Bosonic Qiskit

The practical benefits of hybrid quantum information processing hardware that contains continuous-variable objects (bosonic modes such as mechanical or electromagnetic oscillators) in addition to traditional (discrete-variable) qubits have recently been demonstrated by experiments with bosonic codes that reach the break-even point for quantum error correction and by efficient Gaussian boson sampling simulation of the Franck-Condon spectra of triatomic molecules that is well beyond the capabilities of current qubit-only hardware. The goal of this Co-design Center for Quantum Advantage (C2QA) project is to develop an instruction set architecture (ISA) for hybrid qubit/bosonic mode systems that contains an inventory of the fundamental operations and measurements that are possible in such hardware. The corresponding abstract machine model (AMM) would also contain a description of the appropriate error models associated with the gates, measurements and time evolution of the hardware. This information has been implemented as an extension of Qiskit. Qiskit is an opensource software development toolkit (SDK) for simulating the quantum state of a quantum circuit on a system with Python 3.7+ and for running the same circuits on prototype hardware within the IBM Quantum Lab. We introduce the Bosonic Qiskit software to enable the simulation of hybrid qubit/bosonic systems using the existing Qiskit software development kit. This implementation can be used for simulating new hybrid systems, verifying proposed physical systems, and modeling systems larger than can currently be constructed. We also cover tutorials and example use cases included within the software to study Jaynes- Cummings models, bosonic Hubbard models, plotting Wigner functions and animations, and calculating maximum likelihood estimations using Wigner functions

Finite-Wavevector Electromagnetic Response of Fractional Quantized Hall States

A fractional quantized Hall state with filling fraction $\nu = p/(2mp+1)$ can be modeled as an integer quantized Hall state of transformed fermions, interacting with a Chern-Simons field. The electromagnetic response function for these states at arbitrary frequency and wavevector can be calculated using a semiclassical approximation or the Random Phase Approximation (RPA). However, such calculations do not properly take into account the large effective mass renormalization which is present in the Chern-Simons theory. We show how the mass renormalization can be incorporated in a calculation of the response function within a Landau Fermi liquid theory approach such that Kohn's theorem and the $f$-sum rules are properly satisfied. We present results of such calculations.Comment: 19 pages (REVTeX 3.0), 5 figures available on request; HU-CMT-93S0

Quantum nano-electromechanics with electrons, quasiparticles and Cooper pairs: effective bath descriptions and strong feedback effects

Using a quantum noise approach, we discuss the physics of both normal metal and superconducting single electron transistors (SET) coupled to mechanical resonators. Particular attention is paid to the regime where transport occurs via incoherent Cooper-pair tunneling (either via the Josephson quasiparticle (JQP) or double Josephson quasiparticle (DJQP) process). We show that, surprisingly, the back-action of tunneling Cooper pairs (or superconducting quasiparticles) can be used to significantly cool the oscillator. We also discuss the physical origin of negative damping effects in this system, and how they can lead to a regime of strong electro-mechanical feedback, where despite a weak SET - oscillator coupling, the motion of the oscillator strongly effects the tunneling of the Cooper pairs. We show that in this regime, the oscillator is characterized by an energy-dependent effective temperature. Finally, we discuss the strong analogy between back-action effects of incoherent Cooper-pair tunneling and ponderomotive effects in an optical cavity with a moveable mirror; in our case, tunneling Cooper pairs play the role of the cavity photons.Comment: 27 pages, 7 figures; submitted to the New Journal of Physics focus issue on Nano-electromechanical Systems; error in references correcte

Freezing of the quantum Hall liquid at ν=\nu = 1/7 and 1/9

We compare the free energy computed from the ground state energy and low-lying excitations of the 2-D Wigner solid and the fractional quantum Hall liquid, at magnetic filling factors $\nu = 1/7$ and 1/9. We find that the Wigner solid melts into the fractional quantum Hall liquid at roughly the same temperature as that of some recent luminescence experiments, while it remains a solid at the lower temperatures characteristic of the transport experiments. We propose this melting as a consistent interpretation of both sets of experiments.Comment: uses RevTeX 2.0 or 3.

