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DOE OSTI2023

Quantum Computing and Visualization: A Disruptive Technological Change Ahead

The focus of this Visualization Viewpoints article is to provide some background on quantum computing (QC), to explore ideas related to how visualization helps in understanding QC, and examine how QC might be useful for visualization with the growth and maturation of both technologies in the future. In a quickly evolving technology landscape, QC is emerging as a promising pathway to overcome the growth limits in classical computing. In some cases, QC platforms offer the potential to vastly outperform the familiar classical computer by solving problems more quickly or that may be intractable on any known classical platform. As further performance gains for classical computing platforms are limited by diminishing Moore’s Law scaling, QC platforms might be viewed as a potential successor to the current field of exascale-class platforms. Importantly, while present-day QC hardware platforms are still limited in scale, the field of quantum computing is robust and rapidly advancing in terms of hardware capabilities, software environments for developing quantum algorithms, and educational programs for training the next generation of scientists and engineers. After a brief introduction to QC concepts, the focus of this article is to explore the interplay between the fields of visualization and QC. First, visualization has played a role in QC by providing the means to show representations of the quantum state of single-qubits in superposition states and multiple-qubits in entangled states. Second, there are a number of ways in which the field of visual data exploration and analysis may potentially benefit from this disruptive new technology though there are challenges going forward.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Surf-Deformer: Mitigating Dynamic Defects on Surface Code via Adaptive Deformation

In this paper, we introduce Surf-Deformer, a code deformation framework that seamlessly integrates adaptive defect mitigation functionality into the current surface code workflow. It crafts several basic deformation instructions based on fundamental gauge transformations, which can be combined to explore a larger design space than previous methods. This enables more optimized deformation processes tailored to specific defect situations, restoring the QEC capability of deformed codes more efficiently with minimal qubit resources. Additionally, we design an adaptive code layout that accommodates our defect mitigation strategy while ensuring efficient execution of logical operations. Our evaluation shows that Surf-Deformer outperforms previous methods by significantly reducing the end-to-end failure rate of various quantum programs by 35× to 70×, while requiring only about 50% of the qubit resources compared to the previous method to achieve the same level of failure rate. Ablation studies show that Surf-Deformer surpasses previous defect removal methods in preserving QEC capability and facilitates surface code communication by achieving nearly optimal throughput.

Yin, Keyi↗

DOE OSTI2020

Digital zero noise extrapolation for quantum error mitigation

Zero-noise extrapolation (ZNE) is an increasingly popular technique for mitigating errors in noisy quantum computations without using additional quantum resources. We review the fundamentals of ZNE and propose several improvements to noise scaling and extrapolation, the two key components in the technique. We introduce unitary folding and parameterized noise scaling. Furthermore, these are digital noise scaling frameworks, i.e. one can apply them using only gate-level access common to most quantum instruction sets. We also study different extrapolation methods, including a new adaptive protocol that uses a statistical inference framework. Benchmarks of our techniques show error reductions of 18X to 24X over non-mitigated circuits and demonstrate ZNE effectiveness at larger qubit numbers than have been tested previously. In addition to presenting new results, this work is a self-contained introduction to the practical use of ZNE by quantum programmers.

quantum computing↗

DOE OSTI2020

Scalable quantum processor noise characterization

Measurement fidelity matrices (MFMs) (also called error kernels) are a natural way to characterize state preparation and measurement errors in near-term quantum hardware. They can be employed in post processing to mitigate errors and substantially increase the effective accuracy of quantum hardware. However, the feasibility of using MFMs is currently limited as the experimental cost of determining the MFM for a device grows exponentially with the number of qubits. In this work we present a scalable way to construct approximate MFMs for many-qubit devices based on cumulant expansions. Our method can also be used to characterize various types of correlation error.

Hamilton, Kathleen↗

DOE OSTI2023

Mitigation of Cosmic Rays-Induced Errors in Superconducting Quantum Processors

Environmental radioactivity and cosmic-rays have recently been identified as a source of decoherence in super-conducting quantum bits (qubits). In particular, the absorption of cosmic-ray muons and gamma rays emitted by naturally occurring radioactive isotopes in the qubit substrate leads to correlated errors in superconducting quantum processors, posing significant challenges to quantum error correction. To enable quantum computing to scale, it is therefore necessary the devel-opment of mitigation strategies to prevent, or keep under control, error bursts due to particle impacts in the chip. While most environmental radioactive sources can be effectively suppressed using dedicated shielding, cosmic-ray muons, with their high penetration capability, can only be mitigated by moving the entire facility in a deep underground laboratory. This work explores the potential for developing a novel class of quantum processors equipped with an active veto system to protect superconducting-based quantum computers from the detrimental effects of atmospheric muons. Such a device would enable the identification of an atmospheric muon interaction within the processor and veto all operations performed during the occurrence of such an interaction. By demonstrating high detection efficiency and negligible dead time, we aim to establish that the future of quantum processors can be envisioned in above-around facilities.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2023

