We formulate the control over quantum matter, so as to perform arbitrary quantum computation, as an optimization problem. We then provide a schematic machine learning algorithm for its solution. Imagine a long strip of 'quantum stuff', endowed with certain assumed physical properties, and equipped with regularly spaced wires to provide input settings and to read off outcomes. After showing how the corresponding map from settings to outcomes can be construed as a quantum circuit, we provide a machine learning framework to tomographically 'learn' which settings implement the members of a universal gate set. To that end, we devise a loss function measuring how badly a proposed encoding has failed to implement a given circuit, and prove the existence of 'tomographically complete' circuit sets: should a given encoding minimize the loss function for each member of such a set, it also will for an arbitrary circuit. At optimum, arbitrary quantum gates, and thus arbitrary quantum programs, can be implemented using the stuff.
We formulate the control over quantum matter, so as to perform arbitrary quantum computation, as an optimization problem. We then provide a schematic machine learning algorithm for its solution. Imagine a long strip of 'quantum stuff', endowed with certain assumed physical properties, and equipped with regularly spaced wires to provide input settings and to read off outcomes. After showing how the corresponding map from settings to outcomes can be construed as a quantum circuit, we provide a machine learning framework to tomographically 'learn' which settings implement the members of a universal gate set. To that end, we devise a loss function measuring how badly a proposed encoding has failed to implement a given circuit, and prove the existence of 'tomographically complete' circuit sets: should a given encoding minimize the loss function for each member of such a set, it also will for an arbitrary circuit. At optimum, arbitrary quantum gates, and thus arbitrary quantum programs, can be implemented using the stuff.
A possible approach to tackling computationally demanding issues beyond the capabilities of conventional algorithms is the use of quantum circuits, which provide a fundamental foundation for utilizing the power of quantum computation. This abstract examines how quantum circuits are implemented, emphasizing important topics such as circuit optimization, gate operations, and qubit manipulation. We explore different methods of encoding quantum information into topological qubits, trapped ions, and superconducting circuits, among other physical qubit formats. Furthermore, we go over the function of gate operations in quantum circuits, emphasizing crucial gates like phase, Hadamard, and CNOT gates, which serve as the foundation for quantum algorithms. Additionally, we look at methods for maximizing the efficiency and dependability of quantum processing by designing quantum circuits to minimize gate counts, depth, and error rates. To enhance the capabilities of quantum computing, this abstract presents a novel synthesis of quantum neural networks (QNNs) and quantum parameterized circuits. Through the use of parameterized quantum circuits' inherent flexibility, our approach makes it easier to design and optimize quantum circuits with flexible parameters, providing a flexible foundation for a variety of quantum algorithms. Using this amalgamation, we unleash the capacity of quantum computers to address intricate optimization and machine learning assignments with unparalleled effectiveness and expandability. Our solution bridges the gap between traditional machine learning approaches and quantum computing paradigms by enabling the smooth integration of classical data processing techniques with quantum computation. We use quantum states as data representations in our implementation of quantum neural networks, and we optimize trainable parameters to meet predetermined goals. This new paradigm opens up the investigation of the inherent features of quantum states and provides new perspectives on their processing power compared to their classical counterparts. We show, by thorough testing and analysis, how effective quantum parameterized circuits and QNNs are at solving practical problems in a variety of fields. Our work sets the ground for revolutionary breakthroughs in quantum information processing by pushing the boundaries of quantum computation and machine learning integration, offering hitherto unseen insights and solutions to challenging challenges in science, engineering, and beyond.
Fault-tolerant quantum computing requires encoding the quantum information into logical qubits and performing the quantum information processing in a code-space. Quantum error correction codes, then, can be employed to diagnose and remove the possible errors in the quantum information, thereby avoiding the loss of information. Although a series of single- and two-qubit gates can be employed to construct a quantum error correcting circuit, however this decomposition approach is not practically desirable because it leads to circuits with long operation times. An alternative approach to designing a fast quantum circuit is to design quantum gates that act on a multi-qubit gate. Here I devise quantum control schemes to design high-fidelity single-shot multi-qubit (up to three) quantum gates. Quantum control task is to steer quantum dynamics towards closely realizing specific quantum operation by varying the external control parameters (external field) such that the resultant evolution closely approximates the desired evolution. A set of instructions that determines the control parameters, and hence the effectiveness of the control scheme, is called a policy. Machine learning algorithms can be employed to find successful policies for designing quantum gates. In particular, we employ supervised machine learning techniques to generate these successful policies. Finding successful policies is a feasibility problem for which optimization algorithms can be employed. Greedy algorithms are at the heart of machine learning techniques. They converge faster onto a successful policy and require less-computational resource than non-greedy algorithms. However, there is no guarantee that greedy algorithms succeed to a feasible solution when there exist constraints on i) gate operation time ii) computational resources, and iii) experimental resources. Our results show the failure of standard greedy machine learning algorithms and the superiority of non-greedy machine learning algorithms over greedy ones for designing quantum logic gates, when there exist constraints on the quantum system. We have also observed the failure of existing greedy and non-greedy techniques for designing high-fidelity three-qubit gates. Hence, we devised our machine learning technique called Subspace-Selective Self-adaptive Differential Evolution (SuSSADE). Each three-qubit gate designed by SuSSADE operates as fast as an entangling two-qubit gate under the same experimental constraints.
