Usual metrics, such as the fidelity, used to characterize the success of implementing superconducting qubit-based quantum gates are analyzed. By numerically solving time-dependent Schr\"odinger equations for a transmon system, it is found that such metrics are not reliable to predict the performance of a quantum algorithm when the gates are used repeatedly.
Usual metrics, such as the fidelity, used to characterize the success of implementing superconducting qubit-based quantum gates are analyzed. By numerically solving time-dependent Schr"odinger equations for a transmon system, it is found that such metrics are not reliable to predict the performance of a quantum algorithm when the gates are used repeatedly.
We develop a simulator for quantum computers composed of superconducting transmon qubits. The simulation model supports an arbitrary number of transmons and resonators. Quantum gates are implemented by time-dependent pulses. Nontrivial effects such as crosstalk, leakage to non-computational states, entanglement between transmons and resonators, and control errors due to the pulses are inherently included. The time evolution of the quantum computer is obtained by solving the time-dependent Schrödinger equation. The simulation algorithm shows excellent scalability on high-performance supercomputers. We present results for the simulation of up to 16 transmons and resonators. Additionally, the model can be used to simulate environments, and we demonstrate the transition from an isolated system to an open quantum system governed by a Lindblad master equation. We also describe a procedure to extract model parameters from electromagnetic simulations or experiments. We compare simulation results to experiments on several NISQ processors of the IBM Q Experience. We find nearly perfect agreement between simulation and experiment for quantum circuits designed to probe crosstalk in transmon systems. By studying common gate metrics such as the fidelity or the diamond distance, we find that they cannot reliably predict the performance of repeated gate applications or practical quantum algorithms. As an alternative, we find that the results from two-transmon gate set tomography have an exceptional predictive power. Finally, we test a protocol from the theory of quantum error correction and fault tolerance. We find that the protocol systematically improves the performance of transmon quantum computers in the presence of characteristic control and measurement errors.
Over the past decades, tremendous effort has gone into building a universal quantum computer. In theory, such a device can solve certain problems such as factoring exponentially faster than digital computers. The leading technological prototypes are based on superconducting circuits and contain about 10-50 qubits. Controlling these fragile systems requires an enormous amount of precision, posing a difficult challenge for the experimentalists. We study such quantum systems in detail by solving the time-dependent Schrödinger equation for a generic model Hamiltonian. For this purpose, we have developed efficient product-formula algorithms that are tailored to key features of the model Hamiltonian. This allows us to simulate each individual voltage pulse that is used in experiments to realize a certain quantum gate, as dictated by the computational model of a quantum computer. By optimizing the pulse parameters, we find that even in the ideal case, the best pulses still contain undesirable errors in the realization of the intended quantum gate. The common gate metrics measured and reported in experiments or computed in theory are shown to provide insufficient practical information about the significance of these errors.
Abstract Implementing arbitrary single-qubit gates with near perfect fidelity is among the most fundamental requirements in gate-based quantum information processing. In this work, we fabricate a transmon qubit with long coherence times and demonstrate single-qubit gates with the average gate error below 10 −4 , i.e. (7.42 ± 0.04) × 10 −5 by randomized benchmarking (RB). To understand the error sources, we experimentally obtain an error budget, consisting of the decoherence errors lower bounded by (4.62 ± 0.04) × 10 −5 and the leakage rate per gate of (1.16 ± 0.04) × 10 −5 . Moreover, we reconstruct the process matrices for the single-qubit gates by the gate set tomography (GST), with which we simulate RB sequences and obtain single-qubit fidelities consistent with experimental results. We also observe non-Markovian behavior in the experiment of long-sequence GST, which may provide guidance for further calibration. The demonstration extends the upper limit that the average fidelity of single-qubit gates can reach in a transmon-qubit system, and thus can be an essential step towards practical and reliable quantum computation in the near future.
Superconducting qubits have emerged as a leading platform for realizing quantum computers. Accurate modeling of these devices is essential for predicting performance, improving design, and optimizing control. Many modeling approaches currently rely on lumped circuit approximations or other simplified treatments that can be limited in resolving the interplay between the qubit dynamics and the electromagnetic circuitry, leading to significant experimental deviations from numerical predictions at times. To address many of these limitations, methods that self-consistently solve the Schrödinger equation for qubit dynamics with the classical Maxwell's equations have been developed and shown to accurately predict a wide range of effects related to superconducting qubit control and readout. Despite these successes, these methods have not been able to consider multi-qubit effects that give rise to qubit-qubit entanglement. Here, we address this by rigorously deriving how multi-qubit coupling effects between transmon qubits can be embedded into Maxwell-Schrödinger methods. To support this, we build on earlier first-principles derivations of Maxwell-Schrödinger methods for the specific case of two transmon qubits coupled together through a common electromagnetic system in the dispersive regime. To aid in validating aspects of the Maxwell-Schrödinger framework, we also provide a new interpretation of Maxwell-Schrödinger methods as an efficient simulation strategy to capture the class of non-Markovian open quantum system dynamics. Our results demonstrate that these effects can give rise to strong classical crosstalk that can significantly alter multi-qubit dynamics, which we demonstrate for the cross-resonance gate. These classical crosstalk effects have been noted in cross-resonance experiments, but previous quantum theory and device analysis could not explain their origin.
Quantum computers have the potential to solve problems which are classically intractable. Superconducting qubits present a promising path to building such a computer. Recent experiments with these qubits have demonstrated the principles of quantum error correction, quantum simulation, quantum annealing, and more. Current research with superconducting qubits is focused on two primary goals: creating a fully fault tolerant logical qubit out of many physical qubits using surface code error correction, and demonstrating an exponential speedup over any classical computer for a well-defined computational problem. To achieve either of these goals requires high precision control of three components: single qubit gates, two qubit gates, and qubit measurement. In this thesis, we use randomized benchmarking to characterize single qubit gates with 99.95\\% fidelity and two qubit gates wiht 99.5\\% fidelity in superconducting transmon qubits. In addition, we use standard decoherence measurements as well as newly developed extensions of randomized benchmarking to determine the limiting sources of error. Finally, we explore the surprisingly complicated dynamics of measuring the transmon state through a coupled resonator, and show that fully understanding this process requires breaking a few "standard" assumptions.
Constructing a quantum computer requires immensely precise control over a quantum system. A lack of precision is often quantified by gate-error metrics, such as the average infidelity or the diamond distance. However, usually such gate-error metrics are only considered for individual gates, and not the errors that accumulate over consecutive gates. Furthermore, it is not well known how susceptible the metrics are to the assumptions which make up the model. Here, we investigate these issues using realistic simulation models of quantum computers with flux-tunable transmons and coupling resonators. Our main findings reveal that (1) gate-error metrics are indeed affected by the many assumptions of the model, (2) consecutive gate errors do not accumulate linearly, and (3) gate-error metrics are poor predictors for the performance of consecutive gates. Additionally, we discuss a potential limitation in the scalability of the studied device architecture.