Geometric Gate Research Articles

Quantum computation in silicon-vacancy centers based on nonadiabatic geometric gates protected by dynamical decoupling

Quantum computation in silicon-vacancy centers based on nonadiabatic geometric gates protected by dynamical decoupling

Inertial geometric quantum logic gates

Inertial geometric quantum logic gates

Proposal for a nonadiabatic geometric gate with an Andreev spin qubit

Proposal for a nonadiabatic geometric gate with an Andreev spin qubit

Geometric Phase of a Transmon in a Dissipative Quantum Circuit.

Superconducting circuits reveal themselves as promising physical devices with multiple uses. Within those uses, the fundamental concept of the geometric phase accumulated by the state of a system shows up recurrently, as, for example, in the construction of geometric gates. Given this framework, we study the geometric phases acquired by a paradigmatic setup: a transmon coupled to a superconductor resonating cavity. We do so both for the case in which the evolution is unitary and when it is subjected to dissipative effects. These models offer a comprehensive quantum description of an anharmonic system interacting with a single mode of the electromagnetic field within a perfect or dissipative cavity, respectively. In the dissipative model, the non-unitary effects arise from dephasing, relaxation, and decay of the transmon coupled to its environment. Our approach enables a comparison of the geometric phases obtained in these models, leading to a thorough understanding of the corrections introduced by the presence of the environment.

Noncyclic nonadiabatic geometric quantum gates in a superconducting circuit

Noncyclic nonadiabatic geometric quantum gates in a superconducting circuit

State‐Independent Geometric Quantum Gates via Nonadiabatic and Noncyclic Evolution

AbstractGeometric phases are robust to local noises and the nonadiabatic ones can reduce the evolution time, thus nonadiabatic geometric gates have strong robustness and can approach high fidelity. However, the advantage of geometric phase has not been fully explored in previous investigations. Here,a scheme is proposed for universal quantum gates with pure nonadiabatic and noncyclic geometric phases from smooth evolution paths. In the scheme, only geometric phase can be accumulated in a fast way, and thus it not only fully utilizes the local noise resistant property of geometric phase but also reduces the difficulty in experimental realization. Numerical results show that the implemented geometric gates have stronger robustness than dynamical gates and the geometric scheme with cyclic path. Furthermore, it proposes to construct universal quantum gate on superconducting circuits, with the fidelities of single‐qubit gate and nontrivial two‐qubit gate can achieve 99.97% and 99.87%, respectively. Therefore, these high‐fidelity quantum gates are promising for large‐scale fault‐tolerant quantum computation.

Genuinely noncyclic geometric gates in two-pulse schemes

Genuinely noncyclic geometric gates in two-pulse schemes

Realization of high-fidelity and robust geometric gates with time-optimal control technique in superconducting quantum circuit

One of the key features required to realize fault-tolerant quantum computation is the robustness of quantum gates against errors. Since geometric quantum gate is naturally insensitivity to noise, it appears to be a promising routine to achieve high-fidelity, robust quantum gates. The implementation of geometric quantum gate however faces some troubles such as its complex interaction among multiple energy levels. Moreover, traditional geometric schemes usually take more time than equivalent dynamical ones. Here, we experimentally demonstrate a geometric gate scheme with the time-optimal control (TOC) technique in a superconducting quantum circuit. With a transmon qubit and operations restricted to two computational levels, we implement a set of geometric gates which exhibit better robustness features against control errors than the dynamical counterparts. The measured fidelities of TOC X gate and X/2 gate are 99.81% and 99.79% respectively. Our work shows a promising routine toward scalable fault-tolerant quantum computation.

Experimental Implementation of Short-Path Nonadiabatic Geometric Gates in a Superconducting Circuit

Nonadiabatic geometric quantum computation (NGQC) has attracted a lot of attention for noise-resilient quantum control. However, previous implementations of NGQC require long evolution paths that make them more vulnerable to incoherent errors than their dynamical counterparts. In this work, we experimentally realize a universal short-path nonadiabatic geometric gate set (SP NGQC) with a 2-times shorter evolution path on a superconducting quantum processor. Characterizing with both quantum process tomography and randomized benchmarking methods, we report an average single-qubit gate fidelity of $99.86\mathrm{%}$ and a two-qubit gate fidelity of $97.9\mathrm{%}$. Additionally, we demonstrate superior robustness of single-qubit SP NGQC gate to Rabi frequency error in some certain parameter space by comparing their performance to those of the dynamical gates and the former NGQC gates.