Variational quantum Monte Carlo study of two-dimensional Wigner crystals: exchange, correlation, and magnetic field effects

The two-dimensional Wigner crystals are studied with the variational quantum Monte Carlo method. The close relationship between the ground-state wavefunction and the collective excitations in the system is illustrated, and used to guide the construction of the ground-state wavefunction of the strongly correlated solid. Exchange, correlation, and magnetic field effects all give rise to distinct physical phenomena. In the absence of any external magnetic field, interesting spin-orderings are observed in the ground-state of the electron crystal in various two-dimensional lattices. In particular, two-dimensional bipartite lattices are shown not to lead necessarily to an antiferromagnetic ground-state. In the quantum Hall effect regime, a strong magnetic field introduces new energy and length scales. The magnetic field quenches the kinetic energy and poses constraints on how the electrons may correlate with each other. Care is taken to ensure the appropriate translational properties of the wavefunction when the system is in a uniform magnetic field. We have examined the exchange, intra-Landau-level correlation as well as Landau-level-mixing effects with various variational wavefunctions. We also determine their dependences on the experimental parameters such as the carrier effective mass at a modulation-doped semiconductor heterojunction. Our results, when combined with some recent calculations for the energy of the fractional quantum Hall liquid including Landau-level-mixing, show quantitatively that in going from $n$-doping to $p$-doping in $GaAS/AlGaAS$ heterojunction systems, the crossover filling factor from the fractional quantum Hall liquid to the Wigner crystal changes from filling factor $\nu \sim 1/5$ to $\nu \sim 1/3$. This lends strong support to the claim that theComment: LaTex file, 14 figures available from [email protected]

Architectures for Multinode Superconducting Quantum Computers

Many proposals to scale quantum technology rely on modular or distributed designs where individual quantum processors, called nodes, are linked together to form one large multinode quantum computer (MNQC). One scalable method to construct an MNQC is using superconducting quantum systems with optical interconnects. However, a limiting factor of these machines will be internode gates, which may be two to three orders of magnitude noisier and slower than local operations. Surmounting the limitations of internode gates will require a range of techniques, including improvements in entanglement generation, the use of entanglement distillation, and optimized software and compilers, and it remains unclear how improvements to these components interact to affect overall system performance, what performance from each is required, or even how to quantify the performance of each. In this paper, we employ a `co-design' inspired approach to quantify overall MNQC performance in terms of hardware models of internode links, entanglement distillation, and local architecture. In the case of superconducting MNQCs with microwave-to-optical links, we uncover a tradeoff between entanglement generation and distillation that threatens to degrade performance. We show how to navigate this tradeoff, lay out how compilers should optimize between local and internode gates, and discuss when noisy quantum links have an advantage over purely classical links. Using these results, we introduce a roadmap for the realization of early MNQCs which illustrates potential improvements to the hardware and software of MNQCs and outlines criteria for evaluating the landscape, from progress in entanglement generation and quantum memory to dedicated algorithms such as distributed quantum phase estimation. While we focus on superconducting devices with optical interconnects, our approach is general across MNQC implementations.Comment: 23 pages, white pape

Building a Quantum Engineering Undergraduate Program

Contribution: A roadmap is provided for building a quantum engineering education program to satisfy U.S. national and international workforce needs. Background: The rapidly growing quantum information science and engineering (QISE) industry will require both quantum-aware and quantum-proficient engineers at the bachelor\u27s level. Research Question: What is the best way to provide a flexible framework that can be tailored for the full academic ecosystem? Methodology: A workshop of 480 QISE researchers from across academia, government, industry, and national laboratories was convened to draw on best practices; representative authors developed this roadmap. Findings: 1) For quantum-aware engineers, design of a first quantum engineering course, accessible to all STEM students, is described; 2) for the education and training of quantum-proficient engineers, both a quantum engineering minor accessible to all STEM majors, and a quantum track directly integrated into individual engineering majors are detailed, requiring only three to four newly developed courses complementing existing STEM classes; 3) a conceptual QISE course for implementation at any postsecondary institution, including community colleges and military schools, is delineated; 4) QISE presents extraordinary opportunities to work toward rectifying issues of inclusivity and equity that continue to be pervasive within engineering. A plan to do so is presented, as well as how quantum engineering education offers an excellent set of education research opportunities; and 5) a hands-on training plan on quantum hardware is outlined, a key component of any quantum engineering program, with a variety of technologies, including optics, atoms and ions, cryogenic and solid-state technologies, nanofabrication, and control and readout electronics