Current technology for building digital computers is predicted to reach its limit within the next 10 years due to the increasing miniaturization of digital components. By reaching sizes of a few nanometers, electrons stop behaving as particles and start behaving as waves, obeying essentially the principles of Quantum Mechanics, and effects such as interference, superposition and entanglement become dominant. The utilization of those effects allows more that just an evolution of the miniaturization process. It allows for a computational parallelism impossible to be obtained efficiently through classical computational methods or devices. Several algorithms utilizing such effects have been proposed and indicated that Quantum Computation is significantly more efficient at solving certain class of problems than classical computation. Actually, there is not yet any hardware (a quantum computer) able to compute a useful algorithm outside of research labs. A turn-around to that problem is to simulate the behavior of a quantum computer by a classical computer. There are, to this day, a number of quantum computer simulators available which, in general, use the quantum circuit model defined by Deutsch. Just a few of them are universal. We have developed a novel universal quantum circuit simulator, called Zeno, to the design and test of quantum algorithms. Zeno offers a set of features that engulfs most of the features presented by the other existing universal quantum circuit simulators and that also allows it to be used in the design and simulation of quantum channels.
Current technology for building digital computers is predicted to reach its limit within the next 10 years due to the increasing miniaturization of digital components. By reaching sizes of a few nanometers, electrons stop behaving as particles and start behaving as waves, obeying essentially the principles of Quantum Mechanics, and effects such as interference, superposition and entanglement become dominant. The utilization of those effects allows more that just an evolution of the miniaturization process. It allows for a computational parallelism impossible to be obtained efficiently through classical computational methods or devices. Several algorithms utilizing such effects have been proposed and indicated that Quantum Computation is significantly more efficient at solving certain class of problems than classical computation. Actually, there is not yet any hardware (a quantum computer) able to compute a useful algorithm outside of research labs. A turn-around to that problem is to simulate the behavior of a quantum computer by a classical computer. There are, to this day, a number of quantum computer simulators available which, in general, use the quantum circuit model defined by Deutsch. Just a few of them are universal. We have developed a novel universal quantum circuit simulator, called Zeno, to the design and test of quantum algorithms. Zeno offers a set of features that engulfs most of the features presented by the other existing universal quantum circuit simulators and that also allows it to be used in the design and simulation of quantum channels.
Simulation fulfills an important mechanism for the study and the development of many areas. Quantum computation simulation tools have become essential, because no effective quantum hardware has been implemented yet. However, the currently available simulators have serious deficiencies, which makes the description of this new computational paradigm incomplete. This article presents a universal quantum circuit simulator, called Zeno, and the symbolic extension that is being developed to it. The extension will allow a symbolic description of the system's state allied to the graphical representation of the circuit to be visualized together. Users will be able to work in a faster and more efficient way than making this calculations by hand. The extension will make possible a faithful description of the system computation like the descriptions observed in related literature.
Quantum-mechanical phenomena are playing an increasing role in information processing as transistor sizes approach the nanometer level, while the securest forms of communication rely on quantum data encoding. When they involve a finite number of basis states, these phenomena can be modeled as quantum circuits, the quantum analogue of conventional or classical logic circuits. Simulation of quantum circuits can therefore be used as a tool to evaluate issues in the design of quantum information processors. Unfortunately, simulating such phenomena efficiently is exceedingly difficult. The matrices representing quantum operators (gates) and vectors modeling quantum states grow exponentially with the number of quantum bits. The information represented by quantum states and operators often exhibits structure that can be exploited when simulating certain classes of quantum circuits. We study the development of simulation methods that run on classical computers and take advantage of such repetitions and redundancies. In particular, we define a new data structure for simulating quantum circuits called the quantum information decision diagram (QuIDD). A QuIDD is a compressed graph representation of a vector or matrix and permits computations to be performed directly on the compressed data. We develop a comprehensive set of algorithms for operating on QuIDDs in both the state-vector and density-matrix formats, and evaluate their complexity. These algorithms have been implemented in a general-purpose simulator program for quantum-mechanical applications called QuIDDPro. Through extensive experiments conducted on representative quantum simulation applications, including Grover's search algorithm, error characterization, and reversible circuits, we demonstrate that QuIDDPro is faster than other existing quantum-mechanical simulators such as the National Institute of Standards and Technology's QCSim program, and is far more memory-efficient. Using QuIDDPro, we explore the advantages of quantum computation over classical computation, simulate quantum errors and error correction, and study the impact of numerical precision on the fidelity of simulations. We also develop several novel algorithms for testing quantum circuit equivalence and compare them empirically. The QuIDDPro software is equipped with a user-friendly interface and is distributed with numerous example scripts. It has been used as a laboratory supplement for quantum computing courses at several universities.
