Quantum computing and quantum simulation can be implemented by concatenation of one- and two-qubit gates and interactions. For most physical implementations, however, it may be advantageous to explore state components and interactions that depart from this universal paradigm and offer faster or more robust access to more advanced operations on the system. In this article, we show that adiabatic passage along the dark eigenstate of excitation exchange interactions can be used to implement fast multi-qubit Toffoli (C$_k$-NOT) and fan-out (C-NOT$^k$) gates. This mechanism can be realized by simultaneous excitation of atoms to Rydberg levels, featuring resonant exchange interaction. Our theoretical estimates and numerical simulations show that these multi-qubit Rydberg gates are possible with errors below 1% for up to 20 qubits. The excitation exchange mechanism is ubiquitous across experimental platforms and we show that similar multi-qubit gates can be implemented in superconducting circuits.
We develop new protocols for high-fidelity single qubit gates that exploit and extend theoretical ideas for accelerated adiabatic evolution. Our protocols are compatible with qubit architectures with highly isolated logical states, where traditional approaches are problematic; a prime example are superconducting fluxonium qubits. By using an accelerated adiabatic protocol we can enforce the desired adiabatic evolution while having gate times that are comparable to the inverse adiabatic energy gap (a scale that is ultimately set by the amount of power used in the control pulses). By modelling t…
High fidelity two-qubit gates are fundamental for scaling up the superconducting number. We use two qubits coupled via a frequency-tunable coupler which can adjust the coupling strength, and demonstrate the CZ gate using two different schemes, adiabatic and diabatic methods. The Clifford based Randomized Benchmarking (RB) method is used to assess and optimize the CZ gate fidelity. The fidelity of adiabatic and diabatic CZ gates are 99.53(8)% and 98.72(2)%, respectively. We also analyze the errors induced by the decoherence. Comparing to 30 ns duration time of adiabatic CZ gate, the duration ti…
Based on a `shortcut-to-adiabaticity' (STA) scheme, we theoretically design and experimentally realize a set of high-fidelity single-qubit quantum gates in a superconducting Xmon qubit system. Through a precise microwave control, the qubit is driven to follow a fast `adiabatic' trajectory with the assistance of a counter-diabatic field and the correction of derivative removal by adiabatic gates. The experimental measurements of quantum process tomography and interleaved randomized benchmarking show that the process fidelities of our STA quantum gates are higher than 94.9% and the gate fideliti…
For a frequency-tunable two-qubit system, a controlled-Z (CZ) gate can be realized by adiabatically driving the qubit system through an avoided level crossing between an auxiliary state and computational levels. Here, we theoretically propose a fast CZ gate using a shortcut-to-adiabaticity (STA). Experimentally, the STA CZ gate is implemented with a 52 ns control pulse for two coupled superconducting Xmon qubits. Measured fidelity of the STA CZ gate is higher than 96.0%, in both quantum process tomography and randomized benchmarking. The protocol allows a flexible design of the evolution time …
Implementation of controlled phase shift gates and Collins version of Deutsch-Jozsa algorithm on a quadrupolar spin-7/2 nucleus using non-adiabatic geometric phases
High-fidelity non-adiabatic dark state gates for neutral atoms
Zentrum für Optische Quantentechnologien, Universität Hamburg（汉堡大学光学量子技术中心）；The Hamburg Centre for Ultrafast Imaging, Universität Hamburg（汉堡超快成像中心，汉堡大学）；UTC Quantum Center, University of Tennessee, Chattanooga（田纳西大学查塔努加分校UTC量子中心）
Alternative scheme for two-qubit conditional phase gate by adiabatic passage under dissipation
我们检查最近的一个建议[H。Goto和K。Ichimura Phys. Rev. A 70，012305（2004）]中描述的方法，用于在自发发射和腔衰减的影响下通过绝热通道的受控相位门。我们证明了上述建议的修改可以用于在两量子比特Grover搜索中生成必要的条件相位门。在门控期间没有来自原子激发态和腔模的光子泄漏的条件下，数值分析了绝热通过的两量子比特条件相位门的成功概率和保真度.我们提出的门控方案和以前的方案之间的比较表明，Goto和Ichimura的方案是一种替代的和可行的方式在光学腔制度的两个量子位门，并可以推广到多量子位门的原则。
