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Quantum Gates and Decoupling in Qubits with Fixed Transverse Coupling

Guiyang Han

Published May 25, 2017• 0 citations
OpenAlex

Abstract

Among all the quantum computer candidates, the superconducting system is one of the most convincing platforms due to its strong couplings and scalability. To be more specific, this thesis focuses on the superconducting system, in which the artificial atoms are controlled longitudinally and coupled without any intermediate devices. We propose a superconducting decoupling method in this thesis. Firstly, we state that our algorithm can effectively ‘turn off’ arbitrary couplings. Then, we analyze the errors of our decoupling method and prove that the errors are ignorable when a sequence of decoupling gates are applied on non-nearest-neighboring qubits. We verify the efficiency of our decoupling method using the numerical simulations, which are well-matched with the theoretical predictions. Using 99.6% fidelity isolated CNOT and 99.89% single-qubit gates, we obtain a fidelity of 97.8% with the CNOT implementation in a five-qubit system over 14.84 ns.

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Among all the quantum computer candidates, the superconducting system is one of the most convincing platforms due to its strong couplings and scalability. To be more specific, this thesis focuses on the superconducting system, in which the artificial atoms are controlled longitudinally and coupled without any intermediate devices. We propose a superconducting decoupling method in this thesis. Firstly, we state that our algorithm can effectively ‘turn off’ arbitrary couplings. Then, we analyze the errors of our decoupling method and prove that the errors are ignorable when a sequence of decoupling gates are applied on non-nearest-neighboring qubits. We verify the efficiency of our decoupling method using the numerical simulations, which are well-matched with the theoretical predictions. Using 99.6% fidelity isolated CNOT and 99.89% single-qubit gates, we obtain a fidelity of 97.8% with the CNOT implementation in a five-qubit system over 14.84 ns.
Maintaining or even improving gate performance with growing numbers of parallel controlled qubits is a vital requirement for fault-tolerant quantum computing.For superconducting quantum processors, though isolated one-or two-qubit gates have been demonstrated with high fidelity, implementing these gates in parallel commonly shows worse performance.Generally, this degradation is attributed to various crosstalks between qubits, such as quantum crosstalk due to residual inter-qubit coupling.An understanding of the exact nature of these crosstalks is critical to figuring out respective mitigation schemes and improved qubit architecture designs with low crosstalk.Here we give a theoretical analysis of quantum crosstalk impact on simultaneous gate operations in a qubit architecture, where fixed-frequency transmon qubits are coupled via a tunable bus, and sub-100-ns controlled-Z (CZ) gates can be realized by applying a baseband flux pulse on the bus.Our analysis shows that for microwave-driven single-qubit gates, the dressing from the qubit-qubit coupling can cause non-negligible cross-driving errors when qubits operate near frequency collision regions.During CZ gate operations, although unwanted nearest-neighbor interactions are nominally turned off, sub-MHz parasitic next-nearest-neighbor interactions involving spectator qubits can still exist, causing considerable leakage or control error when one operates qubit systems around these parasitic resonance points.To ensure high-fidelity simultaneous operations, a request could be raised to figure out a better way to balance the gate error from target qubit systems themselves and the error from nonparticipating spectator qubits.Overall, our analysis suggests that towards useful quantum processors, the qubit architecture should be examined carefully in the context of high-fidelity simultaneous gate operations in a scalable qubit lattice.
Tunable couplers in superconducting quantum computers have enabled fast and accurate two-qubit gates, with reported high fidelities over 99% in various architectures and gate-implementation schemes. However, there are few tunable couplers whose performance in multiqubit systems is clarified, except for the most widely used one: single-transmon coupler (STC). Achieving similar accuracy to isolated two-qubit systems remains challenging due to various undesirable couplings but is necessary for scalability. In this work, we numerically analyze a system of three fixed-frequency qubits coupled via two double-transmon couplers (DTCs) where nearest-neighbor qubits are highly detuned and also next-nearest-neighbor ones are nearly resonant. The DTC is a recently proposed tunable coupler, which consists of two fixed-frequency transmons coupled through a common loop with an additional Josephson junction. We find that the DTC cannot only reduce undesired residual couplings sufficiently, as well as in isolated two-qubit systems, but also enables implementations of 30-ns CZ gates and individual and simultaneous 10-ns π / 2 pulses with fidelities over 99.99%. For comparison, we also investigate the system where the DTCs are replaced by the STCs. The results show that the DTC outperforms the STC in terms of both residual coupling suppression and gate accuracy in the above systems. From these results, we expect that the DTC architecture is promising for realizing high-performance, scalable superconducting quantum computers. Published by the American Physical Society 2024
