Recent experimental work on superconducting transmon qubits in 3D cavities show that their coherence times are increased by an order of magnitude compared to their 2D cavity counterparts. However to take advantage of these coherence times while scaling up the number of qubits it is advantageous to address individual qubits which are all coupled to the same 3D cavity fields. The challenge in controlling this system comes from spectral crowding, where leakage transition of qubits are close to computational transitions in other. Here it is shown that fast pulses are possible which address single qubits using two quadrature control of the pulse envelope while the DRAG method alone only gives marginal improvements over the conventional Gaussian pulse shape. On the other hand, a first order result using the Magnus expansion gives a fast analytical pulse shape which gives a high fidelity gate for a specific gate time, up to a phase factor on the second qubit. Further numerical analysis corroborates these results and yields to even faster gates, showing that leakage state anharmonicity does not provide a fundamental quantum speed limit.
We numerically study the implementation of a universal two-qubit gate set, composed of CNOT, Hadamard, phase and $π/8$ gates, for transmon-based systems. The control signals to implement such gates are obtained using the Chopped Random Basis optimal control technique, with a target gate infidelity of $10^{-2}$. During the optimization processes we account for the leakage toward non-computational states, an important non-ideality affecting transmon qubits. We also test and benchmark the optimal control solutions against the introduction of Gaussian white noise and spectral distortion, two key n…
We experimentally constructed an all-microwave scheme for the controlled-NOT (cNOT) gate between two superconducting transmon qubits in a three dimensional cavity. Our cNOT gate is based on the microwave-activated phase (MAP) gate, which requires an additional procedure to compensate the accumulated phases during the operation of the MAP gate. We applied Z-axis phase gates using microwave hyperbolic secant pulse on both qubits with adequate rotation angles systematically calibrated by separate measurements.We evaluated the gate performance of the constructed cNOT gate by performing two-qubit q…
We have embedded two fixed-frequency Al/AlO$_{\textrm{x}}$/Al transmons, with ground-to-excited transition frequencies at 6.0714 GHz and 6.7543 GHz, in a single 3D Al cavity with a fundamental mode at 7.7463 GHz. Strong coupling between the cavity and each transmon results in an effective qubit-qubit coupling strength of 26 MHz and a -1 MHz dispersive shift in each qubit's transition frequency, depending on the state of the other qubit. Using the all-microwave SWIPHT (Speeding up Waveforms by Inducing Phases to Harmful Transitions) technique, we demonstrate the operation of a generalized contr…
High-fidelity iSWAP gate with Double Transmon Coupler
University of Massachusetts, Lowell（马萨诸塞大学洛厄尔分校）；RTX BBN Technologies（RTX BBN科技公司）；University of Colorado, Boulder（科罗拉多大学博尔德分校）；National Institute of Standards and Technology（美国国家标准与技术研究院）；Air Force Research Laboratory（空军研究实验室）；Northwestern University（西北大学）
Cross-Resonant Gates in Hybrid Fluxonium-Transmon Systems
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；SEEQC, Inc.（SEEQC公司）；University of Massachusetts-Amherst（马萨诸塞大学阿默斯特分校）；Ecole Polytechnique Federale de Lausanne（洛桑联邦理工学院）
We analyse the implementation of a fast nonadiabatic CZ gate between two transmon qubits with tuneable coupling. The gate control method is based on a theory of dynamical invariants which leads to reduced leakage and robustness against decoherence. The gate is based on a description of the resonance between the $|11\rangle$ and $|20\rangle$ using an effective Hamiltonian with the 6 lowest energy states. A modification of the invariants method allows us to take into account the higher-order perturbative corrections of this effective model. This enables a gate fidelity several orders of magnitud…
Parametrically Driven iSWAP Gate Using a Capacitively Shunted Double-Transmon Coupler at the Zero-Flux Sweet Spot
RIKEN Center for Quantum Computing (RQC)（理化学研究所量子计算中心）；Department of Applied Physics, Graduate School of Engineering, The University of Tokyo（东京大学大学院工学研究科应用物理系）；Corporate Laboratory, Toshiba Corporation（东芝公司企业实验室）
Quantum computation requires the precise control of the evolution of a quantum system, typically through application of discrete quantum logic gates on a set of qubits. Here, we use the cross-resonance interaction to implement a gate between two superconducting transmon qubits with a direct static dispersive coupling. We demonstrate a practical calibration procedure for the optimization of the gate, combining continuous and repeated-gate Hamiltonian tomography with step-wise reduction of dominant two-qubit coherent errors through mapping to microwave control parameters. We show experimentally …
Experimental Realization of a C-Shunt Flux-Qubit Coupler for Controlled-Z Gates between Transmons
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室）；School of Physics, University of Chinese Academy of Sciences（中国科学院大学物理学院）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）
Fast microwave-driven two-qubit gates between fluxonium qubits with a transmon coupler
