Abstract Currently, there are many physical systems for quantum computing and to adapt to the physical characteristics of different systems, engineers have designed different basic gate groups for gate circuit calculation models. The quantum algorithm realizes the evolution of the quantum state by applying unitary operators to the quantum states, and the results are obtained by measuring the outputs. These operators will be done in the corresponding physical system by compiling and decomposing into hardware supported basic gates. Universal fundamental gates can construct all quantum algorithms, but their computational efficiency is limited. Drawing on the idea of meta operators in classical machine learning, by constructing a deep learning framework for deep learning models, the common computational logic of operators in different deep learning frameworks is abstracted as ‘meta operators’ [1, 2]. This article aims to study and propose the common computational logic of quantum computing with geometric equivalence class distribution methods, using the volume size of the equivalence class space as a performance indicator for meta operators and identifying the optimal meta operators to optimize the depth of the circuits in the experiments. Which proves the effectiveness of the design method proposed and provides solutions for quantum circuit optimization and dedicated gate design.
Abstract Currently, there are many physical systems for quantum computing and to adapt to the physical characteristics of different systems, engineers have designed different basic gate groups for gate circuit calculation models. The quantum algorithm realizes the evolution of the quantum state by applying unitary operators to the quantum states, and the results are obtained by measuring the outputs. These operators will be done in the corresponding physical system by compiling and decomposing into hardware supported basic gates. Universal fundamental gates can construct all quantum algorithms, but their computational efficiency is limited. Drawing on the idea of meta operators in classical machine learning, by constructing a deep learning framework for deep learning models, the common computational logic of operators in different deep learning frameworks is abstracted as ‘meta operators’ [1, 2]. This article aims to study and propose the common computational logic of quantum computing with geometric equivalence class distribution methods, using the volume size of the equivalence class space as a performance indicator for meta operators and identifying the optimal meta operators to optimize the depth of the circuits in the experiments. Which proves the effectiveness of the design method proposed and provides solutions for quantum circuit optimization and dedicated gate design.
Quantum computing combined with machine learning, is a promising emerging field for tackling problems that are extremely expensive or fundamentally infeasible for classical computers. Nonetheless, design of the optimal quantum circuit for machine learning is a major challenge, which can be attributed to the exponential search space of the quantum gate arrangement and unmatched structured design methods. To resolve this, our work introduces a novel automated framework for quantum architecture search (AQAS) that adopts both meta-learning and evolutionary algorithms to automatically learn, transfer, and optimize quantum circuit architectures to suit different machine learning tasks. Our strategy relies on meta-learning to introduce a learning scheme, i.e. it allows the AQAS system to generalize across distributions by learning from a shared structural and functional prior from the distribution of machine learning problems. This enables the approach to quickly home in effective quantum circuit implementations for new tasks with low data or retraining. At the same time, we use evolutionary algorithms– mimicking natural selection– to breed populations of quantum circuit architectures. These circuits are represented in genotypes, are varied under mutation and crossover, and are selected according to a fitness function that blends quantum resource utilization (e.g., depth, qubits) with task-specific performance (e.g., classification accuracy or loss). The architecture is realized in a mixed quantum-classical environment, with quantum circuits simulated on quantum simulators and/or Noisy-Intermediate-Scale-Quantum (NISQ) devices. We verify the effectiveness of our approach on a number of benchmarked datasets and tasks which range from quantum-aided image recognition, time series prediction to medical diagnostics. We demonstrate that AQAS can discover compact, high-performing quantum models, which generalize better and are computationally more efficient than the custom-built quantum models.
Quantum computing promises revolutionary advancements in optimization, particularly in complex search spaces and machine learning. However, designing optimal quantum circuits for these tasks presents significant challenges, largely due to the inherent variability of problem landscapes. This research proposes a novel adaptive quantum circuit design methodology leveraging meta-learning to dynamically adjust circuit parameters based on the characteristics of the optimization problem. We introduce a meta-learning framework that learns optimal circuit configurations from a representative set of problem instances, enabling the circuit to adapt to the unique properties of each new problem. The core mechanism centers around a feedback loop that continuously assesses the circuit's performance and adjusts parameters to improve solution quality. This approach aims to overcome the limitations of traditional fixed-parameter circuit design, offering a path towards more robust and efficient optimization solutions. This work explores the potential for significant improvements in solution quality across a range of benchmark problems, demonstrating the efficacy of the proposed adaptive design strategy.
Optimization of circuits is an essential task for both quantum and classical computers to improve their efficiency. In contrast, classical logic optimization is known to be difficult, and a lot of heuristic approaches have been developed so far. In this paper, we define and construct a quantum algorithmic primitive called quantum circuit unoptimization, which makes a given quantum circuit complex by introducing some redundancies while preserving circuit equivalence, i.e., the inverse operation of circuit optimization. Using quantum circuit unoptimization, we propose the quantum circuit equivalence test, a decision problem contained both in NP and BQP classes, but is not trivially included in the P class. Furthermore, as a practical application, we construct concrete unoptimization recipes to generate compiler benchmarks and evaluate circuit optimization performance using and . Our numerical simulations demonstrate that the quantum circuit unoptimizer systematically generates redundant circuits that are challenging for compilers to optimize, which can be used to compare the performance of different compilers and improve them. We also offer potential applications of quantum circuit unoptimization, such as generating quantum advantageous machine learning data sets and quantum computer fidelity benchmarks.
Quantum algorithms can be expressed as quantum circuits when the circuit model of computation is adopted. Such a circuit description is usually hardware-agnostic, that is, it does not consider the limitations that the quantum hardware might have. In order to make quantum algorithms executable on quantum devices they need to comply to their constraints, which mainly affect the parallelism of quantum operations and the possible interactions between the qubits. The process of adapting a quantum circuit to meet the quantum chip restrictions is known as mapping. The resulting circuit usually has a higher number of gates and depth, decreasing the algorithm's reliability. Different mapping solutions have been already proposed. Most of them are meant for a specific quantum processor and differ in methodology, approach and features. In addition, they are usually only compared in terms of added gates, circuit depth and compilation time. No thorough comparative analysis of the different mapping solutions performance and features has been performed so far.In this paper, we propose to apply structured design space exploration (DSE) methodologies to the mapping procedures. This will allow not only to have a more in depth and structured analysis of their performance but also to identify what features are key and worth to implement. By using DSE we will be able to: i) determine in what regimes some mapping solutions outperform others; ii) derive optimal mapping strategies for specific quantum algorithms and quantum processors; and iii) perform an scalability analysis. In addition, DSE techniques cannot only be applied to the mapping layer that is key for bridging quantum applications to quantum devices, but also to the full-stack quantum computing system allowing for its crosslayer co-design.
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
Quantum programs are difficult for humans to develop due to their complex semantics that are rooted in quantum physics. It is therefore preferable to write specifications and then use techniques such as genetic programming (GP) to generate quantum programs instead. We present a new genetic programming system for quantum circuits which can evolve solutions to the full-adder and quantum Fourier transform problems in fewer generations than previous work, despite using a general set of gates. This means that it is no longer required to have any previous knowledge of the solution and choose a specialised gate set based on it.