Quantum computing is an emerging technology that has the potential to change the perspectives and applications of computing in general. A wide range of applications are enabled: from faster algorithmic solutions of classically still difficult problems to theoretically more secure communication protocols. A quantum computer uses the quantum mechanical effects of particles or particle-like systems, and a major similarity between quantum and classical computers consists of both being abstracted as information processing machines. Whereas a classical computer operates on classical digital information, the quantum computer processes quantum information, which shares similarities with analog signals. One of the central differences between the two types of information is that classical information is more fault-tolerant when compared to its quantum counterpart. Faults are the result of the quantum systems being interfered by external noise, but during the last decades quantum error correction codes (QECC) were proposed as methods to reduce the effect of noise. Reliable quantum circuits are the result of designing circuits that operate directly on encoded quantum information, but the circuit’s reliability is also increased by supplemental redundancies, such as sub-circuit repetitions. Reliable quantum circuits have not been widely used, and one of the major obstacles is their vast associated resource overhead, but recent quantum computing architectures show promising scalabilities. Consequently the number of particles used for computing can be more easily increased, and that the classical control hardware (inherent for quantum computation) is also more reliable. Reliable quantum circuits haev been investigated for almost as long as general quantum computing, but their limited adoption (until recently) has not generated enough interest into their systematic design. The continuously increasing practical relevance of reliability motivates the present thesis to investigate some of the first answers to questions related to the background and the methods forming a reliable quantum circuit design stack. The specifics of quantum circuits are analysed from two perspectives: their probabilistic behaviour and their topological properties when a particular class of QECCs are used. The quantum phenomena, such as entanglement and superposition, are the computational resources used for designing quantum circuits. The discrete nature of classical information is missing for quantum information. An arbitrary quantum system can be in an infinite number of states, which are linear combinations of an exponential number of basis states. Any nontrivial linear combination of more than one basis states is called a state superposition. The effect of superpositions becomes evident when the state of the system is inferred (measured), as measurements are probabilistic with respect to their output: a nontrivial state superposition will collapse to one of the component basis states, and the measurement result is known exactly only after the measurement. A quantum system is, in general, composed from identical subsystems, meaning that a quantum computer (the complete system) operates on multiple similar particles (subsystems). Entanglement expresses the impossibility of separating the state of the subsystems from the state of the complete system: the nontrivial interactions between the subsystems result into a single indivisible state. Entanglement is an additional source of probabilistic behaviour: by measuring the state of a subsystem, the states of the unmeasured subsystems will probabilistically collapse to states from a well defined set of possible states. Superposition and entanglement are the building blocks of quantum information teleportation protocols, which in turn are used in state-of-the-art fault-tolerant quantum computing architectures. Information teleportation implies that the state of a subsystem is moved to a second subsystem without copying any information during the process. The probabilistic approach towards the design of quantum circuits is initiated by the extension of classical test and diagnosis methods. Quantum circuits are modelled similarly to classical circuits by defining gate-lists, and missing quantum gates are modelled by the single missing gate fault. The probabilistic approaches towards quantum circuits are facilitated by comparing these to stochastic circuits, which are a particular type of classical digital circuits. Stochastic circuits can be considered an emulation of analogue computing using digital components. A first proposed design method, based on the direct comparison, is the simulation of quantum circuits using stochastic circuits by mapping each quantum gate to a stochastic computing sub-circuit. The resulting stochastic circuit is compiled and simulated on FPGAs. The obtained results are encouraging and illustrate the capabilities of the proposed simulation technique. However, the exponential number of possible quantum basis states was translated into an exponential number of stochastic computing elements. A second contribution of the thesis is the proposal of test and diagnosis methods for both stochastic and quantum circuits. Existing verification (tomographic) methods of quantum circuits were targeting the reconstruction of the gate-lists. The repeated execution of the quantum circuit was followed by different but specific measurement at the circuit outputs. The similarities between stochastic and quantum circuits motivated the proposal of test and diagnosis methods that use a restricted set of measurement types, which minimise the number of circuit executions. The obtained simulation results show that the proposed validation methods improve the feasibility of quantum circuit tomography for small and medium size circuits. A third contribution of the thesis is the algorithmic formalisation of a problem encountered in teleportation-based quantum computing architectures. The teleportation results are probabilistic and require corrections represented as quantum gates from a particular set. However, there are known commutation properties of these gates with the gates used in the circuit. The corrections are not applied as dynamic gate insertions (during the circuit’s execution) into the gate-lists, but their effect is tracked through the circuit, and the corrections are applied only at circuit outputs. The simulation results show that the algorithmic solution is applicable for very large quantum circuits. Topological quantum computing (TQC) is based on a class of fault-tolerant quantum circuits that use the surface code as the underlying QECC. Quantum information is encoded in lattice-like structures and error protection is enabled by the topological properties of the lattice. The 3D structure of the lattice allows TQC computations to be visualised similarly to knot diagrams. Logical information is abstracted as strands and strand interactions (braids) represent logical quantum gates. Therefore, TQC circuits are abstracted using a geometrical description, which allows circuit