Quantum Information for Fusion Energy Sciences (Final Technical Report)

The simulation of plasma dynamics is a critical area of Fusion Energy Sciences (FES) due to it’s usefulness in predicting, controlling, and confining plasmas in the context of potential fusion reactors. The simulation of plasmas is a computationally difficult problem in both classical and quantum physics, motivating investigation into the potential of quantum computers to simulate these systems. This project took several concrete steps towards this goal by developing tools for improving the control, characterization, and calibration of quantum gates on a superconducting quantum computer, developing error suppression and mitigation tools to reduce errors on the quantum computer, and utilizing these advancements to simulate reduced models of plasma dynamics on the quantum computer.

Quantum computers are on the verge of becoming a commercially available reality. They represent a paradigm shift in computing, with a steep learning gradient. The creation of games is a way to ease the transition for beginners. We present a game similar to the Poker variant Texas hold ’em with the intention to serve as an engaging pedagogical tool to learn the basics rules of quantum computing. The concepts of quantum states, quantum operations and measurement can be learned in a playful manner. The difference to the classical variant is that the community cards are replaced by a quantum register that is “randomly” initialized, and the cards for each player are replaced by quantum gates, randomly drawn from a set of available gates. Each player can create a quantum circuit with their cards, with the aim to maximize the number of 1’s that are measured in the computational basis. The basic concepts of superposition, entanglement and quantum gates are employed. We provide a proof-of-concept implementation using Qiskit (Aleksandrowicz et al. in An open-source framework for quantum computing, 2019). A comparison of the results for the created circuits using a simulator and IBM machines is conducted, showing that error rates on contemporary quantum computers are still very high. For the success of noisy intermediate scale quantum (NISQ) computers, improvements on the error rates and error mitigation techniques are necessary, even for simple circuits. We show that quantum error mitigation (QEM) techniques can be used to improve expectation values of observables on real quantum devices.

Quantum computation, a paradigm of computing that is completely different from classical methods, benefits from theoretically proved speed-ups for certain problems and can be used to study the properties of quantum systems1. Yet, because of the inherently fragile nature of the physical computing elements (qubits), achieving quantum advantages over classical computation requires extremely low error rates for qubit operations, as well as substantialphysical qubits, to realize fault tolerance via quantum error correction2,3. However, recent theoretical work4,5 has shown that the accuracy of computation (based on expectation values of quantum observables) can be enhanced through an extrapolation of results from a collection of experiments of varying noise. Here we demonstrate this errormitigation protocol on a superconducting quantum processor, enhancing its computational capability, with no additional hardware modifications. We apply the protocol to mitigate errors in canonical single- and two-qubit experiments and then extend its application to the variational optimization6-8 of Hamiltonians for quantum chemistry and magnetism9. We effectively demonstrate that the suppression of incoherent errors helps to achieve an otherwise inaccessible level of accuracy in the variational solutions using our noisy processor. These results demonstrate that error mitigation techniques will enable substantial improvements in the capabilities of near-term quantum computing hardware.

Quantum error control and mitigation techniques help improve how quantum computers handle errors, making algorithms run more efficiently despite noisy hardware. These strategies work at the software level and are built into programs before they run on quantum machines. Unlike quantum error correction, which actively detects and fixes errors during computation, error mitigation does not use real-time corrections but instead reduces the impact of errors after computations. Error mitigation can also help reduce the extra resources needed for full error correction. This chapter explains how these techniques relate to each other, provides an overview of key error mitigation methods and their limitations, and highlights leading academic and technological players in this field. It also covers current trends, such as integrating error-aware programming, benchmarking performance, and ensuring access to quantum hardware for testing. To advance quantum computing, it is recommended that research ecosystems support specialized centers and contribute to key strategic areas in the field.

