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Robust Optimal Control of the Cross-Resonance Gate in Superconducting Qubits

Allen, Joseph

Published Jul 15, 2019• 1 citation
Publisher

Abstract

Superconducting circuits are one of the leading architectures in quantum computing. To undertake quantum computing one must be able to perform quantum gates; however, two-qubit gates are still limited in fidelity and gate time. The cross-resonance gate is a two-qubit gate that uses direct microwave drives and has seen much success in its implementation; but, there are theoretical indications that it has not yet reached the coherence limited fidelity value and its gate time is still relatively long compared with other quantum gate methods. Quantum optimal control theory is a powerful tool in the design of controls for quantum operations and has shown the capability to improve gate fidelities and reduce gate times. Robust quantum optimal control methodologies have further built on this to develop high fidelity quantum gates that are robust to uncertainties and noise in the system. In this thesis we use robust quantum optimal control theory to achieve these goals for the cross-resonance gate in a variety of superconducting qubit architectures. First, we investigate two superconducting qubits embedded in a common 3D microwave cavity in which the control drive is implemented via the common cavity mode of the cavity. We determine pulse shapes that implement the cross-resonance gate that are robust to uncertainty in the qubit transition frequencies for both a strictly two-level superconducting qubit and a three-level qubit. Second, we look at the cross-resonance gate with direct drives on each qubit, finding the minimal time to perform the cross-resonance gate with pulses that are robust to uncertainty in a measured system parameter for three cases: two three-level qubits with no drive crosstalk, two three-level qubits with some drive crosstalk, and two two-level qubits. Lastly, we report on simulations undertaken towards implementing a robust, high fidelity cross-resonance gate in a novel superconducting quantum device known as the coaxmon.