input-output transformations (correlations) to be represented as geometric sub-structures. TQC design methods were not investigated prior to this work, and the thesis introduces the topological computational model by first analysing the necessary concepts. The proposed TQC design stack follows a top-down approach: an arbitrary quantum circuit is decomposed into the TQC supported gate set; the resulting circuit is mapped to a lattice of appropriate dimensions; relevant resulting topological properties are extracted and expressed using graphs and Boolean formulas. Both circuit representations are novel and applicable to TQC circuit synthesis and validation. Moreover, the Boolean formalism is broadened into a formal mechanism for proving circuit correctness. The thesis introduces TQC circuit synthesis, which is based on a novel logical gate geometric description, whose formal correctness is demonstrated. Two synthesis methods are designed, and both use a general planar representation of the circuit. Initial simulation results demonstrate the practicality and performance of the methods. An additional group of proposed design methods solves the problem of automatic correlation construction. The methods use validity criteria which were introduced and analysed beforehand in the thesis. Input-output correlations existing in the circuit are inferred using both the graph and the Boolean representation. The thesis extends the TQC state-of-the-art by recognising the importance of correlations in the validation process: correlation construction is used as a sub-routine for TQC circuit validation. The presented cross-layer validation procedure is useful when investigating both the QECC and the circuit, while a second proposed method is QECC-independent. Both methods are scalable and applicable even to very large circuits. The thesis completes with the analysis of TQC circuit identities, where the developed Boolean formalism is used. The proofs of former known circuit identities were either missing or complex, and the presented approach reduces the length of the proofs and represents a first step towards standardising them. A new identity is developed and detailed during the process of illustrating the known circuit identities. Reliable quantum circuits are a necessity for quantum computing to become reality, and specialised design methods are required to support the quest for scalable quantum computers. This thesis used a twofold approach towards this target: firstly by focusing on the probabilistic behaviour of quantum circuits, and secondly by considering the requirements of a promising quantum computing architecture, namely TQC. Both approaches resulted in a set of design methods enabling the investigation of reliable quantum circuits. The thesis contributes with the proposal of a new quantum simulation technique, no
Abstract Currently, there is an ongoing “race” to build the first practically useful quantum computer that provides substantial speed-ups for certain problems compared to conventional computers. In addition to the development of such devices, this also requires the development of automated tools and methods that provide assistance in the simulation and design of corresponding applications. Otherwise, a situation might be reached where we have powerful quantum computers but hardly any proper means to actually use them. This work provides an overview of corresponding solutions for the task of quantum circuit simulation, the task of quantum circuit design, as well as corresponding mapping tasks. The covered solutions utilise expertise on efficient data structures and algorithms gained in the design of conventional circuits and systems over the last decades. While the respective descriptions are kept brief and mainly convey the general ideas, references to further readings are provided for a more detailed treatment.
Molecules are serious candidates for building hardware for quantum computers. They can encode quantum information onto electron or nuclear spins and some of them show important features as the scalability of the number of qubits and a universal set of quantum gates. In this paper we present our advances in the development of a classical simulation infrastructure for molecular Quantum Computing: starting from the definition of simplified models taking into account the main physical features of each analyzed molecule, quantum gates are defined over these models, thus permitting to take into account the real behavior of each technology during the simulation. An interface with a hardware-agnostic description language has been also developed. The knowledge of the behavior of real systems permits to optimize the design of quantum circuits at both physical and compilation levels. Elementary quantum algorithms have been simulated on three different molecular technologies by changing the physical parameters of polarization and manipulation and quantum circuit design strategies. Results confirm the dependency of the fidelity of the results on both levels, thus proving that the choice of optimal operating points and circuit optimization techniques as virtual-Z gates are fundamental for ensuring the execution of quantum circuits with negligible errors.
Computer graphics relies on computing hardware for everything from animation to rendering. An emerging new technology exploits the properties of quantum objects to offer radically new ways to think about, create, and run algorithms. For example, quantum computers can evaluate many different input values simultaneously, where "many" can be larger than the number of atoms in the visible universe. The catch is that only one output can be obtained from each run. Quantum computing may change how we think about computer graphics. For example, future quantum computers may be able to intersect astronomical numbers of rays with a similarly massive database of objects in a single execution, or evaluate enormous numbers of simulation parameters in parallel to return the one set that produces a desired result. This course describes, without advanced math, the core ideas of quantum computing. We start with the quantum version of the classical bit (called a qubit) and the basic operators that modify qubits. We introduce the four essential properties that distinguish quantum computers from familiar classical computers: superposition, interference, entanglement, and measurement. We show how these properties are orchestrated to build quantum algorithms. We conclude with a brief overview of some of the most well-known quantum algorithms, and some of their possible applications in computer graphics. Quantum computers are already here, and are increasing in size and reliability at a rapid pace. Open-source simulators abound, and small quantum computers are even available for free use on the web. Classical hardware has served computer graphics well. Quantum computing offers a fundamentally new way to design and execute algorithms, which could change our field in fundamental ways. Now is the perfect time to starting thinking about quantum computing for graphics.