Engineering high-fidelity two-qubit gates is an indispensable step toward practical quantum computing. For superconducting quantum platforms, one important setback is the stray interaction between qubits, which causes significant coherent errors. For transmon qubits, protocols for mitigating such errors usually involve fine-tuning the hardware parameters or introducing usually noisy flux-tunable couplers. In this work, we propose a simple scheme to cancel these stray interactions. The coupler used for such cancelation is a driven high-coherence resonator, where the amplitude and frequency of the drive serve as control knobs. Through the resonator-induced-phase interaction, the static ZZZZZZ coupling can be entirely neutralized. We numerically show that such a scheme can enable short and high-fidelity entangling gates, including cross-resonance controlled-not (cnot) gates within 40 ns and adiabatic controlled-ZZZ gates within 140 ns. Our architecture is not only ZZZZZZ-free, but also contains no extra noisy components, such that it preserves the coherence times of fixed-frequency transmon qubits. With the state-of-the-art coherence times, the error of our cross-resonance cnot gate can be reduced to below ${10}^{\ensuremath{-}4}$.
We present a circuit construction for a fixed-frequency superconducting qubit and show how it can be scaled up to a grid with strictly local interactions. The circuit QED realization we propose implements ${\ensuremath{\sigma}}_{z}$ type coupling between a superconducting qubit and any number of LCLCLC resonators. The resulting longitudinal coupling is inherently different from the usual ${\ensuremath{\sigma}}_{x}$ type transverse coupling, which is the one that has been most commonly used for superconducting qubits. In a grid of fixed-frequency qubits and resonators with a particular pattern of always-on interactions, coupling is strictly confined to nearest and next-nearest neighbor resonators; there is never any direct qubit-qubit coupling. We note that just a single unique qubit frequency suffices for the scalability of this scheme. The same is true for the resonators, if the resonator-resonator coupling constants are varied instead. A controlled phase gate between two neighboring qubits can be realized with microwave drives on the qubits, without affecting the other qubits. This fact is a significant advantage for the scalability of this scheme.
We apply the quantum optimal control theory based on the Krotov method to implement single-qubit XXX and ZZZ gates and two-qubit cnot gates for inductively coupled superconducting flux qubits with fixed qubit transition frequencies and fixed off-diagonal qubit-qubit coupling. Our scheme shares an advantage with other direct-coupling schemes in that it requires no additional coupler subcircuit and control lines. The control lines needed are only for the manipulation of individual qubits (e.g., a time-dependent magnetic flux or field applied on each qubit). The qubits are operated at the optimal coherence points and the gate operation times (less than 1 ns for single-qubit gates and $\ensuremath{\sim}2$ ns for cnotgates) are much shorter than the corresponding qubit decoherence time. A cnot gate or other general quantum gates can be implemented in a single run of the pulse sequence rather than being decomposed into several single-qubit and several entangled two-qubit operations in series by composite pulse sequences. Quantum gates constructed via our scheme are all with very high fidelity (very low error) as our optimal control scheme takes into account the fixed qubit detuning and fixed two-qubit interaction as well as all other time-dependent magnetic-field-induced single-qubit interactions and two-qubit couplings. The effect of leakage to higher-energy-level states and the effect of qubit decoherence on the quantum-gate operations are also discussed.
We demonstrate that in a coupled two-qubit system any single-qubit gate can be decomposed into \ensuremath{\mid}0⟩-controlled and \ensuremath{\mid}1⟩-controlled two-qubit gates which can be implemented by manipulations analogous to that used for a controlled NOT (CNOT) gate. Based on this we present a unified approach to implement universal single-qubit and two-qubit gates in a coupled two-qubit system with fixed always-on coupling. This approach requires neither supplementary circuit or additional physical qubits to control the coupling nor extra hardware to adjust the energy level structure. The feasibility of this approach is demonstrated by numerical simulation of single-qubit gates and creation of two-qubit Bell states in rf-driven inductively coupled two superconducting quantum interference device flux qubits with realistic device parameters and constant always-on coupling.