Design and analysis of digital communication within an SoC-based control system for trapped-ion quantum computing

Electronic control systems used for quantum computing have become increasingly complex as multiple qubit technologies employ larger numbers of qubits with higher fidelity targets. Whereas the control systems for different technologies share some similarities, parameters like pulse duration, throughput, real-time feedback, and latency requirements vary widely depending on the qubit type. In this paper, we evaluate the performance of modern System-on-Chip (SoC) architectures in meeting the control demands associated with performing quantum gates on trapped-ion qubits, particularly focusing on communication within the SoC. A principal focus of this paper is the data transfer latency and throughput of several high-speed on-chip mechanisms on Xilinx multi-processor SoCs, including those that utilize direct memory access (DMA). They are measured and evaluated to determine an upper bound on the time required to reconfigure a gate parameter. Worst-case and average-case bandwidth requirements for a custom gate sequencer core are compared with the experimental results. The lowest-variability, highest-throughput data-transfer mechanism is DMA between the real-time processing unit (RPU) and the PL, where bandwidths up to 19.2 GB/s are possible. For context, this enables reconfiguration of qubit gates in less than 2\mics\!, comparable to the fastest gate time. Though this paper focuses on trapped-ion control systems, the gate abstraction scheme and measured communication rates are applicable to a broad range of quantum computing technologies

Quantum Computation of Hydrogen Bond Dynamics and Vibrational Spectra

Calculating the observable properties of chemical systems is often classically intractable, and is widely viewed as a promising application of quantum information processing. This is because a full description of chemical behavior relies upon the complex interplay of quantum-mechanical electrons and nuclei, demanding an exponential scaling of computational resources with system size. While considerable progress has been made in mapping electronic-structure calculations to quantum hardware, these approaches are unsuitable for describing the quantum dynamics of nuclei, proton- and hydrogen-transfer processes, or the vibrational spectra of molecules. Here, we use the QSCOUT ion-trap quantum computer to determine the quantum dynamics and vibrational properties of a shared proton within a short-strong hydrogen-bonded system. For a range of initial states, we experimentally drive the ion-trap system to emulate the quantum trajectory of the shared proton wavepacket as it evolves along the potential surface generated by the nuclear frameworks and electronic structure. We then extract the characteristic vibrational frequencies for the shared proton motion to spectroscopic accuracy and determine all energy eigenvalues of the system Hamiltonian to > 99.9% fidelity. Our approach offers a new paradigm for studying the quantum chemical dynamics and vibrational spectra of molecules, and when combined with quantum algorithms for electronic structure, opens the possibility to describe the complete behavior of molecules using exclusively quantum computation techniques.Comment: 10 pages, 4 figure

Error mitigation, optimization, and extrapolation on a trapped ion testbed

Current noisy intermediate-scale quantum (NISQ) trapped-ion devices are subject to errors around 1% per gate for two-qubit gates. These errors significantly impact the accuracy of calculations if left unchecked. A form of error mitigation called Richardson extrapolation can reduce these errors without incurring a qubit overhead. We demonstrate and optimize this method on the Quantum Scientific Computing Open User Testbed (QSCOUT) trapped-ion device to solve an electronic structure problem. We explore different methods for integrating this error mitigation technique into the Variational Quantum Eigensolver (VQE) optimization algorithm for calculating the ground state of the HeH+ molecule at 0.8 Angstrom. We test two methods of scaling noise for extrapolation: time-stretching the two-qubit gates and inserting two-qubit gate identity operations into the ansatz circuit. We find the former fails to scale the noise on our particular hardware. Scaling our noise with global gate identity insertions and extrapolating only after a variational optimization routine, we achieve an absolute relative error of 0.363% +- 1.06 compared to the true ground state energy of HeH+. This corresponds to an absolute error of 0.01 +- 0.02 Hartree; outside chemical accuracy, but greatly improved over our non error mitigated estimate. We ultimately find that the efficacy of this error mitigation technique depends on choosing the right implementation for a given device architecture and sampling budget.Comment: 16 pages, 11 figure

Sample-efficient verification of continuously-parameterized quantum gates for small quantum processors