Fast and Robust Geometric Two-Qubit Gates for Superconducting Qubits and beyond

Quantum protocols based on adiabatic evolution are remarkably robust against imperfections of control pulses and system uncertainties. While adiabatic protocols have been successfully implemented for quantum operations such as quantum state transfer and single-qubit gates, their use for geometric two-qubit gates remains a challenge. In this paper, we propose a general scheme to realize robust geometric two-qubit gates in multilevel qubit systems where the interaction between the qubits is mediated by an auxiliary system (such as a bus or coupler). While our scheme utilizes stimulated Raman adiabatic passage (STIRAP), it is substantially simpler than STIRAP-based gates that have been proposed for atomic platforms, requiring fewer control tones and ancillary states, as well as utilizing only a generic dispersive interaction. We also show how our gate can be accelerated using a shortcuts-to-adiabaticity approach, allowing one to achieve a gate that is both fast and relatively robust. We present a comprehensive theoretical analysis of the performance of our two-qubit gate in parametrically modulated superconducting circuits comprising two fluxonium qubits coupled to an auxiliary system.

Optimized Unconventional Geometric Gates in Superconducting Circuits

Nonadiabatic Abelian geometric quantum computation has been extensively studied, due to its fast manipulation and inherent noise resistance. However, to obtain the pure geometric phase, the quantum state is required to evolve along some special paths to eliminate the dynamical phase. This leads to increasing evolution time and weakened gate robustness. The unconventional geometric quantum computation is an effective way to solve the above problems. Here, we propose a general approach to realize the unconventional geometric computation. Then, we discuss the effect of the ratio of geometric phase to dynamic phase on the performance of quantum gates. The results show that the selection of ratio corresponds to different quantum gate robustness. Therefore, we can optimize the ratio to get higher-fidelity quantum gates. At last, we construct the ratio-optimized quantum gates in a superconducting circuit and test its robustness. The fidelities of the T-gate, Hadamard H-gate, and controlled phase gate can be obtained as 99.98%, 99.95%, and 99.85%, respectively. Therefore, our scheme provides a promising way to realize large-scale fault-tolerant quantum computation in superconducting circuits.

Effective implementation of nonadiabatic geometric quantum gates of cat-state qubits using an auxiliary qutrit

We propose an effective protocol for the implementation of nonadiabatic geometric quantum gates of cat-state qubits in Kerr-nonlinear resonators driven by two-photon squeezing drives. Coupling the Kerr-nonlinear resonators with an auxiliary qutrit with proper coupling strengths, the selective transition of the auxiliary qutrit is realized. The selective transition can be exploited in the implementation of a set of useful quantum gates, including the phase gates, the NOT gates, the controlled-phase gates, the controlled NOT gates, and the Toffoli gates. Numerical simulations show the implementations of different types of gates are robust against systematic errors, random noise, and decoherence. Therefore, the protocol may be helpful for robust and scalable quantum computation based on cat-state qubits.

State-Independent Nonadiabatic Geometric Quantum Gates

Quantum computation has demonstrated advantages over classical computation for special hard problems, where a set of universal quantum gates is essential. Geometric phases, which have built-in resilience to local noise, have been used to construct quantum gates with excellent performance. However, this advantage has been smeared in previous schemes. Here, we propose a state-independent nonadiabatic geometric quantum-gate scheme that is able to realize a more fully geometric gate than previous approaches, allowing for the cancelation of dynamical phases accumulated by an arbitrary state. Numerical simulations demonstrate that our scheme has significantly stronger gate robustness than the previous geometric and dynamical ones. Meanwhile, we give a detailed physical implementation of our scheme with the Rydberg atom system based on the Rydberg blockade effect, specifically for multiqubit control-phase gates, which exceeds the fault-tolerance threshold of multiqubit quantum gates within the considered error range. Therefore, our scheme provides a promising way for fault-tolerant quantum computation in atomic systems.

Optimizing nonadiabatic geometric quantum gates against off-resonance error in a silicon-based spin qubit

Geometric quantum gates are performed by using the geometric phase, making them particularly robust to the pulse amplitude error. However, in many systems, such as the silicon-based spin qubits, the off-resonance error is the dominant noise, which can cause dephasing and is always difficult to deal with for a geometric gate. Thus how to combat with the off-resonance error is very significant for the application of the geometric gates. A recent work [S. Li and Z.-Y. Xue, Phys. Rev. Appl. 16, 044005 (2021).] revealed that by inserting two $\ensuremath{\pi}$ pulses into the evolution paths, the holonomic quantum gate is effective to suppress the pulse amplitude error, however, it is still useless for combating the off-resonance error. Inspired by this work, we combine using the techniques of dynamical correction and path design. Surprisingly, we find that, by picking up a specific evolution path inserted by only a $\ensuremath{\pi}$-pulse, the obtained optimized geometric gate is robust to the off-resonance error, assuming the noise is static. Further, by calculating the filter function considering the realistic $1/f$-type noise in silicon, the related results show that the performance of the optimized geometric gate can also surpass both the conventional geometric gate and the naive dynamical gate constructed without using the geometric phase. Our results indicate dynamical correction is a powerful tool to improve the geometric quantum computation to achieve a high-fidelity quantum gate in silicon.

