Superconducting qubits are manufactured solid-state artificial atoms. Their potential for lithographic scalability, compatibility with microwave control, and operability at nanosecond time scales make superconducting qubits a promising candidate for quantum information science and technology applications. To realize their full potential, present limitations to superconducting qubit coherence and lifetimes must be understood and mitigated, and that is the focus of this work. The control of Nuclear Magnetic Resonance systems is remarkably advanced, and one draws on this knowledge to characterize and mitigate noise sources in superconducting qubits. In doing so, one not only brings superconducting qubits closer to application, but addresses fundamental scientific questions regarding the nature of quantum coherence and the degree to which humankind can build, control, and ultimately exploit macroscopic quantum systems.
Quantum information science is driving an information processing revolution, enabling technologies and capabilities that simply cannot be achieved through conventional means. A unique educational feature of this work is the access and participation by students in academic, corporate and government research environments in the U.S., Japan, and Canada. Through this coordinated research effort, including student internships at these facilities, this work will further build the scientific foundations of quantum information science while also advancing a research culture that fosters future scientists with a global perspective, capable of developing and leading interdisciplinary teams across institutional and international boundaries.
A quantum computer is a new type of device that could harness the power of quantum mechanics (e.g., quantum superpositions and quantum entanglement) to speed up computation by performing a large number of operations in parallel. So far, quantum computational operations have only been realized in systems with a small number of quantum bits (qubits). The difficulty is that qubits are very susceptible to noise in their environment, which causes them to lose their "quantum-ness" (their "quantum coherence") before there is enough time to perform any calculations. One way to improve the qubits and make them live longer is to develop new designs, using new materials and more refined fabrication techniques which have lower levels of unwanted noise. A complimentary approach is to actively counteract the adverse influence of the existing noise by applying a sequence of control pulses to the qubit. In this work, we have implemented these so-called dynamical-decoupling techniques to qubits embedded in superconducting circuits. How does "dynamical decoupling" help? Conceptually, it is similar to the following situation. Imagine an entertainer trying to maintain her balance on a unicycle. To maintain balance, our entertainer pedals forwards and backwards repetitively, essentially rocking back and forth on the unicycle. By doing this repetitive pattern, she is able to counter the various noises trying to tip her over, and she stays upright. A simple dynamical-decoupling scheme for qubits is depicted in Fig. 1. The qubit state is represented by an arrow on a sphere (called a "Bloch sphere"), where the north pole corresponds to the qubit in state 0 and the south pole the qubit in state 1. Due to its quantum-mechanical properties, the qubit can be in a superposition of 0 and 1, and these states are represented by points on the equator of the Bloch sphere. An important property of quantum superpositions is that they involve a phase difference between states 0 and 1. This phase determines the qubit’s position around the equator of the Bloch sphere; just as a circle has 360 degrees, so does the relative phase have a value between 0 and 360 degrees depending on its location on the equator. Noise, however, can lead to uncertainty in the phase (called dephasing) and thereby a loss of the quantum coherence. In essence, the noise changes the location of the arrow on the equator from where it should be. On the Bloch sphere, this is visualized by the arrows spreading out along the equator to different locations, as depicted in panels II and III of Fig. 1. If the noise acting on the qubit is not too strong and does not change too quickly, the dephasing it causes can be fixed by rotating the qubit state 180 degrees around the x-axis (panel IV), that is, swapping the red and blue arrows. This inversion of the qubit state will make the noise drive the arrows "backwards" (panel V-VI), eventually "refocusing" the multiple arrows until they all converge on their original location on the equator (final panel in Fig. 1). When this happens, the coherence is recovered. In this work, we have extended the dynamical-decoupling scheme depicted in Fig. 1 (single refocusing pulse on a single qubit) to involve multiple refocusing pulses to correct for noise in two-qubit systems. Figure 2(a) shows the evolution of a two-qubit system without any refocusing pulses. The quantum state is continuously transferred back and forth between the two qubits, giving rise to the oscillations seen in Fig. 2(a). However, due to noise in the environment, the oscillations decay with time. After t=100 ns they have completely disappeared, and the quantum coherence is lost. In Fig 2(b), we show that we can recover the quantum information by periodically applying refocusing pulses to the two-qubit system. After each refocusing pulse, there is a clear "refocusing echo" forming, and the oscillations are clearly visible even after 700 ns. In this project, we have made significant contributions to understanding and mitigating decoherence through the use of such dynamical decoupling sequences. We have developed pulse calibration techniques that have enabled us to measure single-qubit gate fidelities F=99.8%, large enough to begin thinking about building larger systems from these single qubits Using the calibrated pulses, we have demonstrated pulse sequences comprising hundreds of pulses, increasing the pure dephasing times well beyond 100 us. In addition, we used the pulse sequences themselves to get a better understanding of the noise seen by the qubits. We have also demonstrated advanced dynamical decoupling, e.g., coupled two-level systems performing a SWAP gate; and "rotary echo," the spin-echo of driven dynamics. In addition to increasing the qubit lifetime, our findings will help the research community better understand the noise sources that limits quantum coherence in superconducting circuits.