In quantum computing, noisy intermediate-scale quantum (NISQ) devices offer unprecedented computational capabilities but are vulnerable to errors, notably measurement inaccuracies that impact computation accuracy. This study explores the efficacy of error mitigation techniques in improving quantum circuit performance on NISQ devices. Techniques such as dynamic decoupling (DD), twirled readout error extraction (T-REx) and zero-noise extrapolation (ZNE) are examined through extensive experimentation on an ideal simulator, IBM Kyoto, and IBM Osaka quantum computers. Results reveal significant performance discrepancies across scenarios, with error mitigation techniques notably enhancing both estimator result and variance values, aligning more closely with ideal simulator outcomes. The comparison results with ideal simulator (having expected result value 0.8284) shows that T-Rex has improved results on IBM Kyoto and enhanced average expected result value from 0.09 to 0.35. Similarly, DD has improved average expected result values from 0.2492 to 0.3788 on IBM Osaka. These findings underscore the critical role of error mitigation in bolstering quantum computation reliability. The results suggest that selection of mitigation technique depends upon quantum circuit and its depth, type of hardware and operations to be performed.

Superconducting circuits are one of the leading architectures in quantum computing. To undertake quantum computing one must be able to perform quantum gates; however, two-qubit gates are still limited in fidelity and gate time. The cross-resonance gate is a two-qubit gate that uses direct microwave drives and has seen much success in its implementation; but, there are theoretical indications that it has not yet reached the coherence limited fidelity value and its gate time is still relatively long compared with other quantum gate methods. Quantum optimal control theory is a powerful tool in the design of controls for quantum operations and has shown the capability to improve gate fidelities and reduce gate times. Robust quantum optimal control methodologies have further built on this to develop high fidelity quantum gates that are robust to uncertainties and noise in the system. In this thesis we use robust quantum optimal control theory to achieve these goals for the cross-resonance gate in a variety of superconducting qubit architectures. First, we investigate two superconducting qubits embedded in a common 3D microwave cavity in which the control drive is implemented via the common cavity mode of the cavity. We determine pulse shapes that implement the cross-resonance gate that are robust to uncertainty in the qubit transition frequencies for both a strictly two-level superconducting qubit and a three-level qubit. Second, we look at the cross-resonance gate with direct drives on each qubit, finding the minimal time to perform the cross-resonance gate with pulses that are robust to uncertainty in a measured system parameter for three cases: two three-level qubits with no drive crosstalk, two three-level qubits with some drive crosstalk, and two two-level qubits. Lastly, we report on simulations undertaken towards implementing a robust, high fidelity cross-resonance gate in a novel superconducting quantum device known as the coaxmon.

In the past few years, the first commercially available quantum computers have emerged, in an early stage of development, the so-called Noisy Intermediate-Scale Quantum (NISQ) era. Although these devices are still very prone to errors of different natures, they also have shown to deal successfully with small computational problems. Nowadays, one of the challenges in quantum computation is exactly to be able to show that quantum computers are useful, whereby mitigating the effects of the faulty hardware is pivotal. Recently, a wide range of quantum error mitigation techniques have been proposed and successfully implemented, alternative to quantum error correction codes. Herein, we discuss several types of noise in a quantum computer and techniques available to mitigate them, as well as their limitations and conditions of applicability. We also suggest an hierarchy for them, towards the conception of a layered software framework of error mitigation techniques, and implement some of them in a quantum simulation of the Heisenberg model on an IBM quantum computer, improving the fidelity of the simulation by 2.8x.

One of the major obstacles to the adoption of quantum computing is the requirement to define quantum circuits at the quantum gate level. Many programmers are familiar with high-level or low-level programming languages but not quantum gates nor the low-level quantum logic required to derive useful results from quantum computers. The steep learning curve involved when progressing from quantum gates to complex simulations such as Shor's algorithm has proven too much for many developers. The purpose of this paper and the software presented within, addresses this challenge by providing a Software Development Kit (SDK), translation layer, emulator and a framework of techniques for executing Intel 8080/Z80 assembler on a quantum computer, i.e. all salient points of CPU execution, logic, arithmetic and bitwise manipulation will be executed on the quantum computer using quantum circuits. This provides a novel means of displaying the equivalency and interoperability of quantum and classical computers. Developers and researchers can use the SDK to write code in Intel 8080/Z80 assembler which is executed locally via traditional emulation and remotely on a quantum computer in parallel. The emulator features side-by-side code execution with visibility of the running quantum circuit and re-usable/overridable methods. This enables programmers to learn, reuse and contrast techniques for performing any traditional CPU based technique/instruction on a quantum computer; e.g. a programmer may know how to multiply and perform checks on a classical CPU but is not able to perform the same tasks in a quantum implementation, this SDK allows the programmer to pick and choose the methods they would like to use to fulfil their requirements. The SDK makes use of open-source software, specifically Python and Qiskit for the emulation, translation, API calls and execution of user supplied code or binaries.