Most near-term quantum information processing devices will not be capable of implementing quantum error correction and the associated logical quantum gate set. Instead, quantum circuits will be implemented directly using the physical native gate set of the device. These native gates often have a parameterization (e.g., rotation angles) which provide the ability to perform a continuous range of operations. Verification of the correct operation of these gates across the allowable range of parameters is important for gaining confidence in the reliability of these devices. In this work, we demonstrate a procedure for sample-efficient verification of continuously-parameterized quantum gates for small quantum processors of up to approximately 10 qubits. This procedure involves generating random sequences of randomly-parameterized layers of gates chosen from the native gate set of the device, and then stochastically compiling an approximate inverse to this sequence such that executing the full sequence on the device should leave the system near its initial state. We show that fidelity estimates made via this technique have a lower variance than fidelity estimates made via cross-entropy benchmarking. This provides an experimentally-relevant advantage in sample efficiency when estimating the fidelity loss to some desired precision. We describe the experimental realization of this technique using continuously-parameterized quantum gate sets on a trapped-ion quantum processor from Sandia QSCOUT and a superconducting quantum processor from IBM Q, and we demonstrate the sample efficiency advantage of this technique both numerically and experimentally

Superstaq: Deep Optimization of Quantum Programs

We describe Superstaq, a quantum software platform that optimizes the execution of quantum programs by tailoring to underlying hardware primitives. For benchmarks such as the Bernstein-Vazirani algorithm and the Qubit Coupled Cluster chemistry method, we find that deep optimization can improve program execution performance by at least 10x compared to prevailing state-of-the-art compilers. To highlight the versatility of our approach, we present results from several hardware platforms: superconducting qubits (AQT @ LBNL, IBM Quantum, Rigetti), trapped ions (QSCOUT), and neutral atoms (Infleqtion). Across all platforms, we demonstrate new levels of performance and new capabilities that are enabled by deeper integration between quantum programs and the device physics of hardware.Comment: Appearing in IEEE QCE 2023 (Quantum Week) conferenc

Observation of a Persistent Non-Equilibrium State in an Extremely Isotropic Harmonic Potential

Ludwig Boltzmann made tremendously important contributions to the problem of connecting macroscopic, empirical phenomena with microscopic, atomistic dynamics. At the end of the nineteenth century, Boltzmann was confronted with various strong objections to his work. For example, Boltzmann\u27s atomistic explanations presuppose the reality of atoms, a notion that was vigorously rejected in some circles [14, 38]. Then too, there was the critique by Loschmidt that Boltzmann\u27s H-theorem, put forth as a microscopic explanation for the Second Law of Thermodynamics, could hardly account for irreversible physics when the individual two-atom collisions were each reversible [18, 42]. Still intriguing today is the existence of special cases of the Boltzmann equation in which time-varying distributions of atoms resist the imperative of equilibration, even in the presence of collisions. Boltzmann discussed such situations in a paper dedicated to responding to Loschmidt\u27s critique [7, 4]. Perhaps Boltzmann\u27s motivation was to enumerate special cases where his famous H value does not relax as it should, and by enumerating them, point out their nonnaturalness, their artificiality. Damping, or relaxation to equilibrium, of a time-invariant phase-space distribution, is an all-but universal result predicted by the Boltzmann equation. Such improbable systems of atoms have only very recently been realized experimentally. Kinoshita et al. [36] experimentally confirmed that atoms constrained to move in a quasi one-dimensional potential, an atomistic Newtons cradle, exhibit vastly suppressed relaxation. Chevy et al. [15] observed long-lived breathe-mode oscillations in highly elongated but still 3D geometries. Perhaps one of the more interesting cases is the vanishing damping of the monopole breathe-mode oscillation in a spherically symmetric harmonic oscillator [29], where a cloud of atoms experiences undamped temperature oscillations, causing the cloud to expand and contract as if it were breathing. Until now, this phenomenon has been experimentally inaccessible due to the difficulty in generating isotropic harmonic confinement. This thesis discusses a new magnetic trap capable of producing spherical confinement and presents the first experimental realization of this historically significant oddity using a magnetically trapped gas of 87Rb atoms