakage resilience and fault-tolerant quantum computation. We first prove that for a general leakage model, there exists a corresponding noise model in which fault tolerance implies leakage resilience. Then we show how to use constructions for fault-tolerant quantum computation to implement classical circuits that…
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…
Simple analytical flux-tuned iSWAP pulses for leakage suppression
Institute for Quantum Control (PGI-8), Forschungszentrum Jülich（于利希研究中心量子控制研究所）；Institute for Theoretical Physics, University of Cologne（科隆大学理论物理研究所）；Institute for Functional Quantum System (PGI-13), Forschungszentrum Jülich（于利希研究中心功能量子系统研究所）；Department of Physics, RWTH Aachen University（亚琛工业大学物理系）
Quantum state privacy amplification (QSPA) is the quantum analogue of classical privacy amplification. If the state information of a series of single particle states has some leakage, QSPA reduces this leakage by condensing the state information of two particles into the state of one particle. Recursive applications of the operations will eliminate the quantum state information leakage to a required minimum level. In this paper, we report the experimental implementation of a quantum state privacy amplification protocol in a nuclear magnetic resonance system. The density matrices of the states …
We report a substantially simplified procedure, based on group-theoretic reasoning, for the reduction of qubit leakage in exchange-only spin qubits. We to find exchange sequences which accomplish leakage reduction with only two additional spins and with as few as 14 nearest neighbor exchange interactions, less than half than previously reported. We show that the identified sequences are robust in the presence of realistic noise levels in the semiconductor environment. Our procedure also produces flag information that can be helpful in the implementation of quantum algorithms.
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…
Reducing quantum resources for ADAPT-VQE via plateau-operator elimination and correlated mean-field downfolding
Faculty of Physics and Engineering Physics, University of Science（理科大学物理与工程物理学院）；Vietnam National University（越南国立大学）；Phenikaa Institute of Advanced Study (PIAS), Phenikaa University（仙芝大学先进研究院）；Institute of Advanced Technology, Vietnam Academy of Science and Technology（越南科学技术院先进技术研究所）
A practical quantum computer requires quantum bit (qubit) operations with low error rates in extensible architectures. We study a packaging method that makes it possible to address hundreds of superconducting qubits by means of three-dimensional wires: The large-scale quantum socket. A qubit chip is housed in a superconducting box, where both box and chip dimensions lead to unwanted modes that can interfere with qubit operations. We theoretically analyze these interference effects in the context of qubit coherent leakage. We propose two methods to mitigate the resulting errors by detuning the …
