arXiv subjects

P. Z. Zhao

Publications and source records attributed to P. Z. Zhao.

At least 19 recordsLinked to original sources

arXiv2025

Dynamical decoupling protection for three-level systems

In addition to the traditional two-level system, the three-level system serves as another important elemental building block for the manipulation of qubits. However, the quantum information processing in the three-level system is also subject to the decoherence induced by the interaction between the quantum system and its environment or by the crosstalk between different qutrits. In this work, we construct a sequence of physically feasible dynamical decoupling operators for the three-level system to mitigate not only the transverse dephasing between the excited state and ground states but also the longitudinal relaxation among them. Combining the Hamiltonian engineering and our constructed dynamical decoupling sequence, we further realize the dynamical decoupling protection of qutrit-based quantum gates. Our scheme can effectively enhance the fidelity of three-level-based quantum gates through filtering out the environmental noises, which may provide a new horizon to improve the accuracy of three-level-based quantum manipulation.

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arXiv2025

Decoherence mitigation for geometric quantum computation

Geometric phases depend only on the evolution path determined by the closed circuit in the projective Hilbert space but not on evolution details of the quantum system, leading to geometric quantum computation possessing some intrinsic robustness against control errors. Coordinated with dynamical decoupling, geometric quantum computation admits additional resilience to the environment-induced decoherence. However, the previous schemes of geometric quantum computation protected by dynamical decoupling require multiple physical qubits to encode a logical qubit, which undoubtedly increases the consumption of physical-qubit resources and the difficulty in the implementation of the logical-qubit manipulation based on physical-qubit driving. In this work, we put forward a scheme of decoherence-mitigated geometric quantum computation based only on physical qubits rather than logical qubits, hence avoiding the additional overhead of physical-qubit resources for logical-qubit encoding as well as the difficulty in the manipulation of logical qubits. Moreover, our scheme focuses on the most general interaction between an individual qubit and its environment so that it mitigates not just dephasing noise but rather regular decoherence. Our proposal thus represents a more realistic and effective approach towards the realization of geometric control with decoherence mitigation.

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arXiv2025

Nonadiabatic braiding of Majorana modes

The realization and manipulation of Majorana zero modes have drawn significant attention for their crucial role in enabling topological quantum computation. Conventional approaches to the braiding of Majorana zero modes rely on adiabatic processes. In this work, using a composite 2-Kitaev-chain system accommodating Majorana zero modes as a working example, we propose a nonadiabatic and non-Abelian geometry phase-based protocol to execute operations on these Majorana zero modes. This is possible by locally coupling the edge sites of both quantum chains with an embedded lattice defect, successfully simulating the braiding operation of two Majorana modes in a highly nonadiabatic fashion. To further enhance the robustness against control imperfections, we apply a multiple-pulse composite strategy to our quantum chain setting for second-order protection of the braiding operations. Our proposal can also support the fast and robust realization of the π/8 gate, an essential ingredient for universal quantum computation. This work hence offers a potential pathway towards the nonadiabatic and fault-tolerant control of Majorana zero modes.

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arXiv2025

Higher-order protection of quantum gates: Hamiltonian engineering coordinated with dynamical decoupling

Dynamical decoupling represents an active approach towards the protection of quantum memories and quantum gates. Because dynamical decoupling operations can interfere with a system's own time evolution, the protection of quantum gates is more challenging than that of quantum states. In this work, we put forward a simple but general approach towards the realization of higher-order protection of quantum gates and further execute the first cloud-based demonstration of dynamical-decoupling-protected quantum gates at the first order and the second order. The central idea of our approach is to engineer (hence regain the control of) the gate Hamiltonian in coordination with higher-order dynamical decoupling sequences originally proposed for the protection of quantum memories. The physical demonstration on an IBM quantum processor indicates the effectiveness and potential of our approach on noisy intermediate scale quantum computers.