Deterministic quantum computation with one qubit (DQC1) is of significant theoretical and practical interest due to its computational advantages in certain problems, despite its subuniversality with limited quantum resources. In this work, we introduce parametrized DQC1 as a quantum machine learning model. We demonstrate that the gradient of the measurement outcome of a DQC1 circuit with respect to its gate parameters can be computed directly using the DQC1 protocol. This allows for gradient-based optimization of DQC1 circuits, positioning DQC1 as a quantum protocol for both training and inference. We then analyze the expressivity of the parametrized DQC1 circuits characterizing the set of learnable functions, and show that DQC1-based machine learning (ML) is as powerful as quantum neural networks based on universal computation. Our findings highlight the potential of DQC1 as a practical and versatile platform for ML, capable of rivaling more complex quantum computing models while utilizing simpler quantum resources.
This paper explores the development of dynamically reconfigurable quantum circuits tailored for machine learning applications. The core claim is the design of a hardware architecture capable of on-the-fly circuit reconfiguration, optimizing performance and resource utilization. This is achieved through the employment of programmable quantum gates and dynamic routing of quantum information dictated by the input data and algorithm requirements. The research addresses the limitations of static quantum circuit design by enabling adaptive and efficient quantum computation. Specifically, we investigate methods for mapping machine learning algorithms onto reconfigurable quantum circuits, considering factors such as circuit depth, qubit connectivity, and gate fidelity. We propose a framework for defining a quantum circuit's reconfiguration policy, incorporating real-time feedback from the execution of the algorithm. This framework allows the circuit to adapt its structure and operations to maximize computational efficiency. The theoretical analysis and design principles presented here contribute to the advancement of quantum machine learning by offering a pathway toward more flexible and powerful quantum computing architectures. The ultimate goal is to create quantum systems that can learn and adapt in a way analogous to biological neural networks, unlocking the full potential of quantum computation for complex machine learning problems.
Quantum computing is a new and advanced topic that refers to calculations based on the principles of quantum mechanics. It makes certain kinds of problems be solved easier compared to classical computers. This advantage of quantum computing can be used to implement many existing problems in different fields incredibly effectively. One important field that quantum computing has shown great results in machine learning. Until now, many different quantum algorithms have been presented to perform different machine learning approaches. In some special cases, the execution time of these quantum algorithms will be reduced exponentially compared to the classical ones. But at the same time, with increasing data volume and computation time, taking care of systems to prevent unwanted interactions with the environment can be a daunting task and since these algorithms work on machine learning problems, which usually includes big data, their implementation is very costly in terms of quantum resources. Here, in this paper, we have proposed an approach to reduce the cost of quantum circuits and to optimize quantum machine learning circuits in particular. To reduce the number of resources used, in this paper an approach including different optimization algorithms is considered. Our approach is used to optimize quantum machine learning algorithms for big data. In this case, the optimized circuits run quantum machine learning algorithms in less time than the original ones and by preserving the original functionality. Our approach improves the number of quantum gates by 10.7% and 14.9% in different circuits respectively. This is the amount of reduction for one iteration of a given sub-circuit U in the main circuit. For cases where this sub-circuit is repeated more times in the main circuit, the optimization rate is increased. Therefore, by applying the proposed method to circuits with big data, both cost and performance are improved.
To achieve quantum machine learning on imperfect noisy intermediate-scale quantum (NISQ) processors, the entire physical implementation should include as few as possible hand-designed modules with only a few ad hoc parameters to be determined. This work presents such a hardware-friendly end-to-end quantum-machine-learning scheme that can be implemented with imperfect NISQ processors. The proposal transforms the machine-learning task to the optimization of controlled quantum dynamics, in which the learning model is parameterized by experimentally tunable control variables. Our design also enables automated feature selection by encoding the raw input to quantum states through agent control variables. Comparing with the gate-based parameterized quantum circuits, the proposed end-to-end quantum-learning model is easy to implement as there are only a few ad hoc parameters to be determined. Numerical simulations on the benchmarking MNIST (Mixed National Institute of Standards and Technology) dataset of handwritten digits demonstrate that the model can achieve high performance using only 3--5 qubits without downsizing the dataset, which shows great potential for accomplishing large-scale real-world learning tasks on NISQ processors.