Currently, computing paradigm is ruled by the laws of classical physics and will continue till the dimensions of transistors reaches the size of atomic particles. Quantum computing (QC) is a new technology that employs laws of quantum mechanics to address issues such as irreversibility and power dissipation that are outside the scope of conventional computing models. QC offers a powerful stage for solving complex and compound problems like searching and number factoring. A critical task in utilizing quantum physics in many application fields is circuit design using reversible quantum gates. Unitary decomposition is a popular scheme for mapping quantum algorithms to any set of elementary quantum operations. Using decomposition techniques enables transformation of unitary matrices into fundamental quantum gates, which is critical for running algorithms on prevailing quantum computers. Any 3x3 reversible quantum gate can be decomposed into single-qubit rotation gates and two qubit CNOT gates. This paper is the first to present quantum implementations of FRSG1 and JTF1 gates into CNOT gates and single qubit U3 gates with different optimization levels on a platform provided by IBM. These gates are important in a variety of practical applications like Stochastic computing and parity generation circuits. In FRSG1 the implementation count of single qubit gates decreases by 56% and the count of two qubit gates by 15% after optimization, whereas in JTF1 gate the single qubit gate count reduces by 71% and the number of two qubit gates reduces by 41%.
Currently, computing paradigm is ruled by the laws of classical physics and will continue till the dimensions of transistors reaches the size of atomic particles. Quantum computing (QC) is a new technology that employs laws of quantum mechanics to address issues such as irreversibility and power dissipation that are outside the scope of conventional computing models. QC offers a powerful stage for solving complex and compound problems like searching and number factoring. A critical task in utilizing quantum physics in many application fields is circuit design using reversible quantum gates. Unitary decomposition is a popular scheme for mapping quantum algorithms to any set of elementary quantum operations. Using decomposition techniques enables transformation of unitary matrices into fundamental quantum gates, which is critical for running algorithms on prevailing quantum computers. Any 3x3 reversible quantum gate can be decomposed into single-qubit rotation gates and two qubit CNOT gates. This paper is the first to present quantum implementations of FRSG1 and JTF1 gates into CNOT gates and single qubit U3 gates with different optimization levels on a platform provided by IBM. These gates are important in a variety of practical applications like Stochastic computing and parity generation circuits. In FRSG1 the implementation count of single qubit gates decreases by 56% and the count of two qubit gates by 15% after optimization, whereas in JTF1 gate the single qubit gate count reduces by 71% and the number of two qubit gates reduces by 41%.
A critical task in utilizing quantum physics in many application fields is circuit design using reversible quantum gates. Using decomposition techniques enables transformation of unitary matrices into fundamental quantum gates. Any 3x3 reversible quantum gate can be decomposed into single-qubit rotation gates and two qubit CNOT gates. In this chapter, quantum implementations of FRSG1, URG, JTF1 and R gates into CNOT gates and single qubit U3 gates with different optimization levels on a platform provided by IBM have been discussed. FRSG1 and JTF1 gates are important in applications like Stochastic computing, fingerprint authentication system, and parity generation circuits. URG gate is better in terms of number of complex functions and can be utilized to design quantum comparator circuits. R gate plays an important role in inverting and duplicating a signal. In FRSG1, URG, JTF1 and R gates, the implementation count of single qubit gates decreases by 56%, 11%, 71%, and 62%, respectively and the count of two qubit gates reduces by 15%, 26%, 41%, and 5% respectively after optimization.
The current phase of quantum computing is in the Noisy Intermediate-Scale Quantum (NISQ) era. On NISQ devices, two-qubit gates such as CNOTs are much noisier than single-qubit gates, so it is essential to minimize their count. Quantum circuit synthesis is a process of decomposing an arbitrary unitary into a sequence of quantum gates, and can be used as an optimization tool to produce shorter circuits to improve overall circuit fidelity. However, the time-to-solution of synthesis grows exponentially with the number of qubits. As a result, synthesis is intractable for circuits on a large qubit scale. In this paper, we propose a hierarchical, block-by-block optimization framework, QGo, for quantum circuit optimization. Our approach allows an exponential cost optimization to scale to large circuits. QGo uses a combination of partitioning and synthesis: 1) partition the circuit into a sequence of independent circuit blocks; 2) re-generate and optimize each block using quantum synthesis; and 3) re-compose the final circuit by stitching all the blocks together. We perform our analysis and show the fidelity improvements in three different regimes: small-size circuits on real devices, medium-size circuits on noise simulations, and large-size circuits on analytical models. Using a set of NISQ benchmarks, we show that QGo can reduce the number of CNOT gates by 29.9% on average and up to 50% when compared with industrial compilers such as t|ket>. When executed on the IBM Athens system, shorter depth leads to higher circuit fidelity. We also demonstrate the scalability of our QGo technique to optimize circuits of 60+ qubits. Our technique is the first demonstration of successfully employing and scaling synthesis in the compilation toolchain for large circuits. Overall, our approach is robust for direct incorporation in production compiler toolchains.
