Mathematical Methods for Quantum Hardware

The concept of dissipation engineering has enriched the methods available for state preparation, dissipative quantum computing and quantum information processing. Combining such engineered dissipative processes with coherent dynamics allows for new effects to emerge. For example, we found that any factorisable (coherent) Hamiltonian interaction can be rendered nonreciprocal if balanced with the corresponding dissipative interaction. This powerful concept can be exploited to engineer nonreciprocal devices for quantum information processing, computation and communication protocols, Abstract Body: e.g., to achieve control over the direction of propagation of photonic signals. However, although nonreciprocal concepts are realizable in quantum architectures, nonreciprocity itself holds up to the classical level and is not inherently quantum; the fundamental aspects of nonreciprocity in the quantum regime have yet to be fully investigated. In this talk we will address these aspects and discuss routes of how nonreciprocal concepts can find application beyond quantum information processing.

The last decade has seen unparalleled improvements in the performance of quantum information devices. It is a pressing question how hardware modeling can meet the demands of these devices as they increase in both scale and fidelity. In part one of this talk, I will present a model which addresses a combined effect of disjoint error sources that exceeds the sum of their expected individual impacts. In particular, I will discuss recent experimental and theoretical work highlighting the enhanced dissipation of a target qubit due to static longitudinal interaction with neighbouring spectator qubits, and the relaxation decay of these spectators. In part two, I will present a modeling method that improves agreement with experimental observations by incorporating dissipative corrections into the perturbative calculation of effective evolution. I will show the results of this method, an extension of the recently developed time-dependent Schrieffer–Wolff perturbation theory, applied to a transmon qubit dispersively coupled to a resonator.

Quantum mechanics is a century-old theory that successfully describes counterintuitive phenomena of the microscopic world. Phenomena that, until not so long ago, would be considered irrelevant for the “real”, macroscopic world. Quantum technologies are, however, nowadays providing a paradigm shift in this thinking: They offer a wealth of potentially revolutionary applications that could change the field of Information and Communication Technology and lead to tremendous breakthroughs in disciplines such as medicine and chemistry. But building functional quantum technologies requires, among others, the ability to precisely manipulate any quantum state, a task that we are currently not able to perform to the required degree.

In this talk, I will present a very general framework based on the Magnus expansion that allow one to design high-efficiency control sequences that are fully compatible with experimental constraints on available interactions and their tunability. I will then discuss how these methods can be used to generate fast, high-fidelity gates for a superconducting qubits.

In this talk, I will present several strategies that the AWS team has been pursuing for first-principle, accurate simulation of circuit QED systems. Concrete topics include the distinction between static and dynamic simulations, tensor network methods, usefulness of finding a dressing unitary for analyzing a composite system, and convenient interface for dynamic simulations of circuit QED systems. I will also briefly talk about challenges associated with dynamically simulating a flux-tunable circuit component such as tunable transmons.

Fluctuations of the qubit frequencies are one the major problems to overcome on the way to scalable quantum computers. Of particular importance are fluctuations with the correlation time that exceeds the decoherence time due to decay and dephasing by fast processes. The statistics of the fluctuations can be characterized by measuring the correlators of the outcomes of periodically repeated Ramsey measurements. This work suggests a method that allows describing qubit dynamics during repeated measurements in the presence of evolving noise. It made it possible, in particular, to evaluate the two-time correlator for the noise from two-level systems and obtain two- and three-time correlators for a Gaussian noise. The explicit expressions for the correlators are compared with simulations. A significant difference of the three-time correlators of the noise from two-level systems and from a Gaussian noise is demonstrated. A strong broadening of the distribution of outcomes of Ramsey measurements, with a possible fine structure, is found for the data acquisition time comparable to the noise correlation time. Work of Mark Dykman, Filip Wudarski, Yaxing Zhang, Alexander Korotkov, and A. G. Petukhov

In typical circuit quantum electrodynamics experiments, the quantum state of a superconducting qubit is measured by monitoring a readout resonator weakly and off-resonantly coupled to the qubit. As drive power is increased to achieve a higher-fidelity and faster measurement, unwanted transitions occur, which, for example, decrease the qubit’s energy relaxation time T₁. In this talk, we focus on transmon qubits, and we present a time-dependent Schrieffer-Wolff perturbation theory that allows us to catalog nonlinear relaxation processes, and identify stimulated emission as one possible mechanism for spurious qubit relaxation during readout [1]. Turning to numerical techniques, we address the related phenomenon of escape into unconfined states [2,3], and discuss a second mechanism for rate enhancement during measurement: by interactions between the states defining the qubit subspace, and higher-energy chaotic states within the Floquet spectrum. [1] A. Petrescu, M. Malekakhlagh, and H. E. T ̈ureci, Phys. Rev. B 101, 134510 (2020). [2] L. Verney, R. Lescanne, M. H. Devoret, Z. Leghtas, and M. Mirrahimi, Phys. Rev. Applied 11, 024003 (2019) [3] R. Shillito, A. Petrescu, J. Cohen, J. Beall, M. Hauru, M. Ganahl, A. G. M. Lewis, G. Vidal, and A. Blais, “Dynamics of transmon ionization” arXiv: 2203.11235 (2022).

Remarkable advances in qubit hardware have enabled landmark experiments demonstrating small-scale quantum simulations, quantum computational tasks, and error-correction protocols. Nonetheless, achieving scalable, fault-tolerant quantum error correction (FTQEC) necessary for building useful quantum technology remains a challenging task. While developing low-noise quantum hardware is important to ease the requirements for FTQEC, in this talk I will focus on a complementary strategy which is based on the observation that some type of errors are less contagious and easy to correct than others. I will show how the detailed noise properties of the underlying quantum hardware can be leveraged to design high-threshold and low-overhead protocols for FTQEC. I will also discuss the opportunities for practical applications in different hardware platforms, with specific focus on superconducting circuits.

Superconducting circuits have emerged as one of the most versatile platforms in the development of hardware for quantum information applications. Exploring new superconducting circuits and optimizing existing ones naturally relies on accurate modeling. In this talk, I will focus on the open-source package “scqubits” which offers functionality that simplifies the simulation of superconducting qubits and coupled circuit QED systems. A recent addition to the package facilitates automatic circuit quantization of custom circuits. I will highlight the ideas behind automating this analysis and give an outlook on the challenges yet to be addressed.