Nonadiabatic Holonomic Quantum Computation Research Articles

Nonadiabatic Holonomic Quantum Computation Based on Rydberg Ground State Blockade

Quantum gates are crucial for quantum computation and quantum information processing. However, their effectiveness is often hindered by systematic errors and decoherence. Therefore, achieving resilient quantum gates to these factors is of great significance. We present a method to construct nonadiabatic holonomic single- and two-qubit gates in a Rydberg ground-state-blockade regime. Our approach utilizes a far-off-resonant technique for the single-qubit gate and a modified Rydberg antiblockade for the two-qubit gate. The reduction of the population of single- and two-excitation Rydberg states and the nonadiabatic holonomic process during the construction of the gates ensure robustness to decoherence and systematic errors, respectively. Numerical results demonstrate the fidelity and robustness of our scheme. The proposed scheme holds promise for future applications in quantum computation and quantum information processing tasks.

Chiral resolution based on non-adiabatic holonomic quantum control via a transmon qutrit

Once the concept of chiral molecules was proposed, the task of chiral resolution has accompanied around in the related area. Naturally, scientists need fast and accurate methods to distinguish different chiralities. Here, we show a feasible method based on non-adiabatic holonomic quantum computation (NHQC), which can achieve over 99% discrimination of different chiralities. Based on the original scheme, we studied the modified version, NHQC+. The experimental data proved that it has better robustness than the original protocol, indicating a promising development in the relevant fields.

Nonadiabatic holonomic quantum computation and its optimal control

Nonadiabatic holonomic quantum computation and its optimal control

Nonadiabatic holonomic quantum computation based on a commutation relation

Nonadiabatic holonomic quantum computation based on a commutation relation

Decoherence-suppressed nonadiabatic holonomic quantum computation

Nonadiabatic holonomic quantum computation (NHQC) provides an essential way to construct robust and high-fidelity quantum gates due to its geometric features. However, NHQC is more sensitive to decay and dephasing errors than a conventional dynamical gate since it requires an ancillary intermediate state. Here, we utilize the Hamiltonian reverse engineering technique to study the influence of intermediate-state decoherence on NHQC gate fidelity, and propose schemes to construct an arbitrary single-qubit holonomic gate and nontrivial two-qubit holonomic gate with high fidelity and robustness to the decoherence. Although the proposed method is generic and can be applied to many experimental platforms, such as superconducting qubits, trapped ions, and quantum dots, here we take a nitrogen-vacancy center as an example to show that the gate fidelity can be significantly enhanced from 89% to 99.6% in contrast to recent experimental NHQC schemes [Phys. Rev. Lett. 119, 140503 (2017); Nat. Photonics 11, 309 (2017); Opt. Lett. 43, 2380 (2018)], and the robustness against decoherence can also be significantly improved. All in all, our scheme provides a promising way for fault-tolerant geometric quantum computation.

Dark path holonomic qudit computation

Non-adiabatic holonomic quantum computation is a method used to implement high-speed quantum gates with non-Abelian geometric phases associated with paths in state space. Due to their noise tolerance, these phases can be used to construct error resilient quantum gates. We extend the holonomic dark path qubit scheme in [M.-Z. Ai {\t et al.}, Fundam. Res. {\bf 2}, 661 (2022)] to qudits. Specifically, we demonstrate one- and two-qudit universality by using the dark path technique. Explicit qutrit ($d=3$) gates are demonstrated and the scaling of the number of loops with the dimension $d$ is addressed. This scaling is linear and we show how any diagonal qudit gate can be implemented efficiently in any dimension.

Effective non-adiabatic holonomic quantum computation of cavity modes via invariant-based reverse engineering.

In this paper, we propose a protocol to realize non-adiabatic holonomic quantum computation (NHQC) of cavity modes via invariant-based reverse engineering. Coupling cavity modes with an auxiliary atom trapped in a cavity, we derive effective Hamiltonians with the help of laser pulses. Based on the derived Hamiltonians, invariant-based reverse engineering is used to find proper evolution paths for NHQC. Moreover,the systematic-error-sensitivity nullified optimal control method is considered in the parameter selections, making the protocol insensitive to the influence of systematic errors of pulses. We also estimate the imperfections induced by random noise and decoherence. Numerical results show that the protocol holds robustness against these imperfections. Therefore, the protocol may provide useful perspectives to quantum computation with optical qubits in cavity quantum electrodynamics systems. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.

