Applications of quantum string matching can be found in quantum signature scheme and quantum fingerprinting. The major benefit of these applications is computation complexity. Quantum Boolean circuits can check the equivalence function: all in puts are quantum digital state. However, it is difficult to verify quantum strings if all input qubits are quantum superposition state. Quantum switching could be reversible circuits. These circuits have two major benefits: information lossless and energy saving. In this paper, we use quantum circuits to design the control module that can verify the equivalence of quantum strings and satisfy the following condition: all inputs qubits could be quantum superposition state. In the pro posed circuits, the control module can form a special correlation between input sequence and output sequence. This correlation can design the equivalence function of quantum strings to solve the problem: input strings with superposition. In regard to the performance, the scalability of the proposed circuits can be achieved.
Applications of quantum string matching can be found in quantum signature scheme and quantum fingerprinting. The major benefit of these applications is computation complexity. Quantum Boolean circuits can check the equivalence function: all in puts are quantum digital state. However, it is difficult to verify quantum strings if all input qubits are quantum superposition state. Quantum switching could be reversible circuits. These circuits have two major benefits: information lossless and energy saving. In this paper, we use quantum circuits to design the control module that can verify the equivalence of quantum strings and satisfy the following condition: all inputs qubits could be quantum superposition state. In the pro posed circuits, the control module can form a special correlation between input sequence and output sequence. This correlation can design the equivalence function of quantum strings to solve the problem: input strings with superposition. In regard to the performance, the scalability of the proposed circuits can be achieved.
Quantum circuit is a reversible circuit that can be designed the control module to derive the correlation between quantum input sequence and quantum output sequence. In addition, in this paper we use the control module of the quantum circuit to verify the equivalence of the quantum state such that quantum blind signature can achieve the security requirement of the signature scheme and resist eavesdropping from the outsider. The core concept of the proposed signature is based on the correlation of quantum entangled state to investigate that the message string and the signatory string is consistent. In regard to the security, the blindness and the failure of eavesdropping can be preserved by this work. The proposed signature can achieve impossibility of forgery and impossibility of disavowal.
Quantum computation represents a computational paradigm whose distinctive attributes confer the ability to devise algorithms with asymptotic performance levels significantly superior to those achievable via classical computation. Recent strides have been taken to apply this computational framework in tackling and resolving various issues related to text processing. The resultant solutions demonstrate marked advantages over their classical counterparts. This study employs quantum computation to efficaciously surmount text processing challenges, particularly those involving string comparison. The focus is on the alignment of fixed-length substrings within two input strings. Specifically, given two input strings, x and y, both of length n, and a value d≤n, we want to verify the following conditions: the existence of a common prefix of length d, the presence of a common substring of length d beginning at position j (with 0≤j<n) and, the presence of any common substring of length d beginning in both strings at the same position. Such problems find applications as sub-procedures in a variety of problems concerning text processing and sequence analysis. Notably, our approach furnishes polylogarithmic solutions, a stark contrast to the linear complexity inherent in the best classical alternatives.
This paper proposes a novel work to design reversible quantum circuits. The function of this circuit is to investigate quantum transmission integrity in the quantum communication networks. This work is to verify quantum transmission sequence of a quantum frame by using reversible quantum model. This model designs control module to derive the correlation between two quantum strings: quantum input sequence and quantum output sequence. If a quantum frame reserves the correlation, then we can obtain quantum transmission sequence. So, quantum transmission integrity of a quantum frame can be verified.
Boolean matching is an important problem in logic synthesis and verification. Despite being well-studied for conventional Boolean circuits, its treatment for reversible logic circuits remains largely, if not completely, missing. This work provides the first such study. Given two (black-box) reversible logic circuits that are promised to be matchable, we check their equivalences under various input/output negation and permutation conditions subject to the availability/unavailability of their inverse circuits. Notably, among other results, we show that the equivalence up to input negation and permutation is solvable in quantum polynomial time, while its classical complexity is exponential. This result is arguably the first demonstration of quantum exponential speedup in solving design automation problems. Also, as a negative result, we show that the equivalence up to both input and output negations is not solvable in quantum polynomial time unless UNIQUE-SAT is, which is unlikely. This work paves the theoretical foundation of Boolean matching reversible circuits for potential applications, e.g., in quantum circuit synthesis.
Among the post-CMOS technologies currently under investigation, quantum computing (QC) holds a special place. QC offers not only extremely small size and low power, but also exponential speed-ups for important simulation and optimization problems. It also poses new CAD problems that are similar to. but more challenging, than the related problems in classical (non-quantum) CAD. such as determining if two states or circuits are functionally equivalent. While differences in classical states are easy to detect, quantum states, which are represented by complex-valued vectors, exhibit subtle differences leading to several notions of equivalence. This provides flexibility in optimizing quantum circuits, but leads to difficult new equivalence-checking issues for simulation and synthesis. We identify several different equivalence-checking problems and present algorithms for practical benchmarks, including quantum communication and search circuits, which are shown to be very fast and robust for hundreds of qubits.
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