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arXiv2024

Mitigation of systematic amplitude error in nonadiabatic holonomic operations

Nonadiabatic holonomic operations are based on nonadiabatic non-Abelian geometric phases, hence possessing the inherent geometric features for robustness against control errors. However, nonadiabatic holonomic operations are still sensitive to the systematic amplitude error induced by imperfect control of pulse timing or laser intensity. In this work, we present a scheme of nonadiabatic holonomic operations in order to mitigate the said systematic amplitude error. This is achieved by introducing a monitor qubit along with a conditional measurement on the monitor qubit that serves as an error correction device. We shall show how to filter out the undesired effect of the systematic amplitude error, thereby improving the performance of nonadiabatic holonomic operations.

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arXiv2024

Quantum machine learning with indefinite causal order

In a conventional circuit for quantum machine learning, the quantum gates used to encode the input parameters and the variational parameters are constructed with a fixed order. The resulting output function, which can be expressed in the form of a restricted Fourier series, has limited flexibility in the distributions of its Fourier coefficients. This indicates that a fixed order of quantum gates can limit the performance of quantum machine learning. Building on this key insight (also elaborated with examples), we introduce indefinite causal order to quantum machine learning. Because the indefinite causal order of quantum gates allows for the superposition of different orders, the performance of quantum machine learning can be significantly enhanced. Considering that the current accessible quantum platforms only allow to simulate a learning structure with a fixed order of quantum gates, we reform the existing simulation protocol to implement indefinite causal order and further demonstrate the positive impact of indefinite causal order on specific learning tasks. Our results offer useful insights into possible quantum effects in quantum machine learning.

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arXiv2023

Average value estimation in nonadiabatic holonomic quantum computation

Nonadiabatic holonomic quantum computation has been attracting continuous attention since it was proposed. Until now, various schemes of nonadiabatic holonomic quantum computation have been developed and many of them have been experimentally demonstrated. It is known that at the end of a computation, one usually needs to estimate the average value of an observable. However, computation errors severely disturb the final state of a computation, causing erroneous average value estimation. Thus for nonadiabatic holonomic quantum computation, an important topic is to investigate how to better give the average value of an observable under the condition of computation errors. While the above topic is important, the previous works in the field of nonadiabatic holonomic quantum computation pay woefully inadequate attention to it. In this paper, we show that rescaling the measurement results can better give the average value of an observable in nonadiabatic holonomic quantum computation when computation errors are considered. Particularly, we show that by rescaling the measurement results, $56.25\%$ of the computation errors can be reduced when using depolarizing noise model, a widely adopted noise model in quantum computation community, to analyse the benefit of our method.

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arXiv2023

Nonadiabatic holonomic quantum computation based on commutation relation

Nonadiabatic holonomic quantum computation has received increasing attention due to the merits of both robustness against control errors and high-speed implementation. A crucial step in realizing nonadiabatic holonomic quantum computation is to remove the dynamical phase from the total phase. For this reason, previous schemes of nonadiabatic holonomic quantum computation have to resort to the parallel transport condition, i.e., requiring the instantaneous dynamical phase to be always zero. In this paper, we put forward a strategy to design nonadiabatic holonomic quantum computation, which is based on a commutation relation rather than the parallel transport condition. Instead of requiring the instantaneous dynamical phase to be always zero, the dynamical part of the total phase is separated from the geometric part and then removed by properly choosing evolution parameters. This strategy enhances the flexibility to realize nonadiabatic holonomic quantum computation as the commutation relation is more relaxed than the parallel transport condition. It provides more options for realizing nonadiabatic holonomic quantum computation and hence allows us to optimize realizations such as the evolution time and evolution paths.

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arXiv2021

Two geometric phases can dramatically differ from each other even if their evolution paths are sufficiently close in a pointwise manner

One milestone in quantum physics is Berry's seminal work [Proc.~R.~Soc.~Lond.~A \textbf{392}, 45 (1984)], in which a quantal phase factor known as geometric phase was discovered to solely depend on the evolution path in state space. Here, we unveil that even an infinitesimal deviation of the initial state from the eigenstate of the initial Hamiltonian can yield a significant change of the geometric phase accompanying an adiabatic evolution. This leads to the surprising observation that two geometric phases can dramatically differ from each other even if their evolution paths are sufficiently close in a pointwise manner.

