A quantum computer (QC) is a device that performs operations according to the rules of quantum theory. There are various types of QCs of which nowadays the two most important ones considered for practical realization are the gate-based QC and the quantum annealer (QA). Practical realizations of gate-based QCs consist of less than 100 qubits while QAs with more than 2000 qubits are commercially available.In the gate model QC, a universal QC, a computation (or quantum algorithm) consists of a sequence of quantum gate operations (unitary transformations) that changes the internal state of the QC. Quantum annealing is a technique for finding the global minimum of a quadratic function of binary variables by exploiting quantum fluctuations. Its main potential targets are combinatorial optimization problems featuring a discrete search space with many local minima.We present results of simulating on the IBM Quantum Experience devices and on the D-Wave 2X QA with more than 1000 qubits. Simulations of both types of QCs are performed by first modeling them as zero-temperature quantum systems of interacting spin-1/2 particles and then emulating their dynamics by solving the time-dependent Schrödinger equation. Our software allows for the simulation of a 48-qubit gate-based QC on the Sunway TaihuLight supercomputer.We also briefly report about EQUIPE, a user group, established by Forschungszentrum Jülich, to Enable QUantum Information Processing in Europe and about JUNIQ, a Jülich User Infrastructure for Research and Development in Quantum Computing, offering European users from science and industry user support and access to various QC simulators and eventually technologies on various stages of maturity (D-Wave QA, multi-qubit devices for QC without error correction from e.g. IBM, Google, Rigetti Computing, …, and experimental devices).
A quantum computer (QC) is a device that performs operations according to the rules of quantum theory. There are various types of QCs of which nowadays the two most important ones considered for practical realization are the gate-based QC and the quantum annealer (QA). Practical realizations of gate-based QCs consist of less than 100 qubits while QAs with more than 2000 qubits are commercially available.In the gate model QC, a universal QC, a computation (or quantum algorithm) consists of a sequence of quantum gate operations (unitary transformations) that changes the internal state of the QC. Quantum annealing is a technique for finding the global minimum of a quadratic function of binary variables by exploiting quantum fluctuations. Its main potential targets are combinatorial optimization problems featuring a discrete search space with many local minima.We present results of simulating on the IBM Quantum Experience devices and on the D-Wave 2X QA with more than 1000 qubits. Simulations of both types of QCs are performed by first modeling them as zero-temperature quantum systems of interacting spin-1/2 particles and then emulating their dynamics by solving the time-dependent Schrödinger equation. Our software allows for the simulation of a 48-qubit gate-based QC on the Sunway TaihuLight supercomputer.We also briefly report about EQUIPE, a user group, established by Forschungszentrum Jülich, to Enable QUantum Information Processing in Europe and about JUNIQ, a Jülich User Infrastructure for Research and Development in Quantum Computing, offering European users from science and industry user support and access to various QC simulators and eventually technologies on various stages of maturity (D-Wave QA, multi-qubit devices for QC without error correction from e.g. IBM, Google, Rigetti Computing, …, and experimental devices).
This chapter provides a basic overview of Quantum Computers (QCs) used in Quantum Computing (Quacomp) applications. Classical computers utilize silicon-based semiconductor devices. In recent years integrated circuit lateral feature sizes have been reduced to 10 nm, increasing chip density; however, as these sizes progress to be reduced to 5 nm and smaller, silicon-based circuits become impractical. QCs make use of quantum phenomena such as entanglement and superposition to increase and improve the computation speed as compared to classical computers, enabling them to solve some computationally complex problems in practical time windows. At this juncture QCs are not able to act as replacements for general- purpose computers, but they can outperform classical computers in a set of specific computational problems, such as optimization problems or for identifying the best solution from a set of feasible solutions. This chapter covers three QC approaches: the circuit model (or gate model), the adiabatic quantum computation model, and the categorical quantum model. Quacomp has experienced relatively rapid development in recent years, starting with the basic ideation in the early 1980s, then continuing with early proof of concepts for hardware in the next two decades, and now, in the 2020s, with QC hardware that can implement over one-thousand qubits (e.g., [ TIL22 ], [ FEY82 ], [ LEU00 ], [ NEG06 ], [ PLA07 ], [ MON11 ], [ MON16 ], [ CAS23 ]). Figure 5.1 (courtesy of IBM) depicts recent illustrative achievements in practical QC development at IBM, a key player in this arena (in the fall of 2023, IBM® announced the Condor prototype, the world’s first universal QC with 1,121 qubits 1 ). The generation of QCs at the time of this writing is known as Noisy-Intermediate Scale Quantum (NISQ) devices (some proponents cite this as being the third generation). These NISQ QCs are typically cooled to cryogenic temperatures (around −273° C) in order to operate efficiently; these environmental conditions are challenging to maintain in other than laboratory settings. In practical terms, QCs remain of somewhat limited and specialized functionality and are prone to computational errors. Considering these limitations, Hybrid QC (HQC) 170 171 172 arrangements and Hybrid Quantum Applications (HQApps) endeavor to combine classical and QC systems in order to undertake calculations directed at various (but specific) optimization or related use cases; tasks such as preparing inputs for quantum algorithms, storing data, or interacting with the user are typically still performed using classical computers. The number of operations in a QC typically equates with the number of quantum gates and the number of qubits supported; however, the larger the number of gates, the more likely it is that errors, including decoherence, are introduced into the quantum state. NISQ entails a somewhat limited number of logical qubits and associated physical qubits to support error correction schemes. Fortunately, a category of algorithms running on NISQ devices can proceed with only a small number of qubits and exhibit some degree of noise resilience; typically, they are hybrid algorithms, with a portion of the computational steps performed on a quantum device and with other computational steps running on a conventional computer. The bottom line is that with NISQ devices, the number of operations is typically moderate at this juncture, thus the scope and type of algorithms that can be implemented is relatively limited. However, there is research that shows that even these QCs can outperform conventional computers on a set of mathematical problems (e.g., [ PRE18 ], [ BRO19 ], [ MAD22 ]). The next step in the evolution is the interconnection of QCs over a distance network, as discussed in Chapter 6 . A classification of fundamental QC technologies has been proposed the European standards body CEN-CENELEC, specifically the Focus Group on Quantum Technologies (FGQT), which was established in June 2020 to coordinate and support the development of standards relevant for European industry and research [ OVA22 ]. See Table 5.1 .
