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.
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.
A quantum computer is a new kind of computer which utilizes quantum phenomena in computing. This machine has the potential to solve specific tasks faster than the most powerful supercomputers and therefore has potential real-life applications across various sectors of society. One promising approach to realize a quantum computer is to store information in superconducting qubits, which are artificial two-level quantum systems made from superconducting electrical circuits. Extremely precise control of these qubits is essential but also challenging due to the excitations out of the two lowest energy states of the quantum system that constitute the computational subspace. In this thesis, we propose a new way to control a superconducting multimode qubit using the unimon qubit as an example. By coupling differently to the different modes of the multimode qubit circuit, we cancel the transition from the first excited state to the second excited state, which is typically the main transition causing a leakage out of the computational subspace. We present a theoretical description of this model by utilizing methods of circuit quantum electrodynamics to compute the energy spectrum and the transition matrix elements of the qubit. By using these results, we simulate the dynamics of the driven unimon qubit undergoing as a single-qubit gate. The result of the simulation shows that this method decreases the leakage relative to the conventional method of driving a qubit, where only one external drive is applied. However, by improving the conventional method with a more advanced pulse optimization method, the leakage becomes smaller than in the standard case of two drive fields. In addition, we find that the practical implementation of our method may be sensitive to variations in the qubit parameters. Therefore, the practical implementation of the method needs further research in the future. By cancelling one energy-level transition of the qubit, we find that other transitions in modes of similar frequency were strongly suppressed. Therefore, this method might be potentially utilized in other qubit operations than the quantum gates, such as in the qubit resetting process, where driving to higher frequency modes of the unimon is preferred.
High-fidelity control of superconducting qubits requires carefully shaped microwave pulses to avoid several different kinds of error at once. This article is a pedagogical bridging text aimed at upper-level undergraduate and early graduate students who have completed an introductory quantum mechanics course and a first course in quantum computing or quantum information, but who have not yet encountered the physical implementation of qubit gates. We integrate physical intuition for pulse design, analytical gate-level descriptions, and practical hardware considerations into a single, derivation-driven narrative, with explicit learning objectives. We begin with simple pulse envelopes and their spectral properties, showing how finite bandwidth produces leakage outside the computational subspace. This motivates the derivative removal by adiabatic gate (DRAG) technique, which we derive explicitly using the Magnus expansion, obtaining a clear, order-by-order account of which physical error channel appears at which order and why DRAG's cancellation is necessarily incomplete. We discuss the practical hardware realities of control pulse generation, focusing on arbitrary waveform generators (AWG), local oscillators (LO), and IQ mixing. Finally, we extend the discussion to two-qubit operation via the cross-resonance gate, and interpret how driving the control qubit at the target qubit's transition frequency necessarily produces several unwanted interaction terms alongside the desired one, and how successive generations of pulse-engineering strategies have been designed to suppress them.
One of the main enablers in quantum computing is having qubit control that is precise and fast. However, qubits typically have multilevel structures making them prone to unwanted transitions from fast gates. This leakage out of the computational subspace is especially detrimental to algorithms as it has been observed to cause long-lived errors, such as in quantum error correction. This forces a choice between either achieving fast gates or having low leakage. Previous works focus on suppressing leakage by mitigating the first to second excited state transition, overlooking multi-photon transitions, and achieving faster gates with further reductions in leakage has remained elusive. Here, we demonstrate single qubit gates with a total leakage error consistently below 2.0×10−5, and obtain fidelities above 99.98% for pulse durations down to 6.8 ns for both X and X/2 gates. This is achieved by removing direct transitions beyond nearest-neighbor levels using a double recursive implementation of the Derivative Removal by Adiabatic Gate (DRAG) method, which we name the R2D method. Moreover, we find that at such short gate durations and strong driving strengths the main error source is from these higher order transitions. This is all shown in the widely-used superconducting transmon qubit, which has a weakly anharmonic level structure and suffers from higher order transitions significantly. We also introduce an approach for amplifying leakage error that can precisely quantify leakage rates below 10−6. The presented approach can be readily applied to other qubit types as well.