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arXiv2021

Realizing nonadiabatic holonomic quantum computation beyond the three-level setting

Nonadiabatic holonomic quantum computation (NHQC) provides a method to implement error resilient gates and that has attracted considerable attention recently. Since it was proposed, three-level Λ systems have become the typical building block for NHQC and a number of NHQC schemes have been developed based on such systems. In this paper, we investigate the realization of NHQC beyond the standard three-level setting. The central idea of our proposal is to improve NHQC by enlarging the Hilbert space of the building block system and letting it have a bipartite graph structure in order to ensure purely holonomic evolution. Our proposal not only improves conventional qubit-based NHQC by efficiently reducing its duration, but also provides implementations of qudit-based NHQC. Therefore, our proposal provides a further development of NHQC that can contribute significantly to the physical realization of efficient quantum information processors.

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arXiv2021

Dynamical-decoupling-protected nonadiabatic holonomic quantum computation

The main obstacles to the realization of high-fidelity quantum gates are the control errors arising from inaccurate manipulation of a quantum system and the decoherence caused by the interaction between the quantum system and its environment. Nonadiabatic holonomic quantum computation allows for high-speed implementation of whole-geometric quantum gates, making quantum computation robust against control errors. Dynamical decoupling provides an effective method to protect quantum gates against environment-induced decoherence, regardless of collective decoherence or independent decoherence. In this paper, we put forward a protocol of nonadiabatic holonomic quantum computation protected by dynamical decoupling . Due to the combination of nonadiabatic holonomic quantum computation and dynamical decoupling, our protocol not only possesses the intrinsic robustness against control errors but also protects quantum gates against environment-induced decoherence.

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arXiv2020

General approach for constructing Hamiltonians for nonadiabatic holonomic quantum computation

The main challenges in achieving high-fidelity quantum gates are to reduce the influence of control errors caused by imperfect Hamiltonians and the influence of decoherence caused by environment noise. To overcome control errors, a promising proposal is nonadiabatic holonomic quantum computation, which has attracted much attention in both theories and experiments. While the merit of holonomic operations resisting control errors has been well exploited, an important issue following is how to shorten the evolution time needed for realizing a holonomic gate so as to avoid the influence of environment noise as much as possible. In this paper, we put forward a general approach of constructing Hamiltonians for nonadiabatic holonomic quantum computation, which makes it possible to minimize the evolution time and might open a new horizon for the realistic implementation of nonadiabatic holonomic quantum computation.

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arXiv2020

Approach to realizing nonadiabatic geometric gates with prescribed evolution paths

Nonadiabatic geometric phases are only dependent on the evolution path of a quantum system but independent of the evolution details, and therefore quantum computation based on nonadiabatic geometric phases is robust against control errors. To realize nonadiabatic geometric quantum computation, it is necessary to ensure that the quantum system undergoes a cyclic evolution and the dynamical phases are removed from the total phases. To satisfy these conditions, the evolution paths in previous schemes are usually restricted to some special forms, e.g, orange-slice-shaped loops, which make the paths unnecessarily long in general. In this paper, we put forward an approach to the realization of nonadiabatic geometric quantum computation by which a universal set of nonadiabatic geometric gates can be realized with any desired evolution paths. Our approach makes it possible to realize geometric quantum computation with an economical evolution time so the influence of environment noises on the quantum gates can be minimized further.

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arXiv2019

Nonadiabatic holonomic multiqubit controlled gates

Previous schemes of nonadiabatic holonomic quantum computation were focused mainly on realizing a universal set of elementary gates. Multiqubit controlled gates could be built by decomposing them into a series of the universal gates. In this article, we propose an approach for realizing nonadiabatic holonomic multiqubit controlled gates in which a $(n+1)$-qubit controlled-$(\boldsymbol{\mathrm{n}\cdot \mathrmσ})$ gate is realized by $(2n-1)$ basic operations instead of decomposing it into the universal gates, whereas an $(n+1)$-qubit controlled arbitrary rotation gate can be obtained by combining only two such controlled-$(\boldsymbol{\mathrm{n}\cdot \mathrmσ})$ gates. Our scheme greatly reduces the operations of nonadiabatic holonomic quantum computation.