Quantum computing is based on the exploitation of quantum effects to perform some important computations more efficiently than ever possible on classical computers. Well known quantum algorithms are Shors polynomial time factoring algorithm and Grovers data base search scheme. Their potential is due to the parallelism of a quantum computation increasing exponentially with the size of the computing device. IBM has succeeded in building a first working quantum computing device with up to 7 qubits based on NMR technology, however, the construction of large multi-qubit systems appears to become extremely difficult due to the loss of coherence of the quantum states. Like the design process of modern microprocessors which is carried out by means of sophisticated software, modelling and simulation of the entire QC device is even more relevant. Simulation is required in order to understand the functioning of quantum algorithms, to construct novel quantum algorithms, to write quantum programs, to teach quantum computing, to construct real quantum computers, to understand and fight de-coherence and to understand and control the influence of the environment. Since quantum parallelism increases exponentially with the size of the quantum computer, parallel supercomputers are required for realistic simulations. I intend to give an introduction into the simulation of quantum computers using conventional computers. The simulation is based on a generic physical model of quantum computer hardware. Issues like parallel gate level simulators, modelling of QCs, simulators for physical quantum computers are addressed.
Newspapers and websites are reporting with strong emphasys the successes of quantum computing, obtained by the new quantum machines. It is therefore natural to ask ourselves some questions about these machines, in particular how do they operate, where are they physically and what is needed for their running. Actually, we must ask ourselves such questions because the news headlines – sometime bombastic - could lead us to understand quantum machines as actually existing supercomputers, able of solving in a few seconds some calculation problems that classical computers would take millennia to process. To answer questions, this work is proposing a review of existing Quantum Computers. In the panorama of Quantum Computing, we intend to investigate how the future of their infrastructures will be, such as the related basic algorithms. We will try to understand what their logistics will be, where logistics is understood as a new quantum "art of computing". Specific attention will be paid to the quantum advantage, the medium-term strategy related to design algorithms for the next generations of quantum computers. Such algorithms are required by a wide range of strategic applications. Currently, they are mainly simulation algorithms of quantum physics and chemistry, but also algorithms related to quadratic unconstrained binary optimization exist. Here we will illustrate in particular two methods: one based on abiabatic quantum computation, which is obtained through quantum annealing (D-Wave systems), the other based on arrays of quantum gates (IBM, Google and others). We will see, in greater detail, the simulations concerning the Variational Quantum Eigensolver method. Some notions related to qubits, quantum gates and their Hamiltonians will be proposed too. Besides talking of qubits, we will also report about qumodes. In fact, the art of quantum computing has two faces, one based on qubits, the other based on qumodes. Xanadu's Borealis quantum computer is an example of qumode computer. It is capable of developing a hybrid system, with GKP-type qubit emulation along with squeezed light. SpinQ's first three qubits desktop will also be mentioned. A hint of quantum communication will also be provided.
Quantum computing promises unprecedented possibilities for important computing tasks such as quantum simulations in chemistry and materials science or optimization and machine learning. With this potential, quantum computing is increasingly attracting interest from industry and scientific communities that use high performance computing (HPC) for their applications.Practical application requires the integration of quantum computers into existing HPC infrastructures in the form of quantum-classical hybrid computing models.The Jülich UNified Infrastructure for Quantum computing (JUNIQ), a manufacturer-independent quantum computing user facility established at the Jülich Supercomputing Centre (JSC) aims to address these needs.As an example, we present benchmarking results for the quantum approximate optimization algorithm (QAOA) emulated on a supercomputer and for the D-Wave quantum annealers for the tail assignment problem, a planning problem from aircraft industry.
Quantum optimization which is the use of quantum computers and algorithms for solving complex optimization problems, is one of the topics in quantum computing with the highest potential. Two types of approaches are generally used to solve combinatorial optimization problems with quantum computers: exact methods such as the Grover’s search algorithm, and meta-heuristics such as the Quantum Annealing and the Quantum Approximate Optimization Algorithm (QAOA). Exact methods and variational methods like QAOA make use of universal gate-based quantum computers, such as the ones developed by the IBM company.Quantum annealing is designed for analogic quantum computers developed by D-Wave. Solving a combinatorial optimization problem with heuristics generally requires a transformation of the problem to a format suitable for the quantum computer. While some existing frameworks can cope with Constrained Quadratic Models (CQM), Quadratic Unconstrained Binary Optimization (QUBO) is the best option to map an optimization problem to a quantum computer or simulator. We consider in this paper the job shop scheduling problem.