DOI
10.15126/thesis.00852260

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Superconducting circuits are one of the leading architectures in quantum computing. To undertake quantum computing one must be able to perform quantum gates; however, two-qubit gates are still limited in fidelity and gate time. The cross-resonance gate is a two-qubit gate that uses direct microwave drives and has seen much success in its implementation; but, there are theoretical indications that it has not yet reached the coherence limited fidelity value and its gate time is still relatively long compared with other quantum gate methods. Quantum optimal control theory is a powerful tool in the design of controls for quantum operations and has shown the capability to improve gate fidelities and reduce gate times. Robust quantum optimal control methodologies have further built on this to develop high fidelity quantum gates that are robust to uncertainties and noise in the system. In this thesis we use robust quantum optimal control theory to achieve these goals for the cross-resonance gate in a variety of superconducting qubit architectures. First, we investigate two superconducting qubits embedded in a common 3D microwave cavity in which the control drive is implemented via the common cavity mode of the cavity. We determine pulse shapes that implement the cross-resonance gate that are robust to uncertainty in the qubit transition frequencies for both a strictly two-level superconducting qubit and a three-level qubit. Second, we look at the cross-resonance gate with direct drives on each qubit, finding the minimal time to perform the cross-resonance gate with pulses that are robust to uncertainty in a measured system parameter for three cases: two three-level qubits with no drive crosstalk, two three-level qubits with some drive crosstalk, and two two-level qubits. Lastly, we report on simulations undertaken towards implementing a robust, high fidelity cross-resonance gate in a novel superconducting quantum device known as the coaxmon.
High-fidelity quantum gates are crucial for achieving fault-tolerant quantum computing; however, decoherence significantly reduces gate fidelities during long operation times. Although optimal control techniques can theoretically minimize these operation times, they often neglect realistic uncertainties in system parameters. In this work, we demonstrate that by using robust optimal control strategies, the cross-resonance gate in superconducting systems can be operated within 64 ns, achieving fidelities of [Formula: see text] while maintaining robustness against up to 10% uncertainty in a single parameter. Alternatively, by extending the control time to 71 ns, we achieve fidelities of [Formula: see text] with robustness against up to 3% uncertainty. Our results identify the minimal control times attainable with experimentally feasible pulses and system parameters, as well as the maximum allowable static parameter error for high-fidelity operations. Furthermore, we demonstrate simultaneous robustness against both static and time-dependent errors by generating 100 ns control pulses ([Formula: see text]) that maintain robustness against 10% static parameter error and time-dependent parameter fluctuations two orders of magnitude stronger than typical experimental noise. These findings demonstrate a viable open-loop strategy for implementing fast, high-fidelity quantum gates in the presence of realistic system uncertainties that would otherwise degrade conventional control pulses.
Implementing high-fidelity multiqubit gates is critical for reducing circuit depth in near-term quantum processors and fault-tolerant architectures. However, realizing multiqubit interactions and entanglement remains a critical challenge that limits the implementation of multiqubit gates. Here we propose an all-microwave scheme to realize single-step multiqubit gates incorporating n control and m target qubits, tailored for frequency-tunable superconducting transmon networks. By leveraging cross-resonance (CR) drives, this approach induces effective two-body ZX interactions that are significantly stronger than those achieved in conventional resonant regimes, circumventing the need for tunable couplers. The system's effective Hamiltonian is analytically derived using both quad frame rotation and rigorous block diagonalization. These combined theoretical methods facilitate the identification of optimal parameter regimes that simultaneously enhance desired target couplings and suppress parasitic higher-order terms, such as ZXX interactions. Through numerical simulations and gradient-based pulse-shape optimization, we demonstrate three-qubit gates achieving fidelities exceeding 99.9% within a 60 ns gate duration. Furthermore, we evaluate the fundamental scalability of this framework by extending the optimization to a five-qubit CXXXX architecture, confirming the physical viability of the multi-target driving scheme. Because these multiqubit operations naturally emulate stabilizer measurements, this architecture provides a hardware-efficient strategy for reducing the circuit depth of stabilizer-type operations by replacing sequential two-qubit gate decompositions with single-step multiqubit gates.
We present improvements in both theoretical understanding and experimental implementation of the cross resonance (CR) gate that have led to shorter two-qubit gate times and interleaved randomized benchmarking fidelities exceeding 99%. The CR gate is an all-microwave two-qubit gate that does not require tunability and is therefore well suited to quantum computing architectures based on two-dimensional superconducting qubits. The performance of the gate has previously been hindered by long gate times and fidelities averaging 94--96%. We have developed a calibration procedure that accurately measures the full CR Hamiltonian. The resulting measurements agree with theoretical analysis of the gate and also elucidate the error terms that have previously limited gate fidelity. The increase in fidelity that we have achieved was accomplished by introducing a second microwave drive tone on the target qubit to cancel unwanted components of the CR Hamiltonian.
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.
Optimization of the fidelity of control operations is of critical importance in the pursuit of fault-tolerant quantum computation. We apply optimal control techniques to demonstrate that a single drive via the cavity in circuit quantum electrodynamics can implement a high-fidelity two-qubit all-microwave gate that directly entangles the qubits via the mutual qubit-cavity couplings. This is performed by driving at one of the qubits' frequencies which generates a conditional two-qubit gate, but will also generate other spurious interactions. These optimal control techniques are used to find pulse shapes that can perform this two-qubit gate with high fidelity, robust against errors in the system parameters. The simulations were all performed using experimentally relevant parameters and constraints.
Native multiqubit parity gates have various potential quantum computing applications, such as entanglement creation, logical state encoding, and parity measurement in quantum error correction. Here, using simultaneous cross-resonance drives on two control qubits with a common target, we demonstrate an efficient implementation of a three-qubit parity gate. We have developed a calibration procedure based on that for the echoed cross-resonance gate. We confirm that our use of simultaneous drives leads to higher interleaved randomized benchmarking fidelities than a naive implementation with two consecutive controlled not gates. We also demonstrate that our simultaneous parity gates can significantly improve the parity measurement error probability for the heavy-hexagon code on an IBM Quantum processor using seven superconducting qubits with all-microwave control.