Prepare Ground States of Highly Frustrated Magnetic Clusters on Quantum Computers

Solving challenging problems in physical, chemical, and materials sciences is one of the most promising applications of quantum utility that can be realized on current noisy hardware, considering (i) the direct map (encoding) from the quantum particles and their interactions to the qubits and their entangling gates and (ii) the rapidly improved quantum hardware and advanced error-mitigation techniques. Understanding quantum spin liquid in frustrated magnetic materials is a longstanding challenge in condensed matter physics and the nature of the ground-state phases is highly debated among researchers. Using IBM quantum computers with superconducting qubits, we implemented a variational quantum eigensolver (VQE) algorithm to prepare the ground states of two 12-site cluster approximations of these highly frustrated magnetic materials. The interaction graphs of the two corresponding Hamiltonians are (a) the six-pointed star graph (a unit cell of the kagome lattice) and (b) the cuboctahedral graph (the kagome on a sphere). These are also two instances of Quantum Max Cut problem. With the VQE based on the Hamiltonian variational ansatz acting on a valence bond solid initial trial state, we prepared the ground states and obtained the exact ground energy on simulator and high accuracy on noisy hardware. The deep ansatz necessary to reach the ground state of the cuboctahedral graph indicates that it is a hard instance of Quantum Max Cut.

Wang, Yan↗

DOE OSTI2021

Quantum optimal control for pure-state preparation using one initial state

This paper presents a framework for solving the pure-state preparation problem using numerical optimal control. As an example, we consider the case where a number of qubits are dispersively coupled to a readout cavity. Herein, we model open system quantum dynamics using the Markovian Lindblad master equation driven by external control pulses. The main result of this paper develops a basis of density matrices (a parameterization) where each basis element is a density matrix by itself. Utilizing a specific objective function, we show how an ensemble of the basis elements can be used as a single initial state throughout the optimization process—independent of the system dimension. We apply the general framework to the specific application of ground-state reset of one and two qubits coupled to a readout cavity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Fully quantum algorithm for mesoscale fluid simulations with application to partial differential equations

Fluid flow simulations marshal our most powerful computational resources. In many cases, even this is not enough. Quantum computers provide an opportunity to speed up traditional algorithms for flow simulations. We show that lattice-based mesoscale numerical methods can be executed as efficient quantum algorithms due to their statistical features. This approach revises a quantum algorithm for lattice gas automata to reduce classical computations and state preparation at every time step. For this, the algorithm approximates the qubit relative phases and subtracts them at the end of each time step. Phases are evaluated using the iterative phase estimation algorithm and subtracted using single-qubit rotation phase gates. Further, this method optimizes the quantum resource required and makes it more appropriate for near-term quantum hardware. We also demonstrate how the checkerboard deficiency that the D1Q2 scheme presents can be resolved using the D1Q3 scheme. The algorithm is validated by simulating two canonical partial differential equations: the diffusion and Burgers' equations on different quantum simulators. We find good agreement between quantum simulations and classical solutions for the presented algorithm.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Dipolar spin-exchange and entanglement between molecules in an optical tweezer array

Ultracold polar molecules are promising candidate qubits for quantum computing and quantum simulations. Their long-lived molecular rotational states form robust qubits, and the long-range dipolar interaction between molecules provides quantum entanglement. In this work, we demonstrate dipolar spin-exchange interactions between single calcium monofluoride (CaF) molecules trapped in an optical tweezer array. We realized the spin- 1 2 quantum XY model by encoding an effective spin- 1 2 system into the rotational states of the molecules and used it to generate a Bell state through an iSWAP operation. Conditioned on the verified existence of molecules in both tweezers at the end of the measurement, we obtained a Bell state fidelity of 0.89(6). Using interleaved tweezer arrays, we demonstrate single-site molecular addressability.

Science & Technology - Other Topics↗

DOE OSTI2025

A high-resolution molecular spin-photon interface at telecommunication wavelengths

Optically addressable electronic spins in polyatomic molecules are a promising platform for quantum information science, with the potential to enable scalable qubit design and integration through atomistic tunability and nanoscale localization. However, optical state- and site-selection are an open challenge. Here, in this work, we introduce an organo-erbium spin qubit in which narrow (megahertz-scale) optical and spin transitions couple to provide high-resolution access to spin degrees of freedom with telecommunication-frequency light. This spin-photon interface enables demonstration of optical spin polarization and readout that distinguishes between spin states and magnetically inequivalent sites in a molecular crystal. Operation at frequencies compatible with mature photonic and microwave devices provides an opportunity for engineering scalable, integrated molecular spin-optical quantum technologies.

