The task of controlling a quantum system under time and bandwidth limitations is made difficult by unwanted excitations of spectrally neighboring energy levels. In this article we review the Derivative Removal by Adiabatic Gate (DRAG) framework. DRAG is a multi-transition variant of counterdiabatic driving, where multiple low-lying gapped states in an adiabatic evolution can be avoided simultaneously, greatly reducing operation times compared to the adiabatic limit. In its essence, the method corresponds to a convergent version of the superadiabatic expansion where multiple counterdiabaticity conditions can be met simultaneously. When transitions are strongly crowded, the system of equations can instead be favorably solved by an average Hamiltonian (Magnus) expansion, suggesting the use of additional sideband control. We give some examples of common systems where DRAG and variants thereof can be applied to improve performance.
The task of controlling a quantum system under time and bandwidth limitations is made difficult by unwanted excitations of spectrally neighboring energy levels. In this article we review the Derivative Removal by Adiabatic Gate (DRAG) framework. DRAG is a multi-transition variant of counterdiabatic driving, where multiple low-lying gapped states in an adiabatic evolution can be avoided simultaneously, greatly reducing operation times compared to the adiabatic limit. In its essence, the method corresponds to a convergent version of the superadiabatic expansion where multiple counterdiabaticity conditions can be met simultaneously. When transitions are strongly crowded, the system of equations can instead be favorably solved by an average Hamiltonian (Magnus) expansion, suggesting the use of additional sideband control. We give some examples of common systems where DRAG and variants thereof can be applied to improve performance.
Adiabatic or slowly varying gate operations are typically required in order to remain within the qubit subspace in an anharmonic oscillator. However significant speed ups are possible by using the two quadrature derivative-removal-by-adiabatic-gate(DRAG) technique, where a second time derivative pulse component burns a spectral hole near an unwanted transition. It is shown here, that simultaneous optimization of the detuning and the pulse norm in addition, further reduces leakage errors and significantly improve gate fidelities. However, with this optimization accounting for the AC Stark shift, there is a low spectral weight pulse envelope regime, where DRAG is almost not needed and where the two state error fidelities are stable against pulse jitter. Explicit time evolution calculations are carried out in the lab frame for truncated multi-level Transmon qubit models obtained from a tight-binding model.
Many techniques in quantum control rely on frequency separation as a means for suppressing unwanted couplings. In its simplest form, the mechanism relies on the low bandwidth of control pulses of long duration. Here we perform a higher-order quantum-mechanical treatment that allows for higher precision and shorter times. In particular, we identify three kinds of off-resonant effects: (i) simultaneous unwanted driven couplings (e.g., due to drive crosstalk), (ii) additional (initially undriven) transitions such as those in an infinite ladder system, and (iii) sideband frequencies of the driving wave form such as we find in corrections to the rotating-wave approximation. With a framework that is applicable to all three cases, in addition to the known adiabatic error responsible for a shift of the energy levels we typically see in the spectroscopy of such systems, we derive error terms in a controlled expansion corresponding to higher-order adiabatic effects and diabatic excitations. We show, by also expanding the driving wave form in a basis of different order derivatives of a trial function (typically a Gaussian) these different error terms can be corrected for in a systematic way, hence strongly improving quantum control of systems with dense spectra.
Counterdiabatic (CD) driving has the potential to speed up adiabatic quantum state preparation by suppressing unwanted excitations. However, existing approaches either require intractable classical computations or are based on approximations that do not have performance guarantees. We propose and analyze a nonvariational, system-agnostic CD expansion method and analytically show that it converges exponentially quickly in the expansion order. In finite systems, the required resources scale inversely with the spectral gap, which we argue is asymptotically optimal. To extend our method to the thermodynamic limit and suppress errors stemming from high-frequency transitions, we leverage finite-time adiabatic protocols. In particular, we show that a time determined by the quantum speed limit is sufficient to prepare the desired ground state, without the need to optimize the adiabatic trajectory. Numerical tests of our method on the quantum Ising chain show that our method can outperform state-of-the-art variational CD approaches.
We introduce an inertial counterdiabatic (CD) protocol that reformulates shortcut-to-adiabaticity design as a moving-frame diagonalization problem. The method employs the Magnus expansion to construct a variational propagator generated by an accessible CD ansatz. In the new rotating frame, the controls are optimized to suppress the off-diagonal Hamiltonian terms, and the CD terms are defined to counteract the corresponding inertial contribution. The propagator generated with the Magnus expansion naturally exploits additional control directions generated through its nested commutator, while the sequential design of the propagator introduces temporal nonlocality into the optimization. We benchmark the method on a two-qubit system and on the one-dimensional quantum Ising chain, where it consistently outperforms variational CD protocols based on action minimization. The largest improvements are observed near gap-closing regions, demonstrating the advantage of combining temporal and algebraic nonlocality for suppressing diabatic excitations.
Abstract Counterdiabatic driving can suppress diabatic losses during adiabatic ground state preparation. As its implementation necessitates the generation of an adiabatic gauge potential, which requires knowledge of the spectral gap of instantaneous Hamiltonians and involves highly non-local controls in many-body systems, local counterdiabatic driving with approximate adiabatic gauge potential has been widely adopted. In this work, using transverse-field Ising model as an example, we present an in-depth study of the performance of local counterdiabatic protocols and provide a closed-form analysis of ground-state-fidelity optimization. We then propose a two-stage protocol based on local counterdiabatic and simple local single-body control to further improve the performance. The practical implementation of these protocols does not require diagonalization of instantaneous Hamiltonians or spectral gaps, and only additional local single-body driving is involved. To benchmark their performance, we experimentally implement digitized adiabatic quantum evolution in a trapped-ion system. We characterize the quality of the prepared states and explore the scaling behavior with system size up to 14 qubits. Our demonstration of quantum shortcut to adiabaticity opens a path towards preparing ground states of complex systems with accessible local controls.
Quantum computers are a promising new technology that enables the use of quantum algorithms to solve certain problems faster than classical computers. An especially auspicious method for realizing such a device is using a superconducting circuit as the foundational computational unit of the quantum computer, the qubit. These serve as two-level systems allowing for the storage and manipulation of quantum information. For large-scale adoption, precise control of qubits via rapid driving pulses is essential in order to carry out desired operations known as quantum gates. In superconducting qubits, this is often achieved with an external electromagnetic field coupled to the qubit capacitively or inductively. In this case, to achieve faster pulses, the power of the driving field must be increased. This, however, leads to increased heating of the qubit, which in turn can lead to decoherence and the loss of quantum information. One proposed solution is the use of off-resonance driving of the qubit, which enables faster pulses with lower driving power when compared to resonance drive. It also allows for drive line attenuation at the qubit frequency, suppressing decay of the qubit’s energy into the drive line. Another challenge in the operation of the qubit is preventing excitation outside the two states used for computation, known as the computational subspace. In this thesis, we look at optimizing the drive pulse shape as a remedy to this problem in the context of resonance drive, as well as two off-resonant driving methods: subharmonic drive and two-frequency drive. In particular, we make use of the Derivative Removal by Adiabatic Gate (DRAG) method with different pulse shapes in order to attenuate the transition between the first and second excited states of the qubit. The results are obtained with numerical simulation for the transmon, which is a common superconducting qubit. The results show strong suppression of leakage outside the computational subspace using the DRAG method in resonance and two-frequency drive, while in subharmonic drive, no major advantage is gained. We find that in all cases, the edge profiles of driving pulses have major effects on the excitation of unwanted transitions, suggesting that pulse shape optimization is a viable method for improving quantum gate fidelity in all three driving regimes.