Quantum computation is becoming an increasingly interesting field, especially with the rise of real quantum computers. However, current quantum processors contain a few tens of error-prone qubits and the realization of large-scale quantum computers is still very challenging. Therefore, quantum computer simulators are particularly suitable for testing and analysing quantum algorithms without having a real quantum computer at one's disposal. In this thesis, different quantum algorithms such as Grover's and Shor's algorithm as well as key quantum routines such as the Quantum Fourier Transform (QFT) and a quantum adder/subtractor are described and analysed (optimal number of iterations, time complexity). Some of them have been implemented for an arbitrary number of qubits and have been simulated using two different quantum simulators, the QX simulator developed at QuTech and the Liquid simulator from Microsoft. In addition, how errors affect the success rate of the algorithms has been investigated.
Quantum computation is becoming an increasingly interesting field, especially with the rise of real quantum computers. However, current quantum processors contain a few tens of error-prone qubits and the realization of large-scale quantum computers is still very challenging. Therefore, quantum computer simulators are particularly suitable for testing and analysing quantum algorithms without having a real quantum computer at one's disposal. In this thesis, different quantum algorithms such as Grover's and Shor's algorithm as well as key quantum routines such as the Quantum Fourier Transform (QFT) and a quantum adder/subtractor are described and analysed (optimal number of iterations, time complexity). Some of them have been implemented for an arbitrary number of qubits and have been simulated using two different quantum simulators, the QX simulator developed at QuTech and the Liquid simulator from Microsoft. In addition, how errors affect the success rate of the algorithms has been investigated.
With current technologies, it seems to be very difficult to implement quantum computers with many qubits. It is therefore of importance to simulate quantum algorithms and circuits on the existing computers. However, for a large-size problem, the simulation often requires more computational power than is available from sequential processing. Therefore, simulation methods for parallel processors are required. We have developed a general-purpose simulator for quantum algorithms/circuits on the parallel computer (Sun Enterprise4500). It can simulate algorithms/circuits with up to 30 qubits. In order to test efficiency of our proposed methods, we have simulated Shor's factorization algorithm and Grover's database search, and we have analyzed robustness of the corresponding quantum circuits in the presence of both decoherence and operational errors. The corresponding results, statistics, and analyses are presented in this paper.
Quantum computing will be one of the most incredible breakthroughs in science and technology of our generation. Although the ultimate goal of building quantum computers that hold thousands of error-corrected qubits is still beyond our reach, we have made substantial progress. Compared with the first-generation prototypes, holding a few qubits with gate errors of several percent, the latest generation systems can apply more than a hundred gates (with fidelities above 99%) to tens of fully connected qubits. This thesis focuses on the applications of such state-of-the-art ion-trap quantum computers. The latest generation ion-trap quantum computers have become complex enough that automation is necessary for optimal operations. We present a full-stack automation scheme implemented on a system at the University of Maryland. With the automation scheme, the system can operate without human interference for a few days. With automation, such systems can efficiently demonstrate different categories of applications. We present the experimental study of several hybrid algorithms aiming for generation modeling and efficient quantum state preparation. We also present a gate-based digital quantum simulation with the trotterization method. Our result accurately reproduced all the features expected from running the algorithms. Verifying quantum computations with classical simulation is getting increasingly challenging as quantum computers evolve. We present two approaches to validate quantum computations. First, we demonstrate a method based on random measurement for comparing the results from different quantum computers. Our comparison captures the similarities between quantum computers made with the same technology. We then present experimental works in verifying quantum advantage classically with interactive protocols. We show that our results, at scale with real-time interaction, can demonstrate quantum advantages.
Quantum computing (QC) presents transformative potential for solving complex scientific problems that remain intractable for classical computers. Leveraging quantum superposition, entanglement, and interference, quantum algorithms such as Shor’s factoring algorithm, Grover’s search algorithm, variational quantum eigensolvers (VQE), and quantum approximate optimization algorithms (QAOA) enable exponential or polynomial speedups for selected problem classes. This paper explores recent advancements in quantum computing algorithms, their practical implementations, and emerging applications in fields such as molecular simulations, material science, cryptography, optimization, and machine learning. We highlight the strengths and limitations of current approaches, present performance analyses through graphical comparisons, and discuss prospective directions for integrating quantum algorithms into real-world scientific workflows. Our findings demonstrate that quantum computing is gradually transitioning from theoretical frameworks to experimental platforms capable of addressing highly complex computational challenges.
Quantum computing (QC) presents transformative potential for solving complex scientific problems that remain intractable for classical computers. Leveraging quantum superposition, entanglement, and interference, quantum algorithms such as Shor’s factoring algorithm, Grover’s search algorithm, variational quantum eigensolvers (VQE), and quantum approximate optimization algorithms (QAOA) enable exponential or polynomial speedups for selected problem classes. This paper explores recent advancements in quantum computing algorithms, their practical implementations, and emerging applications in fields such as molecular simulations, material science, cryptography, optimization, and machine learning. We highlight the strengths and limitations of current approaches, present performance analyses through graphical comparisons, and discuss prospective directions for integrating quantum algorithms into real-world scientific workflows. Our findings demonstrate that quantum computing is gradually transitioning from theoretical frameworks to experimental platforms capable of addressing highly complex computational challenges.
Quantum computing is rapidly evolving especially after the discovery of several efficient quantum algorithms solving intractable classical problems such as Shor's factoring algorithm. However the realization of a large-scale physical quantum computer is very challenging and the number of qubits that are currently under development is still very low, namely less than 15. In the absence of large size platforms, quantum computer simulation is critical for developing and testing quantum algorithms and investigating the different challenges facing the design of quantum computer hardware. What makes quantum computer simulation on classical computers particularly challenging are the memory and computational resource requirements. In this paper, we introduce a universal quantum computer simulator, called QX, that takes as input a specially designed quantum assembly language, called QASM, and provides, through agressive optimisations, high simulation speeds and large number of qubits. QX allows the simulation of up to 34 fully entangled qubits on a single node using less than 270 GB of memory. Our experiments using different quantum algorithms show that QX achieves significant simulation speedup over similar state-of-the-art simulation environment.
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.