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.
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.
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.
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.
Protecting qubits from environmental noise while maintaining strong coupling for fast high-fidelity control is a central challenge for quantum information processing. Here, we demonstrate a control scheme for superconducting fluxonium qubits that eliminates qubit decay through the control channel by suppressing the environmental density of states at the transition frequency. Adding a low-pass filter on the flux line allows for flux-biasing and, at the same time, coherently controlling the fluxonium qubit by parametrically driving it at integer fractions of its transition frequency. We compare the filtered to the unfiltered configuration and find a 5-times-longer T 1 , and a 10-times-improved T 2 -echo time in the filtered case. We demonstrate coherent control with up to 11-photon subharmonic drives, highlighting the strong nonlinearity of the fluxonium potential. Measured Rabi frequencies and drive-induced frequency shifts show excellent agreement with numerical and analytical models. Furthermore, we show the equivalence of a 3-photon subharmonic drive to an on-resonance drive by benchmarking subharmonic gate fidelities above 99.94%. These results open up a scalable path for full qubit control through a single Purcell-protected channel, providing strong suppression of control-induced decoherence and enabling wiring-efficient superconducting quantum processors.
In this thesis work, the quantum behavior of a superconducting circuit implementing a quantum bit or qubit is studied. With the use of resonant microwave pulses the full manipulation of the quantum state of this system is demonstrated: any rotation of the state vector around the Bloch sphere can be achieved and by using particular NMR inspired sequences of microwave pulses, the robustness of an operation against particular types of errors, like slow fluctuations of the transition frequency of the qubit, can be improved. The phenomenon of decoherence which drives the system from a quantum behavior to a classical one, has been characterized in the free evolution regime. By properly tuning the working point in the external parameter space, the qubit can be decoupled to first order from the fluctuations of its environment, thus enhancing coherence. In these optimal conditions, low frequency charge noise probably of microscopic origin appears to be the limiting source of decoherence for our system. The study of decoherence during driven evolution demonstrated that by suppressing the effect of those fluctuations of the environment slower than that of the driving field, the coherence of the qubit can be improved. Finally a new non-dissipative readout method based on microwave reflectometry has been set up, which improves the sensitivity and could in principle lead to a non-demolition measurement of the qubit state.
In this thesis work, the quantum behavior of a superconducting circuit implementing a quantum bit or qubit is studied. With the use of resonant microwave pulses the full manipulation of the quantum state of this system is demonstrated: any rotation of the state vector around the Bloch sphere can be achieved and by using particular NMR inspired sequences of microwave pulses, the robustness of an operation against particular types of errors, like slow fluctuations of the transition frequency of the qubit, can be improved. The phenomenon of decoherence which drives the system from a quantum behavior to a classical one, has been characterized in the free evolution regime. By properly tuning the working point in the external parameter space, the qubit can be decoupled to first order from the fluctuations of its environment, thus enhancing coherence. In these optimal conditions, low frequency charge noise probably of microscopic origin appears to be the limiting source of decoherence for our system. The study of decoherence during driven evolution demonstrated that by suppressing the effect of those fluctuations of the environment slower than that of the driving field, the coherence of the qubit can be improved. Finally a new non-dissipative readout method based on microwave reflectometry has been set up, which improves the sensitivity and could in principle lead to a non-demolition measurement of the qubit state.