<!--HTML-->There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivities, and coherence times, circuit optimization is essential to make the best use of near-term quantum devices. We introduce two separate ideas for circuit optimization and combine them in a multi-tiered quantum circuit optimization protocol called AQCEL. The first ingredient is a technique to recognize repeated patterns of quantum gates, opening up the possibility of future hardware co-optimization. The second ingredient is an approach to reduce circuit complexity by identifying zero- or low-amplitude computational basis states and redundant gates. As a demonstration, AQCEL is deployed on an iterative and efficient quantum algorithm designed to model final state radiation in high energy physics. For this algorithm, our optimization scheme brings a significant reduction in the gate count without losing any accuracy compared to the original circuit. Additionally, we have investigated whether this can be demonstrated on a quantum computer using polynomial resources. Our technique is generic and can be useful for a wide variety of quantum algorithms.
<!--HTML-->There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivities, and coherence times, circuit optimization is essential to make the best use of near-term quantum devices. We introduce two separate ideas for circuit optimization and combine them in a multi-tiered quantum circuit optimization protocol called AQCEL. The first ingredient is a technique to recognize repeated patterns of quantum gates, opening up the possibility of future hardware co-optimization. The second ingredient is an approach to reduce circuit complexity by identifying zero- or low-amplitude computational basis states and redundant gates. As a demonstration, AQCEL is deployed on an iterative and efficient quantum algorithm designed to model final state radiation in high energy physics. For this algorithm, our optimization scheme brings a significant reduction in the gate count without losing any accuracy compared to the original circuit. Additionally, we have investigated whether this can be demonstrated on a quantum computer using polynomial resources. Our technique is generic and can be useful for a wide variety of quantum algorithms.
There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivities, and coherence times, circuit optimization is essential to make the best use of quantum devices produced over a next decade. We introduce two separate ideas for circuit optimization and combine them in a multi-tiered quantum circuit optimization protocol called AQCEL. The first ingredient is a technique to recognize repeated patterns of quantum gates, opening up the possibility of future hardware optimization. The second ingredient is an approach to reduce circuit complexity by identifying zero- or low-amplitude computational basis states and redundant gates. As a demonstration, AQCEL is deployed on an iterative and effcient quantum algorithm designed to model final state radiation in high energy physics. For this algorithm, our optimization scheme brings a significant reduction in the gate count without losing any accuracy compared to the original circuit. Additionally, we have investigated whether this can be demonstrated on a quantum computer using polynomial resources. Our technique is generic and can be useful for a wide variety of quantum algorithms.
There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivity, and coherence times, a quantum circuit optimization is essential to make the best use of near-term quantum devices. We introduce a new circuit optimizer called AQCEL, which aims to remove redundant controlled operations from controlled gates, depending on initial states of the circuit. Especially, the AQCEL can remove unnecessary qubit controls from multi-controlled gates in polynomial computational resources, even when all the relevant qubits are entangled, by identifying zero-amplitude computational basis states using a quantum computer. As a benchmark, the AQCEL is deployed on a quantum algorithm designed to model final state radiation in high energy physics. For this benchmark, we have demonstrated that the AQCEL-optimized circuit can produce equivalent final states with much smaller number of gates. Moreover, when deploying AQCEL with a noisy intermediate scale quantum computer, it efficiently produces a quantum circuit that approximates the original circuit with high fidelity by truncating low-amplitude computational basis states below certain thresholds. Our technique is useful for a wide variety of quantum algorithms, opening up new possibilities to further simplify quantum circuits to be more effective for real devices.
Abstract While the capabilities of quantum hardware have significantly advanced in recent years, executing quantum algorithms as quantum circuits at the lowest possible cost remains crucial, regardless of the hardware progress. We are developing a quantum-state-dependent circuit optimizer called Aqcel . Our guiding principle, implemented as the Aqcel optimization protocol, is to optimize quantum circuits by measuring the states of the control qubits to identify and eliminate unnecessary control operations. In this paper, we introduce two key improvements: the state label manager that reduces unnecessary state measurements and the C X -pair removal process that eliminates redundant gate pairs. These enhancements significantly reduce the number of two-qubit gates, improving the fidelity of quantum circuits executed on quantum hardware. To demonstrate the effectiveness of our method, we apply Aqcel to quantum circuits for the quantum parton shower algorithm. Experimental results using the IBM quantum computer show a substantial reduction in gate counts and an improvement in fidelity compared to the conventional optimization technique as well as the original Aqcel protocol. These results demonstrate that fixed-initial-state information can enable state-dependent optimizations that are complementary to general-purpose, unitary-equivalence-preserving circuit optimizers.
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.
Quantum computations are typically performed as a sequence of basic operations, called quantum gates. Different gate sequences, called quantum circuits, can implement the same overall quantum computation. Since every additional quantum gate takes time and introduces noise into the system, it is important to find the smallest possible quantum circuit that implements a given computation, especially for near-term quantum devices that can execute only a limited number of quantum gates before noise renders the computation useless. An important building block for many quantum circuit optimization techniques is pattern matching: given a large and small quantum circuit, we would like to find all maximal matches of the small circuit, called a pattern , in the large circuit, considering pairwise commutation of quantum gates. In this work, we present the first classical algorithm for pattern matching that provably finds all maximal matches and is efficient enough to be practical for circuit sizes typical for near-term devices. We demonstrate numerically 1 that combining our algorithm with known pattern-matching-based circuit optimization techniques reduces the gate count of a random quantum circuit by ∼ 30% and can further improve practically relevant quantum circuits that were already optimized with state-of-the-art techniques.
Quantum computing is an emerging technology in which quantum mechanical properties are suitably utilized to perform certain compute-intensive operations faster than classical computers. Quantum algorithms are designed as a combination of quantum circuits that each require a large number of quantum gates, which is a challenge considering the limited number of qubit resources available in quantum computing systems. Our work proposes a technique to optimize quantum arithmetic algorithms by reducing the hardware resources and the number of qubits based on ZX calculus. We have utilised ZX calculus rewrite rules for the optimization of fault-tolerant quantum multiplier circuits where we are able to achieve a significant reduction in the number of ancilla bits and T-gates as compared to the originally required numbers to achieve fault-tolerance. Our work is the first step in the series of arithmetic circuit optimization using graphical rewrite tools and it paves the way for advancing the optimization of various complex quantum circuits and establishing the potential for new applications of the same.