Weiss, Leah R. [University of Chicago, IL (United ↗

DOE OSTI2022

Quantum Algorithm Implementations for Beginners

As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available quantum computers have less than 100 qubits, quantum computing hardware is widely expected to grow in terms of qubit count, quality, and connectivity. This review aims at explaining the principles of quantum programming, which are quite different from classical programming, with straightforward algebra that makes understanding of the underlying fascinating quantum mechanical principles optional. We give an introduction to quantum computing algorithms and their implementation on real quantum hardware. We survey 20 different quantum algorithms, attempting to describe each in a succinct and self-contained fashion. We show how these algorithms can be implemented on IBM’s quantum computer, and in each case, we discuss the results of the implementation with respect to differences between the simulator and the actual hardware runs. This article introduces computer scientists, physicists, and engineers to quantum algorithms and provides a blueprint for their implementations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Automating NISQ Application Design with Meta Quantum Circuits with Constraints (MQCC)

Near-term intermediate scale quantum (NISQ) computers are likely to have very restricted hardware resources, where precisely controllable qubits are expensive, error-prone, and scarce. Programmers of such computers must therefore balance trade-offs among a large number of (potentially heterogeneous) factors specific to the targeted application and quantum hardware. To assist them, we propose Meta Quantum Circuits with Constraints (MQCC), a meta-programming framework for quantum programs. Programmers express their application as a succinct collection of normal quantum circuits stitched together by a set of (manually or automatically) added meta-level choice variables, whose values are constrained according to a programmable set of quantitative optimization criteria. MQCC’s compiler generates the appropriate constraints and solves them via an SMT solver, producing an optimized, runnable program. We showcase a few MQCC’s applications for its generality including an automatic generation of efficient error syndrome extraction schemes for fault-tolerant quantum error correction with heterogeneous qubits and an approach to writing approximate quantum Fourier transformation and quantum phase estimation that smoothly trades off accuracy and resource use. We also illustrate that MQCC can easily encode prior one-off NISQ application designs-–multi-programming (MP), crosstalk mitigation (CM)—as well as a combination of their optimization goals (i.e., a combined MP-CM).

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Q-BEEP: Quantum Bayesian Error Mitigation Employing Poisson Modeling over the Hamming Spectrum

Quantum computing technology has grown rapidly in recent years, with new technologies being explored, error rates being reduced, and quantum processor’s qubit capacity growing. However, near-term quantum algorithms are still unable to be induced without compounding consequential levels of noise, leading to non-trivial erroneous results. Quantum Error Correction (in-situ error mitigation) and Quantum Error Mitigation (post-induction error mitigation) are promising fields of research within the quantum algorithm scene, aiming to alleviate quantum errors, increasing the overall fidelity and hence the overall quality of circuit induction. Earlier this year, a pioneering work, namely HAMMER, published in ASPLOS-22 demonstrated the existence of a latent structure regarding post-circuit induction errors when mapping to the Hamming spectrum. However, they intuitively assumed that errors occur in local clusters, and that at higher average Hamming distances this structure falls away. In this work, we show that such a correlation structure is not only local but extends certain non-local clustering patterns which can be precisely described by a Poisson distribution model taking the input circuit, the device run time status (i.e., calibration statistics) and qubit topology into consideration. Using this quantum error characterizing model, we developed an iterative algorithm over the generated Bayesian network state-graph for post-induction error mitigation. Thanks to more precise modeling of the error distribution latent structure and the new iterative method, our Q-Beep approach provides state of the art performance and can boost circuit execution fidelity by up to 234.6% on Bernstein-Vazirani circuits and on average 71.0% on QAOA solution quality, using 16 practical IBMQ quantum processors. For other benchmarks such as those in QASMBench, the fidelity improvement is up to 17.8%. Q-Beep is a light-weight post-processing technique that can be performed offline and remotely, making it a useful tool for quantum vendors to integrate and provide more reliable circuit induction results.

Stein, Samuel A.↗

DOE OSTI2023

Advancing Comprehension of Quantum Application Outputs: A Visualization Technique

Noise in quantum computers presents a challenge for the users of quantum computing despite the rapid progress we have seen in the past few years in building quantum computers. Existing works have addressed the noise in quantum computers using a variety of mitigation techniques since error correction requires a large number of qubits which is infeasible at present. One of the consequences of quantum computing noise is that users are unable to reproduce similar output from the same quantum computer at different times, let alone from various quantum computers. In this work, we have made initial attempts to visualize quantum basis states for all the circuits that were used in quantum machine learning from various quantum computers and noise-free quantum simulators. We have opened up a pathway for further research into this field where we will be able to isolate noisy states from non-noisy states leading to efficient error mitigation. This is where our work provides an important step in the direction of efficient error mitigation. Our work also provides a ground for quantum noise visualization in the case of large numbers of qubits.

