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arXiv:1502.03665 · Physical Review A

Pulse-controlled quantum gate sequences on a strongly coupled qubit chain

Holger Frydrych, Michael Marthaler, G. Alber

Published Dec 11, 2015• 1 citation
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Abstract

We propose a selective dynamical decoupling scheme on a chain of permanently coupled qubits with XX-type interactions, which is capable of dynamically suppressing any coupling in the chain by applying sequences of local pulses to the individual qubits. We demonstrate that high-fidelity single- and two-qubit gates can be achieved by this procedure and that sequences of gates can be implemented by this pulse control alone. We discuss the applicability and physical limitations of our model specifically for strongly coupled superconducting flux qubits. Since dynamically modifying the couplings between flux qubits is challenging, they are a natural candidate for our approach.

DOI
10.1103/physreva.92.062322

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•May 25, 2017•0 citations
We propose a selective dynamical decoupling scheme on a chain of permanently coupled qubits with XX-type interactions, which is capable of dynamically suppressing any coupling in the chain by applying sequences of local pulses to the individual qubits. We demonstrate that high-fidelity single- and two-qubit gates can be achieved by this procedure and that sequences of gates can be implemented by this pulse control alone. We discuss the applicability and physical limitations of our model specifically for strongly coupled superconducting flux qubits. Since dynamically modifying the couplings between flux qubits is challenging, they are a natural candidate for our approach.
We propose a selective dynamical decoupling scheme on a chain of permanently coupled qubits, which is capable of dynamically suppressing any coupling in the chain by applying sequences of local pulses to the individual qubits. We demonstrate how this pulse control can be used to implement the two-qubit CNS gate on any two neighboring qubits. A sequence of these CNS gates is then applied on the chain to entangle all the qubits in a GHZ state. We find that high entanglement fidelities can be achieved as long as the total number of coupled qubits is not too large.
We propose a scheme with dc control of finite bandwidth to implement a two-qubit gate for superconducting flux qubits at the optimal point. We provide a detailed nonperturbative analysis on the dynamic evolution of the qubits interacting with a common quantum bus. An effective qubit-qubit coupling is induced while decoupling the quantum bus with proposed pulse sequences. The two-qubit gate is insensitive to the initial state of the quantum bus and applicable to nonperturbative coupling regime which enables rapid two-qubit operation. This scheme can be scaled up to multiqubit coupling.
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 present theoretical schemes for performing high-fidelity one- and two-qubit pulsed gates for a superconducting flux qubit. The 'IBM qubit' consists of three Josephson junctions, three loops and a superconducting transmission line. Assuming a fixed inductive qubit–qubit coupling, we show that the effective qubit–qubit interaction is tunable by changing the applied fluxes, and can be made negligible, allowing one to perform high-fidelity single qubit gates. Our schemes are tailored to alleviate errors due to 1/ f noise; we find gates with only 1% loss of fidelity due to this source, for pulse times in the range of 20–30 ns for one-qubit gates ( Z rotations, Hadamard) and 60 ns for a two-qubit gate (controlled- Z ). Our relaxation and dephasing time estimates indicate a comparable loss of fidelity from this source. The control of leakage plays an important role in the design of our shaped pulses, preventing shorter pulse times. However, we have found that imprecision in the control of the quantum phase plays a major role in the limitation of the fidelity of our gates.
As superconducting quantum processors continue to scale, high-performance quantum control becomes increasingly critical. In densely integrated architectures, unwanted interactions between nearby qubits give rise to crosstalk errors that limit operational performance. In particular, direct exchange-type (XY) interactions are typically minimized by designing large frequency detunings between neighboring qubits at the hardware level. However, frequency crowding in large-scale systems ultimately restricts the achievable frequency separation. While such XY coupling facilitates entangling gate operations, its residual presence poses a key challenge during single-qubit controls. Here, we propose a scalable pulse-level control framework, incorporating frequency modulation (FM) and dynamical decoupling (DD), to suppress XY crosstalk errors. This framework operates independently of coupling strengths, reducing calibration overhead and naturally supporting multi-qubit connectivity. Numerical simulations show orders-of-magnitude reductions in infidelity for both idle and single-qubit gates in a two-qubit system. We further validate scalability in a five-qubit layout, where crosstalk between a central qubit and four neighbors is simultaneously suppressed. Our crosstalk suppression framework provides a practical route toward high-fidelity operation in dense superconducting architectures.
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.