The non-adiabatic holonomic quantum computation with the advantages of fast and robustness attracts widespread attention in recent years. Here, we propose the first scheme for realizing universal single-qubit gates based on an optomechanical system working with the non-adiabatic geometric phases. Our quantum gates are robust to the control errors and the parameter fluctuations, and have unique functions to achieve the quantum state transfer and entanglement generation between cavities. We discuss the corresponding experimental parameters and give some simulations. Our scheme may have the pract…
Adiabatic quantum computation (AQC), which is particularly useful for combinatorial optimization, becomes more powerful by using excited states, instead of ground states. However, the excited-state AQC is prone to errors due to dissipation. Here we propose the excited-state AQC started with the most stable state, i.e., the vacuum state. This counterintuitive approach becomes possible by using a driven quantum system, or more precisely, a network of Kerr-nonlinear parametric oscillators (KPOs). By numerical simulations, we show that some hard instances, where standard ground-state AQC with KPOs…
Comment on "Nongeometric Conditional Phase Shift via Adiabatic Evolution of Dark Eigenstates: A New Approach to Quantum Computation"
在[Phys. Rev. Lett. 95，080502（2005）]，Zheng提出了一种通过绝热通道实现条件相移的方案。作者声称，门是“既不是动力学的，也不是几何起源”的理由是，汉密尔顿不遵循循环变化。他进一步指出：“与绝热几何门相比，不需要非平凡的循环回路，从而避免了在获得所需立体角时的误差，这使得这种新的相位门优于几何门。本文指出几何运算，包括绝热完整性，都可以由非循环哈密顿算子导出，并证明了郑门是几何的。我们还认为，负责相移的非平凡环路是存在的，它需要与任何绝热几何门相同的精度。
We propose a method to design pulses in a resonant three-level system to enhance the robustness of non-adiabatic geometric gate operations. By optimizing the shape of the pulse envelope, we show that the gate operations are more robust against frequency detuning than they are with Gaussian and square pulses. Our method provides a way to design pulses that can be employed in a system where robustness against frequency variations or inhomogeneous broadening is required,and may be extended to ensure robustness against other physical imperfections such as intensity fluctuations and random noises.
We extend recent work on a leakage-protected, adiabatic entangling gate for exchange-only spin qubits [Doherty and Wardrop, PRL 111, 050503 (2013)] by adapting to a setting where single spins are not assumed to be polarized on preparation. Previous gate constructions do not function correctly when "gauge spins" are uninitialized, because the entangling gate has different, non-trivial action in different gauge subspaces. Our construction inherits many of the desirable features of the previous work while addressing the gauge-dependent behavior. Using numerical simulation, we show that the result…
In this paperwe propose two theoretical schemes for implementation of quantum phase gates by engineering the phase-sensitive dark state of two atoms subjected to Rydberg-Rydberg interaction. Combining the conventional adiabatic techniques and currently developed approaches of phase control, a feasible proposal for implementation of a geometric phase gate is presented, where the conditional phase shift (Berry phase) is achieved by adiabatically and cyclically changing the parameters of the driving fields. Here we find that the geometric phase acquired is related to the way how the relative phas…
Fast Adiabatic Quantum Gates via Hyperfine Intermediate States
Quantum Institute for Light and Atoms, School of Physics, East China Normal University（华东师范大学物理学院光与原子量子研究所）；School of Physics, Henan Normal University（河南师范大学物理学院）；Chongqing Institute of East China Normal University（华东师范大学重庆研究院）；Collaborative Innovation Center of Extreme Optics, Shanxi University（山西大学极端光学协同创新中心）
Stabilized cat codes can provide a biased noise channel with a set of bias-preserving (BP) gates, which can significantly reduce the resource overhead for fault-tolerant quantum computing. All existing schemes of BP gates, however, require adiabatic quantum evolution, with performance limited by excitation loss and non-adiabatic errors during the adiabatic gates. In this work, we apply a derivative-based leakage suppression technique to overcome non-adiabatic errors, so that we can implement fast BP gates on Kerr-cat qubits with improved gate fidelity while maintaining high noise bias. When ap…
