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1. Speed limits of two-qubit gates with qudits

   Basyildiz, Bora; Jameson, Casey; Gong, Zhexuan (December 2023, arXiv)

   The speed of elementary quantum gates ultimately sets the limit on the speed at which quantum circuits can operate. For a fixed physical interaction strength between two qubits, the speed of any two-qubit gate is limited even with arbitrarily fast single-qubit gates. In this work, we explore the possibilities of speeding up two-qubit gates beyond such a limit by expanding our computational space outside the qubit subspace, which is experimentally relevant for qubits encoded in multi-level atoms or anharmonic oscillators. We identify an optimal theoretical bound for the speed limit of a two-qubit gate achieved using two qudits with a bounded interaction strength and arbitrarily fast single-qudit gates. In addition, we find an experimentally feasible protocol using two parametrically coupled superconducting transmons that achieves this theoretical speed limit in a non-trivial way. We also consider practical scenarios with limited single-qudit drive strengths and off-resonant transitions. For such scenarios, we develop an open-source, machine learning assisted, quantum optimal control algorithm that can achieve a speedup close to the theoretical limit with near-perfect gate fidelity. This work opens up a new avenue to speed up two-qubit gates when the physical interaction strength between qubits cannot be easily increased while extra states outside the qubit subspace can be well controlled. 

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2. A universal quantum gate set for transmon qubits with strong ZZ interactions

   Junling Long, Tongyu Zhao (March 2021, ArXivorg)

   null (Ed.)

   High-fidelity single- and two-qubit gates are essential building blocks for a fault-tolerant quantum computer. While there has been much progress in suppressing single-qubit gate errors in superconducting qubit systems, two-qubit gates still suffer from error rates that are orders of magnitude higher. One limiting factor is the residual ZZ-interaction, which originates from a coupling between computational states and higher-energy states. While this interaction is usually viewed as a nuisance, here we experimentally demonstrate that it can be exploited to produce a universal set of fast single- and two-qubit entangling gates in a coupled transmon qubit system. To implement arbitrary single-qubit rotations, we design a new protocol called the two-axis gate that is based on a three-part composite pulse. It rotates a single qubit independently of the state of the other qubit despite the strong ZZ-coupling. We achieve single-qubit gate fidelities as high as 99.1% from randomized benchmarking measurements. We then demonstrate both a CZ gate and a CNOT gate. Because the system has a strong ZZ-interaction, a CZ gate can be achieved by letting the system freely evolve for a gate time tg=53.8 ns. To design the CNOT gate, we utilize an analytical microwave pulse shape based on the SWIPHT protocol for realizing fast, low-leakage gates. We obtain fidelities of 94.6% and 97.8% for the CNOT and CZ gates respectively from quantum progress tomography. 

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3. High-fidelity parallel entangling gates on a neutral-atom quantum computer

   https://doi.org/10.1038/s41586-023-06481-y  

   Evered, Simon J; Bluvstein, Dolev; Kalinowski, Marcin; Ebadi, Sepehr; Manovitz, Tom; Zhou, Hengyun; Li, Sophie H; Geim, Alexandra A; Wang, Tout T; Maskara, Nishad; et al (October 2023, Nature)

   Abstract The ability to perform entangling quantum operations with low error rates in a scalable fashion is a central element of useful quantum information processing¹. Neutral-atom arrays have recently emerged as a promising quantum computing platform, featuring coherent control over hundreds of qubits^2,3and any-to-any gate connectivity in a flexible, dynamically reconfigurable architecture⁴. The main outstanding challenge has been to reduce errors in entangling operations mediated through Rydberg interactions⁵. Here we report the realization of two-qubit entangling gates with 99.5% fidelity on up to 60 atoms in parallel, surpassing the surface-code threshold for error correction^6,7. Our method uses fast, single-pulse gates based on optimal control⁸, atomic dark states to reduce scattering⁹and improvements to Rydberg excitation and atom cooling. We benchmark fidelity using several methods based on repeated gate applications^10,11, characterize the physical error sources and outline future improvements. Finally, we generalize our method to design entangling gates involving a higher number of qubits, which we demonstrate by realizing low-error three-qubit gates^12,13. By enabling high-fidelity operation in a scalable, highly connected system, these advances lay the groundwork for large-scale implementation of quantum algorithms¹⁴, error-corrected circuits⁷and digital simulations¹⁵. 

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4. Practical implications of SFQ-based two-qubit gates

   https://doi.org/10.1109/QCE52317.2021.00061  

   Jokar, Mohammad Reza; Rines, Richard; Chong, Frederic T. (October 2021, 2021 IEEE International Conference on Quantum Computing and Engineering (QCE))

   Scalability of today’s superconducting quantum computers is limited due to the huge costs of generating/routing microwave control pulses per qubit from room temperature. One active research area in both industry and academia is to push the classical controllers to the dilution refrigerator in order to increase the scalability of quantum computers. Superconducting Single Flux Quantum (SFQ) is a classical logic technology with low power consumption and ultra-high speed, and thus is a promising candidate for in-fridge classical controllers with maximized scalability. Prior work has demonstrated high-fidelity SFQ-based single-qubit gates. However, little research has been done on SFQ-based multi-qubit gates, which are necessary to realize SFQ-based universal quantum computing.In this paper, we present the first thorough analysis of SFQ-based two-qubit gates. Our observations show that SFQ-based two-qubit gates tend to have high leakage to qubit non-computational subspace, which presents severe design challenges. We show that despite these challenges, we can realize gates with high fidelity by carefully designing optimal control methods and qubit architectures. We develop optimal control methods that suppress leakage, and also investigate various qubit architectures that reduce the leakage. After carefully engineering our SFQ-friendly quantum system, we show that it can achieve similar gate fidelity and gate time to microwave-based quantum systems. The promising results of this paper show that (1) SFQ-based universal quantum computation is both feasible and effective; and (2) SFQ is a promising approach in designing classical controller for quantum machines because it can increase the scalability while preserving gate fidelity and performance. 

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5. Practical and fundamental limits of neutral atom entanglement using Rydberg dressing

   https://doi.org/10.48550/arXiv.2205.12866  

   Mitra, A.; Omanakuttan, S.; Martin, M.J.; Biedermann, G.W.; Deutsch, I.H. (July 2022, ArXivorg)

   We revisit the implementation of a two-qubit entangling gate, the Mølmer-Sørensen gate, using the adiabatic Rydberg dressing paradigm. We study the implementation of rapid adiabatic passage using a two-photon transition, which does not require the use of an ultra-violet laser, and can be implemented using only amplitude modulation of one field with all laser frequencies fixed. We find that entangling gate fidelities, comparable to the one-photon excitation, are achievable with the two-photon excitation. Moreover, we address how the adiabatic dressing protocol can be used to implement entangling gates outside the regime of a perfect Rydberg blockade. We show that using adiabatic dressing we can achieve a scaling of gate fidelity set by the fundamental limits to entanglement generated by the Rydberg interactions while simultaneously retaining limited population in the doubly excited Rydberg state. This allows for fast high fidelity gates for atoms separated beyond the blockade radius. 

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