Senapati, Priyabrata↗

DOE OSTI2016

Python GST Implementation v. 0.9 beta

PyGSTi is an implementation of Gate Set Tomography in the python programming language. Gate Set Tomography (GST) is a theory and protocol for simultaneously estimating the state preparation, gate operations, and measurement effects of a physical system of one or many quantum bits (qubits). These estimates are based entirely on the statistics of experimental measurements, and their interpretation and analysis can provide a detailed understanding of the types of errors/imperfections in the physical system. In this way, GST provides not only a means of certifying the "goodness" of qubits but also a means of debugging (i.e. improving) them.

Nielsen, Erik↗

DOE OSTI2019

Python GST Implementation (PyGSTi) v. 0.9

PyGSTi is a Python package for modeling and characterizing noise (errors) in small quantum information processors. In addition to being a basic framework for describing quantum circuits and noise models, it implements mainstream quantum characterization, verification, and validation (QCVV) protocols such as Gate Set Tomography (GST), Randomized Benchmarking (RB), Robust Phase Estimation, and Idle Tomography. It also implements prototype protocols used for timeseries analysis and crosstalk detection, all of which have the goal of better understanding the noise found in existing as-built experimental devices. The central protocol of pyGSTi (from where it derives its name) is Gate Set Tomography. GST is a theory and protocol for simultaneously estimating the state preparation, gate operations, and measurement effects of a physical system of one or many quantum bits (qubits). These estimates are based entirely on the statistics of experimental measurements, and their interpretation and analysis can provide a detailed understanding of the types of errors/imperfections in the physical system. In this way, GST provides not only a means of certifying the “goodness” of qubits but also a means of debugging (i.e. improving) them. The other protocols follow this similar pattern in that they use statistical inference and analysis of experimental data to estimate one or more properties of the noise in a device.

Nielsen, Erik↗

DOE OSTI2020

Quantum Search Compiler (Qsearch) v2.0

Quantum Gate Synthesis is the process of taking a desired quantum gate operation, in this case specified as a unitary matrix, and decomposing it into a list of operations that can actually be performed on a quantum computer. Qsearch is an implementation of a quantum synthesis algorithm based on combining A* search with numerical optimization. It is designed to minimize CNOT count at the expense of having a long runtime. It produces particularly efficient quantum circuits in terms of CNOT count, up until about 4 qubits. It is generally impractical to run Qsearch on circuits with more than 4 qubits, but it can be used as a subroutine in algorithms designed to work with these larger circuits. Qsearch takes the form of a Python package, taking advantage of Numpy and Scipy, with part of the package written in Rust and taking advantage of OpenBLAS, NLOPT, and Google Ceres for faster runtime.

Lancu, Costin↗

DOE OSTI2023

tih_vqe [SWR-23-32]

This software supports the paper, "Exploring the scaling limitations of the variational quantum eigensolver with the bond dissociation of hydride diatomic molecules," published in the International Journal of Quantum Chemistry, whose abstract is as follows: Materials simulations involving strongly correlated electrons pose fundamental challenges to state-of-the-art electronic structure methods but are hypothesized to be the ideal use case for quantum computing. To date, no quantum computer has simulated a molecule of a size and complexity relevant to real-world applications, despite the fact that the variational quantum eigensolver (VQE) algorithm can predict chemically accurate total energies. Nevertheless, because of the many applications of moderately-sized, strongly correlated systems, such as molecular catalysts, the successful use of the VQE stands as an important waypoint in the advancement toward useful chemical modeling on near-term quantum processors. In this paper, we take a significant step in this direction. We lay out the steps, write, and run parallel code for an (emulated) quantum computer to compute the bond dissociation curves of the TiH, LiH, NaH, and KH diatomic hydride molecules using VQE. TiH was chosen as a relatively simple chemical system that incorporates d orbitals and strong electron correlation. Because current VQE implementations on existing quantum hardware are limited by qubit error rates, the number of qubits available, and the allowable gate depth, recent studies have focused on chemical systems involving s and p block elements. Through VQE + UCCSD calculations of TiH, we evaluate the near-term feasibility of modeling a molecule with d-orbitals on real quantum hardware. We demonstrate that the inclusion of d-orbitals and the use of the UCCSD ansatz, which are both necessary to capture the correct TiH physics, dramatically increase the cost of this problem. We estimate the approximate error rates necessary to model TiH on current quantum computing hardware using VQE+UCCSD and show them to likely be prohibitive until significant improvements in hardware and error correction algorithms are available.

Graf, Peter↗