Improving the speed and fidelity of quantum logic gates is essential to reach quantum advantage with future quantum computers. However, fast logic gates lead to increased leakage errors in superconducting quantum processors based on qubits with low anharmonicity, such as transmons. To reduce leakage errors, we propose and experimentally demonstrate two new analytical methods, Fourier ansatz spectrum tuning derivative removal by adiabatic gate (FAST DRAG) and higher-derivative (HD) DRAG, both of which enable shaping single-qubit control pulses in the frequency domain to achieve stronger suppression of leakage transitions compared to previously demonstrated pulse shapes. Using the new methods to suppress the e f transition of a transmon qubit with an anharmonicity of − 212 MHz, we implement R X ( π / 2 ) gates achieving a leakage error below 3.0 × 10 − 5 down to a gate duration of 6.25 ns without the need for iterative closed-loop optimization. The obtained leakage error represents a 20-fold reduction in leakage compared to a conventional cosine DRAG pulse. Employing the FAST DRAG method, we further achieve an error per gate of ( 1.56 ± 0.07 ) × 10 − 4 at a 7.9-ns gate duration, outperforming conventional pulse shapes both in terms of error and gate speed. Furthermore, we study error-amplifying measurements for the characterization of temporal microwave control-pulse distortions, and demonstrate that non-Markovian coherent errors caused by such distortions may be a significant source of error for sub-10-ns single-qubit gates unless corrected using predistortion. Published by the American Physical Society 2024
Recent achievements in the physical size of quantum computers based on superconducting qubits foresee reaching the next milestones of the exponentially growing number of qubits. The promises in the scalability present opportunities in integrated control electronics operating at 4K stage in the dilution refrigerator. In addition to the number of physical qubits, however, commercialization necessitates a further increase in the number of consecutive high-fidelity gate operations within a coherence time of∼100μs. It leads to the stringent requirement on the duration of qubit-driving microwave pulse(i.e.,<20ns). The microwave pulses should only drive∣0⟩↔∣1⟩for single qubit gate operations while avoiding leakage to∣1⟩↔∣2⟩which is the major factor that degrades the gate fidelity. The frequency for∣1⟩↔∣2⟩,ω12, is typically lower than the frequency for∣0⟩↔∣1⟩,ω01, by2π×(160MHz−to−360MHz). The frequency difference(ω01−ω12), called anharmonicity, is an individual qubit characteristic and becomes the margin for spectral management. But, a short driving pulse even with Gaussian, sine, or raised-cosine shapes eventually widens the spectral width. It would range a few hundred MHz and result in a considerable spectral leakage atω12. To mitigate this spectral leakage, the derivative removal by adiabatic gate (DRAG) has been adopted in the pulse shaping [1], [2]. As shown in Fig. 34.4.1, the first-order DRAG pulse shaping is realized by adding two parts as \begin{equation*}\mathsf{O}(\mathrm{t})=\mathsf{S}_{\mathsf{M}}(\mathsf{t})\cdot\mathsf{cos}(\omega_{01}\mathsf{t}+\varphi)+\mathsf{q}_{\mathsf{scale}}\mathsf{S}_{\mathsf{M}}(\mathsf{t})^{\prime}\cdot\mathsf{sin}(\omega_{01}\mathsf{t}+\varphi)\end{equation*} whereSM(t)is the main pulse shape andqscaleis a coefficient inversely proportional to the anharmonicity. This first-order DRAG makes an asymmetrical spectrum that lowers the left frequency side and raises the right frequency side. Since theω12is always on the left side ofω01, the DRAG can effectively minimize the leakage.
Driving qubits with resonant microwave fields has proven to be an effective technique for controlling qubits and is, therefore, the current industry standard. Although the technique can produce impressive fidelities for quantum gate operations, it is not without faults. Noise at the resonant frequency that is present in the qubit’s environment effectively destroys the delicate quantum information contained in the qubit. In principle this noise can be filtered out but it also renders resonant driving useless. This issue can be circumvented with a recently developed alternative method in which the qubit is driven at around an integer fraction of its resonant frequency, namely the 1/3-subharmonic. Effectively, this enables the filtering of noise around the resonant frequency while still allowing the driving field to propagate to the qubit unimpeded. The validity of this technique has been demonstrated experimentally. In this thesis we explore this novel method for qubit control in a computational setting. We perform general simulations on qubits under subharmonic driving in order to investigate the behavior of the system and to compare the dynamics to corresponding analytical predictions. We find that the analytically derived properties, which are based on several approximations, align well with results obtained from simulations of the full unapproximated Hamiltonian. However, our main objective is to examine the fidelity of subharmonic gate operations and to compare it to its resonant counterpart. To that end, we introduced amplitude-phase fluctuations to the classically treated drive field so as to imitate the inherent uncertainties in coherent sates of light. We found that for fields of this nature, subharmonic driving provided no improvement in the scaling of fidelity. Moreover, we investigated the effects of vacuum noise in the transmission line through which the drive field propagates. Under these conditions, the arguably simple simulations reveal that subharmonic driving improves the fidelity of gate operations even at reasonably small field amplitudes. For extreme coupling strengths, noise at the 1/3-subharmonic takes effect and the state of the qubit decoheres.