Despite the rapid development of quantum computing these years, state-of-the-art quantum devices still contain only a limited number of qubits. One possible way to execute more realistic algorithms in near-term quantum devices is to employ dynamic quantum circuits (DQCs). In DQCs, measurements can happen during the circuit, and their outcomes can be processed with classical computers and used to control other parts of the circuit. This technique can help significantly reduce the qubit resources required to implement a quantum algorithm. In this paper, we give a formal definition of DQCs and then characterise their functionality in terms of ensembles of linear operators, following the Kraus representation of superoperators. We further interpret DQCs as tensor networks, implement their functionality as tensor decision diagrams (TDDs), and reduce the equivalence of two DQCs to checking if they have the same TDD representation. Experiments show that embedding classical logic into conventional quantum circuits does not incur a significant time and space burden.
Despite the rapid development of quantum computing these years, state-of-the-art quantum devices still contain only a limited number of qubits. One possible way to execute more realistic algorithms in near-term quantum devices is to employ dynamic quantum circuits (DQCs). In DQCs, measurements can happen during the circuit, and their outcomes can be processed with classical computers and used to control other parts of the circuit. This technique can help significantly reduce the qubit resources required to implement a quantum algorithm. In this paper, we give a formal definition of DQCs and then characterise their functionality in terms of ensembles of linear operators, following the Kraus representation of superoperators. We further interpret DQCs as tensor networks, implement their functionality as tensor decision diagrams (TDDs), and reduce the equivalence of two DQCs to checking if they have the same TDD representation. Experiments show that embedding classical logic into conventional quantum circuits does not incur a significant time and space burden.
Abstract Quantum computing holds the potential to solve complex problems currently beyond the capabilities of classical computers by exploiting the principles of quantum mechanics. However, due to the immaturity of such computers and the inability to know the state of the circuit during execution, efficient quantum simulators on classical computers are needed. This paper compares different methods for the contraction of quantum circuits represented as tensor networks. Tensor Decision Diagrams (TDD) are used to implement two contraction ordering methods that exploit the structure of the circuits to reduce temporal and spatial costs. Experimental results show that these methods improve other well established approaches and that they are faster that other well-known simulation tools based on other circuit representations. In addition, an analysis of different implementations of the same quantum algorithm highlights the impact of gate sets on contraction efficiency.
Tensor networks have been successfully applied in simulation of quantum physical systems for decades. Recently, they have also been employed in classical simulation of quantum computing, in particular, random quantum circuits. This article proposes a decision diagram style data structure, called Tensor Decision Diagram (TDD), for more principled and convenient applications of tensor networks. This new data structure provides a compact and canonical representation for quantum circuits. By exploiting circuit partition, the TDD of a quantum circuit can be computed efficiently. Furthermore, we show that the operations of tensor networks essential in their applications (e.g., addition and contraction) can also be implemented efficiently in TDDs. A proof-of-concept implementation of TDDs is presented and its efficiency is evaluated on a set of benchmark quantum circuits. It is expected that TDDs will play an important role in various design automation tasks related to quantum circuits, including but not limited to equivalence checking, error detection, synthesis, simulation, and verification.
With the rapid development of quantum computing, automatic verification of quantum circuits becomes more and more important. While several decision diagrams (DDs) have been introduced in quantum circuit simulation and verification, none of them supports symbolic computation. Algorithmic manipulations of symbolic objects, however, have been identified as crucial, if not indispensable, for several verification tasks. This paper proposes the first decision-diagram approach for operating symbolic objects and verifying quantum circuits with symbolic terms. As a notable example, our symbolic tensor decision diagrams (symbolic TDD) could verify the functionality of the 160-qubit quantum Fourier transform circuit within three minutes. Moreover, as demonstrated on Bernstein-Vazirani algorithm, Grover's algorithm, and the bit-flip error correction code, the symbolic TDD enables efficient verification of quantum circuits with user-supplied oracles and/or classical controls.
Parameterised quantum circuits (PQCs) hold great promise for demonstrating quantum advantages in practical applications of quantum computation. Examples of successful applications include the variational quantum eigensolver, the quantum approximate optimisation algorithm, and quantum machine learning. However, before executing PQCs on real quantum devices, they undergo compilation and optimisation procedures. Given the inherent error-proneness of these processes, it becomes crucial to verify the equivalence between the original PQC and its compiled or optimised version. Unfortunately, most existing quantum circuit verifiers cannot directly handle parameterised quantum circuits; instead, they require parameter substitution to perform verification. In this paper, we address the critical challenge of equivalence checking for PQCs. We propose a novel compact representation for PQCs based on tensor decision diagrams. Leveraging this representation, we present an algorithm for verifying PQC equivalence without the need for instantiation. Our approach ensures both effectiveness and efficiency, as confirmed by experimental evaluations. The decision-diagram representations offer a powerful tool for analysing and verifying parameterised quantum circuits, bridging the gap between theoretical models and practical implementations.
Quantum computing has proven to be capable of accelerating many algorithms by performing tasks that classical computers cannot. As quantum algorithms and implementations grow more complex, the need for rigorous circuit verification becomes critical, ensuring correct compilation and enhancing circuit fidelity through error correction and assertions. In this paper, we propose QuBEC, a Decision Diagram-based quantum equivalence checking approach, that requires less latency compared to existing techniques, while accounting for circuits with quantum error correction redundancy. QuBEC reduces verification time on benchmark circuits by up to 443×, while the number of Decision Diagram nodes required is reduced by up to 798.31×, compared to state-of-the-art strategies. The proposed QuBEC framework can contribute to the advancement of quantum computing by enabling faster and more efficient verification of quantum circuits, paving the way for the development of larger and more complex quantum algorithms.
Recent advances in fault tolerant quantum systems allow to perform non-unitary operations like mid-circuit measurement, active reset and classically controlled gate operations in addition to the existing unitary gate operations. Real quantum devices that support these non-unitary operations enable us to execute a new class of quantum circuits, known as Dynamic Quantum Circuits (DQC). This helps to enhance the scalability, thereby allowing execution of quantum circuits comprising of many qubits by using at least two qubits. Recently DQC realizations of multi-qubit Quantum Phase Estimation (QPE) and Bernstein-Vazirani (BV) algorithms have been demonstrated in two separate experiments. However the dynamic transformation of complex quantum circuits consisting of Toffoli gate operations have not been explored yet. This motivates us to: (a) explore the dynamic realization of Toffoli gates by extending the design space of DQC for Toffoli networks, and (b) propose a general dynamic transformation algorithm for the first time to the best of our knowledge. More precisely, we introduce two dynamic transformation schemes (dynamic-1 and dynamic-2) for Toffoli gates, that differ with respect to the required number of classically controlled gate operations. For evaluation, we consider the Deutsch-Jozsa (DJ) algorithm composed of one or more Toffoli gates. Experimental results demonstrate that dynamic DJ circuits based on dynamic-2 Toffoli realization scheme provides better computational accuracy over the dynamic-1 scheme. Further, the proposed dynamic transformation scheme is generic and can also be applied to non-Toffoli quantum circuits, e.g. BV algorithm.