Building logical qubits in a superconducting quantum computing system

Abstract

The technological world is in the midst of a quantum computing and quantum information revolution. Since Richard Feynman's famous 'plenty of room at the bottom' lecture (Feynman, Engineering and Science 23, 22 (1960)), hinting at the notion of novel devices employing quantum mechanics, the quantum information community has taken gigantic strides in understanding the potential applications of a quantum computer and laid the foundational requirements for building one. We believe that the next significant step will be to demonstrate a quantum memory, in which a system of interacting qubits stores an encoded logical qubit state longer than the incorporated parts. Here, we describe the important route towards a logical memory with superconducting qubits, employing a rotated version of the surface code. The current status of technology with regards to interconnected superconducting-qubit networks will be described and near-term areas of focus to improve devices will be identified. Overall, the progress in this exciting field has been astounding, but we are at an important turning point, where it will be critical to incorporate engineering solutions with quantum architectural considerations, laying the foundation towards scalable fault-tolerant quantum computers in the near future. 1-3 Loosely speaking, quantum computing targets problems that can exploit entanglement to explore correlations in computations, then selects the correct answer through constructive interference. For example, Shor's algorithm addresses the computational challenge of factoring by exploiting quantum interference to measure the periodicity of arithmetic objects.

Gate-error analysis in simulations of quantum computers with transmon qubits

“…(13) is always bounded above 2%, even though our quantum-theoretical model of the transmon qubit architecture does not account for decoherence or noise. The average gate fidelities are in the same ballpark as those reported for experiments based on the same pulse schemes [1,[12][13][14][15]. In fact, the single-qubit gate fidelities are slightly worse than the ones reported in experiments.…”

“…(1). We obtain the solution numerically by implementing a product-formula algorithm for the total unitary time-evolution operator U total (t) defined by | (t) = U total (t) | (0) (see Appendix A for details on the algorithm).…”

“…The quantum circuits first create the maximally entangled singlet state (|01 − |10 )/ √ 2 and then apply a set of rotations dependent on the angles ϑ 1 and ϑ 2 to analyze the constructed state (see Appendix C for the circuit). We select the two-pulse echoed CR2 gate for the CNOT operation, as also done for the IBMQX.…”

“…In theory, such a device can solve certain problems, such as factoring, exponentially faster than classical digital computers. The leading technological prototypes are based on superconducting transmon qubits containing on the order of 10 qubits [1][2][3][4]. IBM provides public access to such a quantum processor through the IBM Quantum Experience (IBMQX) [5].…”

Untitled

“…Such a resonator-mediated gate can be activated by only microwave control such as in the cross-resonance gate used by the IBM group, see [36,37] with a currently reported error rate of 1.4% [38]. The resonatormediated coupling can also be used to enact an iSWAP gate where flux-tunable qubits are brought into resonance, or the qubit state can be explicitly put on the resonator bus as in the two-qubit gate employed in [39] (a variety of other two-qubit gates are listed in [38]). A resonator-mediated gate is the basic building block in the surface code layout for transmon qubits as described in [40].…”