Nonadiabatic Holonomic Quantum Computation via Path Optimization

Nonadiabatic holonomic quantum computation (NHQC) is implemented by fast evolution processes in a geometric way to withstand local noises. However, recent works of implementing NHQC are sensitive to the systematic noise and error. Here, we present a path-optimized NHQC (PONHQC) scheme based on the non-Abelian geometric phase, and find that a geometric gate can be constructed by different evolution paths, which have different responses to systematic noises. Due to the flexibility of the PONHQC scheme, we can choose an optimized path that can lead to excellent gate performance. Numerical simulation shows that our optimized scheme can greatly outperform the conventional NHQC scheme, in terms of both fidelity and robustness of the gates. In addition, we propose to implement our strategy on superconducting quantum circuits with decoherence-free subspace encoding with the experiment-friendly two-body exchange interaction. Therefore, we present a flexible NHQC scheme that is promising for the future robust quantum computation.

One-step implementation of Rydberg nonadiabatic noncyclic geometric quantum computation in decoherence-free subspaces

Quantum gates constructed by geometric phase are naturally robust to control errors due to the global nature of the geometric evolution path. Therefore, how to cope with the inevitable decoherence errors is worthy of serious attention for geometric quantum computation. Different from conventional nonadiabatic geometric quantum computation (NGQC), which needs the same evolution time for any geometric rotation angle, we have proposed and experimentally demonstrated nonadiabatic noncyclic geometric quantum computation (NNGQC) without the requirement of the cyclic evolution condition, which thus reduces decoherence errors due to shortened evolution time [J. W. Zhang et al., Phys. Rev. Lett. 127, 030502 (2021)]. In addition, the use of decoherence-free subspaces (DFS) is another effective strategy to protect quantum gates from dephasing error and has been studied in nonadiabatic holonomic quantum computation [G. F. Xu et al., Phys. Rev. Lett. 109, 170501 (2012)]. Motivated by previous studies, we propose a one-step scheme to implement single-qubit NNGQC operation in DFS constructed by two Rydberg atoms, and then generalize the scheme to the two-logical-qubit case in one step. The numerical results show that our scheme is robust against decoherence in contrast to the NGQC counterparts. The present scheme combines the features of NNGQC and DFS and can further reduce the impact of decoherence on gate infidelity, which may provide an option for the realization of Rydberg-atom-based quantum computation in the future.

Composite Short-Path Nonadiabatic Holonomic Quantum Gates

Nonadiabatic holonomic quantum computation (NHQC) has attracted significant attention due to its fast evolution and the geometric nature-induced resilience to local noises. However, its long operation time and complex physical implementation make it hard to surpass the dynamical scheme, and thus hindering its wide application. Here, we present to implement NHQC with the shortest path under some conditions, through the inverse Hamiltonian engineering technique, which posseses higher fidelity and stronger robustness than previous NHQC schemes. Meanwhile, the gate performance in our scheme can be further improved by using the proposed composite dynamical decoupling pulses, which can efficiently improve both the gate fidelity and robustness, making our scheme outperform the optimal dynamical scheme in a certain parameter range. Remarkably, our scheme can be readily implemented with Rydberg atoms, and a simplified implementation of the controlled-not gate in the Rydberg blockade regime can be achieved. Therefore, our scheme represents a promising progress towards future fault-tolerant quantum computation in atomic systems.

One-Step Implementation of Time-Optimal-Control Three-Qubit Nonadiabatic Holonomic Controlled Gates in Rydberg Atoms

We propose a one-step scheme to implement the time-optimal nonadiabatic holonomic three-qubit controlled gates in Rydberg atoms by modulating Rabi frequencies of driving fields on the target atom. We perform the time-optimal operations following the brachistochrone curve, after which the scheme manifests completely different characteristics in contrast to the conventional nonadiabatic holonomic quantum computation (NHQC) that all operations require exactly the same evolution time, even for small angular rotations. Since the present three-qubit controlled-gate scheme significantly reduces the evolution time, the influence of decoherence can be greatly reduced. On the other hand, the robustness on the systematic error can also be guaranteed by the feature of geometric phase. The simulation through master equation verifies the high fidelity and robustness of our scheme. Although we use the Rydberg-atom system to verify the feasibility of our scheme, any quantum platforms capable of achieving the same form of effective Hamiltonian is feasible, which means the proposed three-qubit time-optimal-control nonadiabatic holonomic gates is independent of the particular physical platform and may have the potential for wider application.