Robust three-qubit search algorithm in Rydberg atoms via geometric control

Rydberg atoms possess long coherence time and inherent scalability, which makes it promising to implement quantum algorithms. An exact and robust quantum search algorithm (SA) is essential to some practical applications. Here we propose a multisolution three-qubit SA by employing quantum circuit and geometric operations, in which the target states can be successfully searched with the fidelity of at least 99.8$%$ and the geometric operators guarantee robustness against systematic errors. In particular, the geometric three-qubit gate operators employed reduce the implementation time and help to resist against the detrimental influence of decoherence. Moreover, our scheme can be straightforwardly extended to multiqubit cases. We have carried out numerical simulations based on the master equation to illustrate the superiority of our scheme. We consider that our study provides an alternative method for executing quantum SAs with high success probability.

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.

Fault-Tolerant Multiqubit Geometric Entangling Gates Using Photonic Cat-State Qubits

We propose a theoretical protocol to implement multiqubit geometric gates (i.e., the M{\o}lmer-S{\o}rensen gate) using photonic cat-state qubits. These cat-state qubits stored in high-$Q$ resonators are promising for hardware-efficient universal quantum computing. Specifically, in the limit of strong two-photon drivings, phase-flip errors of the cat-state qubits are effectively suppressed, leaving only a bit-flip error to be corrected. Because this dominant error commutes with the evolution operator, our protocol preserves the error bias, and, thus, can lower the code-capacity threshold for error correction. A geometric evolution guarantees the robustness of the protocol against stochastic noise along the evolution path. Moreover, by changing detunings of the cavity-cavity couplings at a proper time, the protocol can be robust against parameter imperfections (e.g., the total evolution time) without introducing extra noises into the system. As a result, the gate can produce multi-mode entangled cat states in a short time with high fidelities.

Two-Qubit Geometric Gates Based on Ground-State Blockade of Rydberg Atoms

We achieve the robust nonadiabatic holonomic two-qubit controlled gate in one step based on the ground-state blockade mechanism between two Rydberg atoms. By using the Rydberg-blockade effect and the Raman transition mechanism, we can produce the blockade effect of double occupation of the corresponding ground state, i.e., ground-state blockade, to encode the computational subspace into the ground state, thus effectively avoiding the spontaneous emission of the excited Rydberg state. On the other hand, the feature of geometric quantum computation independent of the evolutionary details makes the scheme robust to control errors. In this way, the controlled quantum gate constructed by our scheme not only greatly reduces the gate infidelity caused by spontaneous emission but is also robust to control errors.

Conditions for Equivalent Noise Sensitivity of Geometric and Dynamical Quantum Gates

Geometric quantum gates are often expected to be more resilient than dynamical gates against certain types of error, which would make them ideal for robust quantum computing. However, this is still up for debate due to seemingly conflicting results in the literature. Here we use dynamical invariant theory in conjunction with filter functions in order to analytically characterize the noise sensitivity of an arbitrary quantum gate. For any control Hamiltonian that produces a geometric gate, we find that under certain common conditions one can construct another control Hamiltonian that produces an equivalent dynamical gate with identical noise sensitivity (as characterized by the filter function). Our result holds for a Hilbert space of arbitrary dimensions, but we illustrate our result by examining experimentally relevant single-qubit scenarios and providing explicit examples of equivalent geometric and dynamical gates.

Fast multiqubit Rydberg geometric fan-out gates with optimal control technology

Practical quantum computation requires highly efficient implementation of quantum logic gates. The fan-out gate represents such a type of multiqubit controlled gate with one qubit controlling a number of target qubits. Recent efforts for fan-out gates using Rydberg atoms include adiabatic operations along with the dark-state dynamics of Rydberg states [M. Khazali and K. M\o{}lmer, Phys. Rev. X 10, 021054 (2020)] and implementation based on the asymmetric Rydberg-Rydberg interaction [J. T. Young et al., Phys. Rev. Lett. 127, 120501 (2021)]. Inspired by these advances, we propose a fast-operation scheme for geometric multiqubit fan-out gates, in which the target qubits can be executed with arbitrary operations based on the asymmetric Rydberg-Rydberg interaction and time-optimal control technology. One of the main favorable features of our scheme is its performance in a nonadiabatic way and with the time-optimal control technology, by which the shortest smooth geometric path is found. Another feature, that the target qubits could be executed with arbitrary geometric quantum operations, makes our scheme general and useful. Therefore, our scheme provides a promising alternative route toward scalable fault-tolerant quantum information processing based on Rydberg atoms.