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arXiv2019

Experimental realization of nonadiabatic geometric gates with a superconducting Xmon qubit

Geometric phases are only dependent on evolution paths but independent of evolution details so that they own some intrinsic noise-resilience features. Based on different geometric phases, various quantum gates have been proposed, such as nonadiabatic geometric gates based on nonadiabatic Abelian geometric phases and nonadiabatic holonomic gates based on nonadiabatic non-Abelian geometric phases. Up to now, nonadiabatic holonomic one-qubit gates have been experimentally demonstrated with the supercondunting transmon, where three lowest levels with cascaded configuration are all applied in the operation. However, the second excited states of transmons have relatively short coherence time, which results in a lessened fidelity of quantum gates. Here, we experimentally realize Abelian-geometric-phase-based nonadiabatic geometric one-qubit gates with a superconducting Xmon qubit. The realization is performed on two lowest levels of an Xmon qubit and thus avoids the influence from the short coherence time of the second excited state. The experimental result indicates that the average fidelities of single-qubit gates can be up to 99.6% and 99.7% characterized by quantum process tomography and randomized benchmarking, respectively.

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arXiv2018

Single-shot realization of nonadiabatic holonomic gates with a superconducting Xmon qutrit

Nonadiabatic holonomic quantum computation has received increasing attention due to its robustness against control errors as well as high-speed realization. The original protocol of nonadiabatic holonomic one-qubit gates has been experimentally demonstrated with superconducting transmon qutrit. However, the original protocol requires two noncommuting gates to realize an arbitrary one-qubit gate, which doubles the exposure time of gates to error sources and therefore makes the gates vulnerable to environment-induced decoherence. Single-shot protocol was subsequently proposed to realize an arbitrary one-qubit nonadiabatic holonomic gate. In this paper, we experimentally realize the single-shot protocol of nonadiabatic holonomic single qubit gates with a superconducting Xmon qutrit, where all the Clifford element gates are realized by a single-shot implementation. Characterized by quantum process tomography and randomized benchmarking, the single-shot gates reach a fidelity larger than 99%.

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arXiv2018

Nonadiabatic holonomic quantum computation with Rydberg superatoms

Nonadiabatic holonomic quantum computation has received increasing attention due to its robustness against control errors as well as high-speed realization. Several schemes of its implementation have been put forward based on various physical systems, each of which has some particular merits. In this paper, we put forward an alternative scheme of nonadiabatic holonomic quantum computation, in which a universal set of quantum gates is realized based on Rydberg superatoms. A Rydberg superatom is a mesoscopic atomic ensemble that allows for only a single Rydberg excitation shared by many atoms within a blockade radius and can be used to generate the collective states to encode the qubits. In our scheme, the qubit is encoded into two collective ground states of Rydberg superatoms and the interaction between two long-range Rydberg superatoms is mediated by a microwave cavity with the aid of two additional collective Rydberg states. Different from the previous schemes,which are based on the systems in the microscope scale, the present scheme is based on atomic ensembles in the mesoscopic scale. Besides the common merits of nonadiabatic holonomic quantum computation such as the robustness and the speediness, the Rydberg-superatom-based scheme has the following particular merits: the long coherence time of Rydberg states and the operability of the mesoscopic systems.

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arXiv2017

Rydberg-atom-based scheme of nonadiabatic geometric quantum computation

Nonadiabatic geometric quantum computation provides a means to perform fast and robust quantum gates. It has been implemented in various physical systems, such as trapped ions, nuclear magnetic resonance and superconducting circuits. Another system being adequate for implementation of nonadiabatic geometric quantum computation may be Rydberg atoms, since their internal states have very long coherence time and the Rydberg-mediated interaction facilitates the implementation of a two-qubit gate. Here, we propose a scheme of nonadiabatic geometric quantum computation based on Rydberg atoms, which combines the robustness of nonadiabatic geometric gates with the merits of Rydberg atoms.

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