QuTech and Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学量子技术与卡弗里纳米科学研究所）；Netherlands Organization for Applied Scientific Research (TNO)（荷兰应用科学研究组织（TNO））；Quantum Engineering Centre for Doctoral Training, H. H. Wills Physics Laboratory and Department of Electrical and Electronic Engineering, University of Bristol（布里斯托大学量子工程博士培训中心、H.H.威尔斯物理实验室及电气与电子工程系）
We describe and implement a family of entangling gates activated by radio-frequency flux modulation applied to a tunable transmon that is statically coupled to a neighboring transmon. The effect of this modulation is the resonant exchange of photons directly between levels of the two-transmon system, obviating the need for mediating qubits or resonator modes and allowing for the full utilization of all qubits in a scalable architecture. The resonance condition is selective in both the frequency and amplitude of modulation and thus alleviates frequency crowding. We demonstrate the use of three …
With the long coherence time, the fixed-frequency transmon qubit is a promising qubit modality for quantum computing. Currently, diverse qubit architectures that utilize fixed-frequency transmon qubits have been demonstrated with high-fidelity gate performance. Nevertheless, the relaxation times of transmon qubits can have large temporal fluctuations, causing instabilities in gate performance. The fluctuations are often believed to be caused by nearly on-resonance couplings with sparse two-level-system (TLS) defects. To mitigate their impact on qubit coherence and gate performance, one direct …
Portland State University（波特兰州立大学）；Intel Labs, Intel Corporation（英特尔实验室，英特尔公司）
We use machine learning techniques to design a 50 ns three-qubit flux-tunable controlled-controlled-phase gate with fidelity of >99.99% for nearest-neighbor coupled transmons in circuit quantum electrodynamics architectures. We explain our gate design procedure where we enforce realistic constraints, and analyze the new gate's robustness under decoherence, distortion, and random noise. Our controlled-controlled-phase gate in combination with two single-qubit gates realizes a Toffoli gate which is widely used in quantum circuits, logic synthesis, quantum error correction, and quantum games.
We develop a simulator for quantum computers composed of superconducting transmon qubits. The simulation model supports an arbitrary number of transmons and resonators. Quantum gates are implemented by time-dependent pulses. Nontrivial effects such as crosstalk, leakage to non-computational states, entanglement between transmons and resonators, and control errors due to the pulses are inherently included. The time evolution of the quantum computer is obtained by solving the time-dependent Schrödinger equation. The simulation algorithm shows excellent scalability on high-performance supercomput…
Quantum computation is conventionally performed using quantum operations acting on two-level quantum bits, or qubits. Qubits in modern quantum computers suffer from inevitable detrimental interactions with the environment that cause errors during computation, with multi-qubit operations often being a primary limitation. Most quantum devices naturally have multiple accessible energy levels beyond the lowest two traditionally used to define a qubit. Qudits offer a larger state space to store and process quantum information, reducing complexity of quantum circuits and improving efficiency of quan…
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…
Fast CZ gate in hybrid fluxonium-transmon systems with tunable couplers
Nanjing University of Posts and Telecommunications（南京邮电大学）；Nanjing University（南京大学）；Shanxi University（山西大学）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）
In the model of gate-based quantum computation, the qubits are controlled by a sequence of quantum gates. In superconducting qubit systems, these gates can be implemented by voltage pulses. The success of implementing a particular gate can be expressed by various metrics such as the average gate fidelity, the diamond distance, and the unitarity. We analyze these metrics of gate pulses for a system of two superconducting transmon qubits coupled by a resonator, a system inspired by the architecture of the IBM Quantum Experience. The metrics are obtained by numerical solution of the time-dependen…
We analyze the coupling of two qubits via an epitaxial semiconducting junction. In particular, we consider three configurations that include pairs of transmons or gatemons as well as gatemon-like two qubits formed by an epitaxial four-terminal junction. These three configurations provide an electrical control of the interaction between the qubits by applying voltage to a metallic gate near the semiconductor junction and can be utilized to naturally realize a controlled-Z gate (CZ). We calculate the fidelity and timing for such CZ gate. We demonstrate that in the absence of decoherence, the CZ …
Implementation of high-fidelity two-qubit operations is a key ingredient for scalable quantum error correction. In superconducting qubit architectures tunable buses have been explored as a means to higher fidelity gates. However, these buses introduce new pathways for leakage. Here we present a modified tunable bus architecture appropriate for fixed-frequency qubits in which the adiabaticity restrictions on gate speed are reduced. We characterize this coupler on a range of two-qubit devices achieving a maximum gate fidelity of $99.85\%$. We further show the calibration is stable over one day.