Abstract: Quantum computing is on the brink of transforming computation, cryptography, artificial intelligence, and materials science, with quantum computing chips at the core of this revolution. "Quantum Computing Chips: Advances in Superconducting and Topological Qubits" provides an in-depth exploration of the latest advancements in quantum hardware, focusing on superconducting and topological qubits, two of the most promising approaches for scalable, fault-tolerant quantum computing. The book examines the fundamental principles of quantum computing, qubit architectures, and fabrication techniques, highlighting how Josephson junctions, transmon qubits, and Majorana fermions contribute to quantum logic operations. It delves into quantum chip integration, error correction strategies, hybrid quantum-classical computing, and emerging quantum networking technologies, offering insights into how industry leaders such as Google, IBM, and Microsoft are advancing quantum processor development. The book also explores the commercialization, industrial impact, and policy challenges of quantum computing chips, discussing applications in cryptography, AI acceleration, quantum simulation, and financial modeling. Through technical analysis, case studies, and expert insights, this book serves as a comprehensive resource for scientists, engineers, researchers, and technology leaders navigating the rapidly evolving quantum computing landscape. Keywords: Quantum computing, superconducting qubits, topological qubits, Josephson junctions, transmon qubits, Majorana fermions, non-Abelian anyons, quantum error correction, quantum chip fabrication, cryogenic quantum systems, hybrid quantum-classical computing, quantum networking, quantum supremacy, quantum cryptography, quantum AI acceleration, quantum materials science, fault-tolerant quantum computing, scalable quantum processors, quantum circuit design, quantum gate fidelity, quantum simulation, IBM quantum computing, Google quantum computing, Microsoft quantum computing, quantum industry, quantum economy, quantum policy, quantum innovation.

From Pharmacology to Cryptography and from Geology to Astronomy are some of the scientific fields in which Quantum Computing potentially will take off and fly high. Big Quantum Computing vendors invest a large amount of money in improving the hardware and they claim that soon enough a quantum program will be hundreds of thousands of times faster than a typical one we know nowadays. But still the reliability of such systems is the main obstacle. In this work, the reliability of real quantum devices is tested and techniques of noise and error correction are presented while measurement error mitigation is explored. In addition, a well-known string matching algorithm (Bernstein-Vazirani) was applied to the real quantum computing device in order to measure its accuracy and reliability. Simulated environments were also used in order to evaluate the results. The results obtained, even if these were not 100% accurate, are very promising which proves that even these days a quantum computer working side by side with a typical one is reliable and especially when error mitigation techniques are applied.

Quantum volume is a full-stack benchmark for near-term quantum computers. It quantifies the largest size of a square circuit which can be executed on the target device with reasonable fidelity. Error mitigation is a set of techniques intended to remove the effects of noise present in the computation of noisy quantum computers when computing an expectation value of interest. Effective quantum volume is a proposed metric that applies error mitigation to the quantum volume protocol to evaluate the effectiveness not only of the target device but also of the error mitigation algorithm. Digital zero-noise extrapolation is an error mitigation technique that estimates the noiseless expectation value using circuit folding to amplify errors by known scale factors and then extrapolating computed expectation values to the zero-noise limit. Here we demonstrate that zero-noise extrapolation, with global and local unitary folding with fractional scale factors, in conjunction with dynamical decoupling, can increase the effective quantum volume over the vendor-measured quantum volume. Specifically, we measure the effective quantum volume of four IBM Quantum superconducting processor units, obtaining values that are larger than the vendor-measured quantum volume on each device. This is the first such increase reported.