The current phase of quantum computing is in the Noisy Intermediate-Scale Quantum (NISQ) era. On NISQ devices, two-qubit gates such as CNOTs are much noisier than single-qubit gates, so it is essential to minimize their count. Quantum circuit synthesis is a process of decomposing an arbitrary unitary into a sequence of quantum gates, and can be used as an optimization tool to produce shorter circuits to improve overall circuit fidelity. However, the time-to-solution of synthesis grows exponentially with the number of qubits. As a result, synthesis is intractable for circuits on a large qubit scale. In this paper, we propose a hierarchical, block-by-block opti-mization framework, QGo, for quantum circuit optimization. Our approach allows an exponential cost optimization to scale to large circuits. QGo uses a combination of partitioning and synthesis: 1) partition the circuit into a sequence of independent circuit blocks; 2) re-generate and optimize each block using quantum synthesis; and 3) re-compose the final circuit by stitching all the blocks together. We perform our analysis and show the fidelity improvements in three different regimes: small-size circuits on real devices, medium-size circuits on noisy simulations, and large-size circuits on analytical models. Our technique can be applied after existing optimizations to achieve higher circuit fidelity. Using a set of NISQ benchmarks, we show that QGo can reduce the number of CNOT gates by 29.9% on average and up to 50% when compared with industrial compiler optimizations such as t|ket). When executed on the IBM Athens system, shorter depth leads to higher circuit fidelity. We also demonstrate the scalability of our QGo technique to optimize circuits of 60+ qubits, Our technique is the first demonstration of successfully employing and scaling synthesis in the compilation tool chain for large circuits. Overall, our approach is robust for direct incorporation in production compiler toolchains to further improve the circuit fidelity.
Unitary decomposition is a widely used method to map quantum algorithms to an arbitrary set of quantum gates. Efficient implementation of this decomposition allows for the translation of bigger unitary gates into elementary quantum operations, which is key to executing these algorithms on existing quantum computers. The decomposition can be used as an aggressive optimization method for the whole circuit, as well as to test part of an algorithm on a quantum accelerator. For the selection and implementation of the decomposition algorithm, perfect qubits are assumed. We base our decomposition technique on Quantum Shannon Decomposition, which generates O(344n) controlled-not gates for an n-qubit input gate. In addition, we implement optimizations to take advantage of the potential underlying structure in the input or intermediate matrices, as well as to minimize the execution time of the decomposition. Comparing our implementation to Qubiter and the UniversalQCompiler (UQC), we show that our implementation generates circuits that are much shorter than those of Qubiter and not much longer than the UQC. At the same time, it is also up to 10 times as fast as Qubiter and about 500 times as fast as the UQC.
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.
Quantum computing faces challenges such as noise, short coherence time, and limited qubit connections. These challenges worsen as quantum circuits become more complex. One major issue is the increasing depth of quantum circuits. This research proposes an optimization framework targeting depth and gate count reduction in quantum circuits, specifically for Noisy Intermediate-Scale Quantum (NISQ) devices. The proposed approach combines unitary merging of single-qubit gates, CNOT cancellation, gate commuting, and rotation gate rewriting strategies. Consecutive gates acting on the same qubit, such asRx(θ1)⋅Rx(θ2), are algebraically merged into a single rotation, while pairs of redundant CNOT gates are eliminated based on gate identity relations. The technique is implemented using Qiskit and validated across five diverse circuits including complex, random, and multi-qubit configurations. Experimental results show an average depth reduction of 33.33% and gate count reduction of 32.14%, with runtime improvement of up to 25%. For instance, an input circuit with a depth of 7 and gate count of 11 was reduced to a depth of 2 and 4 gates. All optimized circuits preserve functional correctness with a fidelityF≥0.99. High-resolution circuit diagrams are presented to visually demonstrate improvements before and after optimization. Additionally, global phase shifts such aseiπ/4are preserved or analytically characterized where relevant. This work enhances the viability of quantum computations on near-term hardware and opens pathways for future AI-driven quantum optimizations.