Superconducting transmon qubits are of great interest for quantum computing and quantum simulation. A key component of quantum chemistry simulation algorithms is breaking up the evolution into small steps, which naturally leads to the need for non-maximally entangling, arbitrary CPHASE gates. Here we design such microwave-based gates using an analytically solvable approach leading to smooth, simple pulses. We use the local invariants of the evolution operator in $SU(4)$ to develop a method of constructing pulse protocols, which allows for the continuous tuning of the phase. We find CPHASE fide…
In the gate model of quantum computing, a program is typically decomposed into a sequence of 1- and 2-qubit gates that are realized as control pulses acting on the system. A key requirement for a scalable control system is that the qubits are addressable - that control pulses act only on the targeted qubits. The presence of control crosstalk makes this addressability requirement difficult to meet. In order to provide metrics that can drive requirements for decreasing crosstalk, we present three measurements that directly quantify the DC and AC flux crosstalk present between tunable transmons, …
We identify optimal operating conditions of an entangling two-qubit gate realized by a capacitive coupling of two superconducting charge qubits in a transmission line resonator (the so called "transmons"). We demonstrate that the sensitivity of the optimized gate to 1/f flux and critical current noise is suppressed to leading order. The procedure only requires a preliminary estimate of the 1/f noise amplitudes. No additional control or bias line beyond those used for the manipulation of individual qubits are needed. The proposed optimization is effective also in the presence of relaxation proc…
The cross-resonant gate is an entangling gate for fixed frequency superconducting qubits introduced for untunable qubits. While being simple and extensible, it suffers from long duration and limited fidelity. Using two different optimal control algorithms, we probe the quantum speed limit for a CNOT gate in this system. We show that the ability to approach this limit depends strongly on the ansatz used to describe the optimal control pulse. A piecewise constant ansatz with a single carrier leads to an experimentally feasible pulse shape, shorter than the one currently used in experiments, but …
In this work we analyze the implementation of a control-phase gate through the resonance between the $|11\rangle$ and $|20\rangle$ states of two statically coupled transmons. We find that there are many different controls for the transmon frequency that implement the same gate with fidelities around $99.8\%$ ($T_1=T_2^{*}=17$ $μ$s) and $99.99\%$ ($T_1=T_2^{*}=300$ $μ$s) within a time that approaches the theoretical limit. All controls can be brought to this accuracy by calibrating the waiting time and the destination frequency near the $|11\rangle-|20\rangle$ resonance. However, some controls,…
Based on a microwave-photon quantum processor with two superconducting resonators coupled to one transmon qutrit, we construct the controlled-phase (c-phase) gate on microwave-photon-resonator qudits, by combination of the photon-number-dependent frequency-shift effect on the transmon qutrit by the first resonator and the resonant operation between the qutrit and the second resonator. This distinct feature provides us a useful way to achieve the c-phase gate on the two resonator qudits with a higher fidelity and a shorter operation time, compared with the previous proposals. The fidelity of ou…
Novel qubits with intrinsic noise protection constitute a promising route for improving the coherence of quantum information in superconducting circuits. However, many protected superconducting qubits exhibit relatively low transition frequencies, which could make their integration with conventional transmon circuits challenging. In this work, we propose and study a scheme for entangling a tunable transmon with a Cooper-pair parity-protected qubit, a paradigmatic example of a low-frequency protected qubit that stores quantum information in opposite Cooper-pair parity states on a superconductin…
A challenge for scaling up quantum processors using frequency-crowded, weakly anharmonic qubits is to drive individual qubits without causing leakage into non-computational levels of the others, while also minimizing the number of control lines. To address this, we implement single-qubit Wah-Wah control in a circuit QED processor with a single feedline for all transmon qubits, operating at the maximum gate speed achievable given the frequency crowding. Randomized benchmarking and quantum process tomography confirm alternating qubit control with $\leq$1% average error per computational step and…