Superrobust Geometric Control of a Superconducting Circuit

Geometric phases accompanying adiabatic quantum evolutions can be used to construct robust quantum control for quantum information processing due to their noise-resilient feature. A significant development along this line is to construct geometric gates using nonadiabatic quantum evolutions to reduce errors due to decoherence. However, it has been shown that nonadiabatic geometric gates are not necessarily more robust than dynamical ones, in contrast to an intuitive expectation. Here we experimentally investigate this issue for the case of nonadiabatic holonomic quantum computation~(NHQC) and show that conventional NHQC schemes cannot guarantee the expected robustness due to a cross coupling to the states outside the computational space. We implement a different set of constraints for gate construction in order to suppress such cross coupling to achieve an enhanced robustness. Using a superconducting quantum circuit, we demonstrate high-fidelity holonomic gates whose infidelity against quasi-static transverse errors can be suppressed up to the fourth order, instead of the second order in conventional NHQC and dynamical gates. In addition, we explicitly measure the accumulated dynamical phase due to the above mentioned cross coupling and verify that it is indeed much reduced in our NHQC scheme. We further demonstrate a protocol for constructing two-qubit NHQC gates also with an enhanced robustness.

Dynamically Corrected Nonadiabatic Holonomic Quantum Gates

The key for realizing fault-tolerant quantum computation lies in maintaining the coherence of all qubits so that high-fidelity and robust quantum manipulations on them can be achieved. One of the promising approaches is to use geometric phases in the construction of universal quantum gates, due to their intrinsic robustness against certain types of local noises. However, due to limitations in previous implementations, the noise-resilience feature of nonadiabatic holonomic quantum computation (NHQC) still needs to be improved. Here, combining with the dynamical correction technique, we propose a general protocol of universal NHQC with simplified control, which can greatly suppress the effect of the accompanied X errors, retaining the main merit of geometric quantum operations. Numerical simulation shows that the performance of our gate can be much better than previous protocols. Remarkably, when incorporating a decoherence-free subspace encoding for the collective dephasing noise, our scheme can also be robust against the involved Z errors. In addition, we also outline the physical implementation of the protocol that is insensitive to both X and Z errors. Therefore, our protocol provides a promising strategy for scalable fault-tolerant quantum computation.

Ultrafast Holonomic Quantum Gates

Quantum computation based on geometric phase is generally believed to be more robust against certain errors or noises than the conventional dynamical strategy. However, the gate error caused by the decoherence effect is inevitable, and thus faster gate operations are highly desired. Here, we propose a nonadiabatic holonomic quantum computation (NHQC) scheme with detuned interactions on $\Delta$-type three-level system, which combines the time-optimal control technique with the time-independent detuning adjustment to further accelerate universal gate operations, {so that the gate-time can be greatly shortened within the hardware limitation}, and thus high-fidelity gates can be obtained. Meanwhile, our numerical simulations show that the gate robustness is also stronger than previous schemes. Finally, we present an implementation of our proposal on superconducting quantum circuits, with a decoherence-free subspace encoding, based on the experimentally demonstrated parametrically tunable coupling technique, which simplifies previous investigations. Therefore, our protocol provides a more promising alternative for future fault-tolerant quantum computation.

