Quantum computing has recently been a topic of great interest because quantum computers can possibly be used to solve problems that classical computers are unable to. However, the greatest holdback at the moment is that the fidelity of quantum gate operations is not high enough, which leads to inaccurate computations. A key aspect of quantum computing is single-qubit gates, which are executed utilizing external microwave photon sources, called qubit drives. Here, we theoretically investigate a quantum gate operation where a transmon qubit is controlled by two different driving frequencies at the same time. The two-frequency drive is a three-photon process, where the qubit gets excited when it absorbs two photons of one frequency and emits one photon of the other frequency. This allows placing on-chip filters on the drive ports that filter out noise at the qubit's transition frequency. We calculate the fidelity of the gate operation in the two-frequency-driven transmon starting with the Hamiltonian of the system. We assume the drive lines to be noisy, utilizing a classical model of noise, which inflicts small perturbations to the Hamiltonian. Hence, we utilize time-dependent perturbation theory in the calculations. The scaling of infidelity is found to be the same as in the case with resonant and subharmonic drives, being inversely proportional to the average photon numbers of the drives, assuming that the photon numbers are equal. The scaling of Rabi frequency is observed to be the same as with the subharmonic drive and better than with the resonant drive. Therefore, we obtain results for the two-frequency drive that are as good as the results in the subharmonic drive. An interesting observation is that decoherence seems to be partially caused by multi-photon processes at different frequencies.
Quantum computing has recently been a topic of great interest because quantum computers can possibly be used to solve problems that classical computers are unable to. However, the greatest holdback at the moment is that the fidelity of quantum gate operations is not high enough, which leads to inaccurate computations. A key aspect of quantum computing is single-qubit gates, which are executed utilizing external microwave photon sources, called qubit drives. Here, we theoretically investigate a quantum gate operation where a transmon qubit is controlled by two different driving frequencies at the same time. The two-frequency drive is a three-photon process, where the qubit gets excited when it absorbs two photons of one frequency and emits one photon of the other frequency. This allows placing on-chip filters on the drive ports that filter out noise at the qubit's transition frequency. We calculate the fidelity of the gate operation in the two-frequency-driven transmon starting with the Hamiltonian of the system. We assume the drive lines to be noisy, utilizing a classical model of noise, which inflicts small perturbations to the Hamiltonian. Hence, we utilize time-dependent perturbation theory in the calculations. The scaling of infidelity is found to be the same as in the case with resonant and subharmonic drives, being inversely proportional to the average photon numbers of the drives, assuming that the photon numbers are equal. The scaling of Rabi frequency is observed to be the same as with the subharmonic drive and better than with the resonant drive. Therefore, we obtain results for the two-frequency drive that are as good as the results in the subharmonic drive. An interesting observation is that decoherence seems to be partially caused by multi-photon processes at different frequencies.
Increasing the fidelity of single-qubit gates requires a combination of faster pulses and increased qubit coherence. However, these requirements can be contradictory. Additionally, increasing the drive power can heat the qubit’s environment and degrade coherence. In this work, we circumvent this issue and achieve rapid gates by pumping a transmon’s native Kerr at approximately one third of the qubit’s resonant frequency. The subharmonic Rabi rate of the process is proportional to applied drive amplitude cubed, allowing for rapid gates. In addition, we demonstrate that filtering can be used to protect the qubit’s coherence while performing rapid gates. Single qubit gates as short as 37.4 ns are demonstrated with fidelity of 99.91%. We present theoretical calculations indicating that drive induced multi-photon decay will not limit qubit lifetime; calculated power absorption also indicates that this technique could reduce cryostat heating for fast gates, a vital requirement for large-scale quantum computers. There is a trade-off between achieving fast qubit control and preserving long qubit lifetimes. In this work, the authors demonstrate single qubit gates by driving a transmon qubit parametrically at 1/3 of its frequency, creating fast, high-fidelity gates while protecting the qubit lifetime and mitigating heating.
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.
