# Implementation of quantum driving of superconducting qubit for gate error analysis

##### Sah, Aashish Kumar (2021)

Sah, Aashish Kumar

2021

Master's Programme in Science and Engineering

Tekniikan ja luonnontieteiden tiedekunta - Faculty of Engineering and Natural Sciences

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##### Hyväksymispäivämäärä

2021-01-26**Julkaisun pysyvä osoite on**

http://urn.fi/URN:NBN:fi:tuni-202101251652

##### Tiivistelmä

Quantum computers possesses an inherent parallelism that allows for an exponential speedup in carrying out certain tasks compared to classical computers. Superconducting-circuit, a promis- ing candidate for the physical implementation of a qubit from a non-linear LC oscillator, where the nonlinearity is introduced by the Josephson junction. The state of the qubit is controlled by a single-mode electromagnetic field, which is stored in a coplanar waveguide resonator. Con- sequently, desired gate operation can be performed on the qubit by applying microwave pulse through the drive resonator for a certain interaction time. The quality of the gate operation, mea- sured by the gate error, depends on the properties of the microwave pulse such as amplitude, phase and interaction time.

Essentially, the goal is to build a fault-tolerant quantum computer, which employs a large number of physical qubits for the implementation of error correction codes, in particular surface codes. Consequently, large number of physical qubits consumes significant amount of energy. However, by minimizing the intrinsic sources of error such as state preparation, measurement errors and imperfect gate operation, one can significantly decrease the required number of physical qubits for the execution of surface codes.

In this thesis, we focus on improving the error from the Pauli-X gate operation by optimizing the drive state of the resonator. Traditionally, a classical drive is used to implement the Pauli-X gate rotation. Alternatively, we propose a quantum driving of the qubit, where the description of the classical field is replaced by the quantum approximation of the classical field, namely, coherent drive state. A coherent state is characterized by the average photon number n ̄, thus we investi- gate a relationship between average photon number and the performance of the gate operation, numerically and experimentally.

We observe from numerical simulations that by increasing the average photon number in the drive resonator, the gate error is significantly reduced. With an average photon occupation n ̄ = 120, we obtain a gate error of ε = 0.41%. Additionally, we further improve the gate error by decreasing the coupling strength g between the qubit and the drive.

For quantum driving experiments, we design a superconducting-circuit with a qubit–resonator coupling of g/2π = 7.5 MHz. The experimental characterization of the sample yields a enhanced qubit lifetime T1 ∼ 26 μs and dephasing time T2 ∼ 5 μs. Furthermore, a photon number cal- ibration is carried out using power spectroscopy of the qubit. The results of photon calibration measurement are essential for the implementation of the full gate operation protocol, which will be conducted in the future.

Essentially, the goal is to build a fault-tolerant quantum computer, which employs a large number of physical qubits for the implementation of error correction codes, in particular surface codes. Consequently, large number of physical qubits consumes significant amount of energy. However, by minimizing the intrinsic sources of error such as state preparation, measurement errors and imperfect gate operation, one can significantly decrease the required number of physical qubits for the execution of surface codes.

In this thesis, we focus on improving the error from the Pauli-X gate operation by optimizing the drive state of the resonator. Traditionally, a classical drive is used to implement the Pauli-X gate rotation. Alternatively, we propose a quantum driving of the qubit, where the description of the classical field is replaced by the quantum approximation of the classical field, namely, coherent drive state. A coherent state is characterized by the average photon number n ̄, thus we investi- gate a relationship between average photon number and the performance of the gate operation, numerically and experimentally.

We observe from numerical simulations that by increasing the average photon number in the drive resonator, the gate error is significantly reduced. With an average photon occupation n ̄ = 120, we obtain a gate error of ε = 0.41%. Additionally, we further improve the gate error by decreasing the coupling strength g between the qubit and the drive.

For quantum driving experiments, we design a superconducting-circuit with a qubit–resonator coupling of g/2π = 7.5 MHz. The experimental characterization of the sample yields a enhanced qubit lifetime T1 ∼ 26 μs and dephasing time T2 ∼ 5 μs. Furthermore, a photon number cal- ibration is carried out using power spectroscopy of the qubit. The results of photon calibration measurement are essential for the implementation of the full gate operation protocol, which will be conducted in the future.