Fast binomial-code holonomic quantum computation with ultrastrong light-matter coupling

We propose a protocol for bosonic binomial-code nonadiabatic holonomic quantum computation in a system composed of an artificial atom ultrastrongly coupled to a cavity resonator. In our protocol, the binomial codes, formed by superpositions of Fock states, can greatly save physical resources to correct errors in quantum computation. We apply to the system strong driving fields designed by shortcuts-to-adiabatic methods. This reduces the gate time to tens of nanoseconds. Decoherence of the system accumulated over time can be effectively reduced by such a fast evolution. Noise induced by control imperfections can be suppressed by a systematic-error-sensitivity nullification method, thus the protocol is mostly insensitive to such noises. As a result, this protocol can rapidly ($\sim 35$ ns) generate fault-tolerant and high-fidelity ($\gtrsim 98\%$ with experimentally realistic parameters) quantum gates.

Realization of Deutsch–Jozsa Algorithm in Rydberg Atoms by Composite Nonadiabatic Holonomic Quantum Computation with Strong Robustness Against Systematic Errors

AbstractDeutsch–Jozsa (DJ) algorithm, as the first example of quantum algorithm, performs better than any classical algorithm for distinguishing balance and constant functions. Here, a scheme to implement the DJ algorithm in Rydberg atoms using the composite nonadiabatic holonomic quantum computation (NHQC) is presented. Taking advantages of composite loops and holonomic features to resist systematic errors, the scheme of composite NHQC works more robustly compared with the standard dynamic counterparts. By exemplifying the DJ algorithm implementation, the performance of single‐loop NHQC‐, composite NHQC‐, and the dynamic counterpart‐based processes are compared both analytically and numerically, indicating the best robustness of composite scheme to systematic errors. In addition, the combination of composite NHQC and quantum algorithm also provides an alternative pathway for the realization of robust quantum algorithm in the future.

Super-robust nonadiabatic geometric quantum control

Nonadiabatic geometric quantum computation (NGQC) and nonadiabatic holonomic quantum computation (NHQC) have been proposed to reduce the run time of geometric quantum gates. However, in terms of robustness against experimental control errors, the existing NGQC and NHQC scenarios have no advantage over standard dynamical gates in most cases. Here, we give the reasons why nonadiabatic geometric gates are sensitive to the control errors and, further, we propose a scheme of super-robust nonadiabatic geometric quantum control, in which the super-robust condition can guarantee both high speed and robustness of the geometric gate. To illustrate the working mechanism of super-robust geometric quantum gates, we give two simple examples of SR-NGQC and SR-NHQC for two- and three-level quantum systems, respectively. Theoretical and numerical results with the experimental parameters indicate that our scheme can significantly improve the gate performance compared to the previous NGQC, NHQC, and standard dynamical schemes. Super-robust geometric quantum computation can be applied to various physical platforms such as superconducting qubits, quantum dots, and trapped ions. All of these sufficiently show that our scheme provides a promising way towards robust geometric quantum computation.

Experimental Implementation of Universal Holonomic Quantum Computation on Solid-State Spins with Optimal Control

Experimental realization of a universal set of quantum logic gates with high-fidelity is critical to quantum information processing, which is always challenging by inevitable interaction between the quantum system and environment. Geometric quantum computation is noise immune, and thus offers a robust way to enhance the control fidelity. Here, we experimentally implement the recently proposed extensible nonadiabatic holonomic quantum computation with solid spins in diamond at room-temperature, which maintains both flexibility and resilience against decoherence and system control errors. Compared with previous geometric method, the fidelities of a universal set of holonomic single-qubit and two-qubit quantum logic gates are improved in experiment. Therefore, this work makes an important step towards fault-tolerant scalable geometric quantum computation in realistic systems.

Optimized nonadiabatic holonomic quantum computation based on Förster resonance in Rydberg atoms

In this paper, we propose a scheme for implementing the nonadiabatic holonomic quantum computation (NHQC+) of two Rydberg atoms by using invariant-based reverse engineering (IBRE). The scheme is based on Förster resonance induced by strong dipole-dipole interaction between two Rydberg atoms, which provides a selective coupling mechanism to simply the dynamics of system. Moreover, for improving the fidelity of the scheme, the optimal control method is introduced to enhance the gate robustness against systematic errors. Numerical simulations show the scheme is robust against the random noise in control fields, the deviation of dipole-dipole interaction, the Förster defect, and the spontaneous emission of atoms. Therefore, the scheme may provide some useful perspectives for the realization of quantum computation with Rydberg atoms.

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 {\Lambda} 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.