Electron spins trapped in quantum dots have recently proven to be a promising technology for the implementation of qubits, already demonstrating high fidelity single- and two-qubits gates. The next step towards fault-tolerant quantum computing is to increase the number of so-called spin qubits on the processor. However, this poses several challenges, one of which being how to implement single-qubit gates in multi-qubit systems, with high fidelity. This work focused on two aspects. The first one was to identify the physical phenomena and limitations that hinder the realisation of high fidelity single-qubit gates in multi-qubit environments. The second objective was to investigate, implement and optimise methods in order to minimise the impact of these perturbing phenomena. The identified perturbing effects include unwanted driving between a pulse and the neighbouring qubits, as well as frequency shifts induced by drive-spin coupling and non-ideal pulse in experimental setups. Crosstalk was addressed using pulse shaping (i.e. amplitude or phase modulation of the driving pulse to tailor its spectral characteristics and reduce the energy transmitted at unwanted frequencies). The performance of shapes taken from both NMR and signal processing literature was investigated, for various pulse parameters, through an extensive grid search. In addition, a frequency correction algorithm was devised: off-resonant drive frequencies are selected so that the shifted qubits are resonantly driven. It currently accounts for two phenomena: the AC Stark and Bloch-Siegert shifts. The algorithm furthermore tracks the changes caused by the time-dependent characteristics of the shaped pulses. The proposed frequency correction algorithm was shown to almost entirely negate the effects of the considered shifts, leading to unitary fidelity improvements by up to 55%. In addition, pulse shaping was demonstrated to noticeably improve the fidelity of simultaneous single-qubit rotations compared to unshaped driving. Rotations with fidelities as high as 99.98% were obtained for pi/2 rotations on two-qubits systems. Moreover, shapes whose Fourier transform is narrow and sharp, associated with low Rabi frequencies, were demonstrated to generally provide the highest fidelities of the tested configurations. Lastly, the trends and guidelines highlighted by these results were shown to scale to systems with larger numbers of qubits. The correction techniques investigated in this work have proven promising for the implementation of high fidelity single-qubit gates in multi-qubit systems. In particular, the guidelines for selecting a well-performing pulse shape should also be useful for the design of optimised driving schemes, regardless of the number of qubits involved. Additionally, the proposed frequency shift correction algorithm is expected to be able to handle arbitrary shifts, and so to be easily adaptable to use in experiments.
Achieving fast gates and high-fidelity readout in superconducting quantum circuits often benefits from the use of large amplitude microwave drives. As the strength increases, unwanted effects such as excitation out of the logical states also become more prevalent. In transmon qubits, coherent controls relying on sub-resonant drives are fundamentally limited by the eventual appearance of strong hybridization in the spectrum. Understanding how this threshold depends on intrinsic device parameters is vital for the design and operation of circuits utilizing the transmon as a source of nonlinearity. In this work, we present an experimental study of 14 transmons with a wide range of anharmonicities, and use comparison with Floquet branch analysis and semiclassical simulations to establish a straightforward relationship between the critical value of the effective drive amplitude ηmax and the ratio γ=ωq/α, where ωq is the transmon frequency and −α is the anharmonicity. For the case where the transmon is used as a parametrically driven coupler, these results further allow us to estimate maximum parametric interaction rates, which informs the circuit design process for optimizing gate rates and fidelities.
Generating high-fidelity, tunable entanglement between qubits is crucial for realizing gate-based quantum computation. In superconducting circuits, tunable interactions are often implemented using flux-tunable qubits or coupling elements, adding control complexity and noise sources. Here, we realize a tunable ZZ interaction between two transmon qubits with fixed frequencies and fixed coupling, induced by driving both transmons off resonantly. We show tunable coupling over 1 order of magnitude larger than the static coupling, and change the sign of the interaction, enabling cancellation of the idle coupling. Further, this interaction is amenable to large quantum processors: the drive frequency can be flexibly chosen to avoid spurious transitions, and because both transmons are driven, it is resilient to microwave cross talk. We apply this interaction to implement a controlled phase (CZ) gate with a gate fidelity of 99.43(1)% as measured by cycle benchmarking, and we find the fidelity is limited by incoherent errors.
Generating high-fidelity, tunable entanglement between qubits is crucial for realizing gate-based quantum computation. In superconducting circuits, tunable interactions are often implemented using flux-tunable qubits or coupling elements, adding control complexity and noise sources. Here, we realize a tunable ZZ interaction between two transmon qubits with fixed frequencies and fixed coupling, induced by driving both transmons off-resonantly. We show tunable coupling over one order of magnitude larger than the static coupling, and change the sign of the interaction, enabling cancellation of the idle coupling. Further, this interaction is amenable to large quantum processors: the drive frequency can be flexibly chosen to avoid spurious transitions, and because both transmons are driven, it is resilient to microwave crosstalk. We apply this interaction to implement a controlled phase (CZ) gate with a gate fidelity of 99.43(1)% as measured by cycle benchmarking, and we find the fidelity is limited by incoherent errors.