One scheme is presented to construct the robust multi-qubit arbitrary-phase controlled-phase gate (CPG) with one control and multiple target qubits in Rydberg atoms using the Lewis-Riesenfeld (LR) invariant method. The scheme is not limited by adiabatic condition while preserves the robustness against control parameter variations of adiabatic evolution. Comparing with the adiabatic case, our scheme does not require very strong Rydberg interaction strength. Taking the construction of two-qubit $π$ CPG as an example, our scheme is more robust against control parameter variations than non-adiabat…
High-fidelity quantum gates are essential for large-scale quantum computation. However, any quantum manipulation will inevitably affected by noises, systematic errors and decoherence effects, which lead to infidelity of a target quantum task. Therefore, implementing high-fidelity, robust and fast quantum gates is highly desired. Here, we propose a fast and robust scheme to construct high-fidelity holonomic quantum gates for universal quantum computation based on resonant interaction of three-level quantum systems via shortcuts to adiabaticity. In our proposal, the target Hamiltonian to induce …
Fast and robust quantum gates is the cornerstone of fault-tolerance quantum computation. In this paper, we propose to achieve quantum gates based on non-cyclic geometric evolution. Dynamical phase during the evolution is cancelled by spin-echo process and the adiabatic control can be sped up through shortcut to adiabatic manner. Different from geometric gates based on cyclic evolution, the superiority of non-cyclic scheme is that the operation time is proportional to the rotation angle (but not the geometric phase) of quantum state. Therefore, the non-cyclic scheme becomes fairly fast in the c…
We implemented arbitrary single qubit gates of geometric quantum computing for a three-level system in a single-shot manner. The evolution time of the gate has been minimized by considering the shortest trajectory of the state on the Bloch sphere. The duration of gates grows from zero with the rotation angle $γ$, and the tested T gate time can be reduced to $\sim$40\% of those in the traditional orange-sliced-shaped path non-adiabatic holonomic quantum computing (NHQC) scheme by the parametrization of Rabi frequency. We also demonstrated that certain pulses are robust against static detuning e…
High-fidelity two-qubit entangling gates are essential building blocks for fault-tolerant quantum computers. Over the past decade, tremendous efforts have been made to develop scalable high-fidelity two-qubit gates with superconducting quantum circuits. Recently, an easy-to-scale controlled-phase gate scheme that utilizes the tunable-coupling architecture with fixed-frequency qubits [Phys. Rev. Lett. 125, 240502; Phys. Rev. Lett. 125, 240503] has been demonstrated with high fidelity and attracted broad interest. However, in-depth understanding of the underlying mechanism is still missing, prev…
Geometric phases are noise-resilient, and thus provide a robust way towards high fidelity quantum manipulation. Here we experimentally demonstrate arbitrary non-adiabatic holonomic single-qubit quantum gates for both a superconducting transmon qubit and a microwave cavity in a single-loop way. In both cases, an auxiliary state is utilized, and two resonant microwave drives are simultaneously applied with well-controlled but varying amplitudes and phases for the arbitrariness of the gate. The resulting gates on the transmon qubit achieve a fidelity of 0.996 characterized by randomized benchmark…
Shortcuts to adiabaticity is a general method for speeding up adiabatic quantum protocols, and has many potential applications in quantum information processing. Unfortunately, analytically constructing shortcuts to adiabaticity for systems having complex interactions and more than a few levels is a challenging task. This is usually overcome by assuming an idealized Hamiltonian [e.g., only a limited subset of energy levels are retained, and the rotating-wave approximation (RWA) is made]. Here we develop an $analytic$ approach that allows one to go beyond these limitations. Our method is genera…