We introduce Mitiq, a Python package for error mitigation on noisy quantum computers. Error mitigation techniques can reduce the impact of noise on near-term quantum computers with minimal overhead in quantum resources by relying on a mixture of quantum sampling and classical post-processing techniques. Mitiq is an extensible toolkit of different error mitigation methods, including zero-noise extrapolation, probabilistic error cancellation, and Clifford data regression. The library is designed to be compatible with generic backends and interfaces with different quantum software frameworks. We describe Mitiq using code snippets to demonstrate usage and discuss features and contribution guidelines. We present several examples demonstrating error mitigation on IBM and Rigetti superconducting quantum processors as well as on noisy simulators.

Near-term quantum computers have been built as intermediate-scale quantum devices and are fragile against quantum noise effects, namely, NISQ devices. Traditional quantum-error-correcting codes are not implemented on such devices and to perform quantum computation in good accuracy with these machines we need to develop alternative approaches for mitigating quantum computational errors. In this work, we propose quantum error mitigation (QEM) scheme for quantum computational errors which occur due to couplings with environments during gate operations, i.e., decoherence. To establish our QEM scheme, first we estimate the quantum noise effects on single-qubit states and represent them as groups of quantum circuits, namely, quantum-noise-effect circuit groups. Then our QEM scheme is conducted by subtracting expectation values generated by the quantum-noise-effect circuit groups from those obtained by the quantum circuits for the quantum algorithms under consideration. As a result, the quantum noise effects are reduced, and we obtain approximately the ideal expectation values via the quantum-noise-effect circuit groups and the numbers of elementary quantum circuits composing them scale polynomial with respect to the products of the depths of quantum algorithms and the numbers of register bits. To numerically demonstrate the validity of our QEM scheme, we run noisy quantum simulations of qubits under amplitude damping effects for four types of quantum algorithms. Furthermore, we implement our QEM scheme on IBM Q Experience processors and examine its efficacy. Consequently, the validity of our scheme is verified via both the quantum simulations and the quantum computations on the real quantum devices. Our QEM scheme is solely composed of quantum-computational operations (quantum gates and measurements), and thus, it can be conducted by any type of quantum device. In addition, it can be applied to error mitigation for many other types of quantum noise effects as well as noisy quantum computing of long-depth quantum algorithms.

ABSTRACTSuperconducting quantum computing (SQC) has achieved remarkable progress in recent years, garnering significant scientific and technological interests. This review provides a concise overview of the historical development of SQC, detailing fabrication methodologies for superconducting quantum chips and implementations of quantum gate operations. It compiles experimental progress in SQC over the past few years, including the preparation of multi-qubit entangled states, random circuit sampling experiments, demonstrations of quantum error correction based on surface codes, error mitigation techniques and quantum simulations. This review also discusses experimental progress related to boson-encoded qubits, fluxoniums and qudits. Finally, the current challenges in scaling are analyzed, and potential solutions for addressing these limitations are explored.

We explore the potential for hybrid development of quantum hardware where currently available quantum computers simulate open cavity quantum electrodynamical (CQED) systems for applications in optical quantum communication, simulation and computing. Our simulations make use of a recent quantum algorithm that maps the dynamics of a singly excited open Tavis–Cummings model containing N atoms coupled to a lossy cavity. We report the results of executing this algorithm on two noisy intermediate-scale quantum computers: a superconducting processor and a trapped ion processor, to simulate the population dynamics of an open CQED system featuring N = 3 atoms. By applying technology-specific transpilation and error mitigation techniques, we minimize the impact of gate errors, noise, and decoherence in each hardware platform, obtaining results which agree closely with the exact solution of the system. These results can be used as a recipe for efficient and platform-specific quantum simulation of cavity–emitter systems on contemporary and future quantum computers.