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International Conference on Information and Communication Technology Convergence (ICTC)

Circuit depth reduction algorithm for QUBO and Ising models in gate-model quantum computers

Sun Woo Park, Hyunju Lee, Byung Chun Kim, Youngho Woo, Kyungtaek Jun

Published Oct 20, 2021• 3 citations
Publisher

Abstract

Gate-model quantum computers, including IBM and IonQ, have gained considerable attention as backbones for implementing near-term quantum computer architectures and quantum devices. Their performances rely on circuit depths, whose minimization ensures optimal results and reduced noises. We develop an algorithm which rearranges the terms in the quadratics of the QUBO model and the Ising model, when implementing the Quantum Approximate Optimization Algorithm for the Hamiltonian of a linear system. We test the algorithm on IBM quantum computer and IBM simulator to verify the effectiveness of our algorithm for minimizing circuit depths.

DOI
10.1109/ictc52510.2021.9621203

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Gate-model quantum computers, including IBM and IonQ, have gained considerable attention as backbones for implementing near-term quantum computer architectures and quantum devices. Their performances rely on circuit depths, whose minimization ensures optimal results and reduced noises. We develop an algorithm which rearranges the terms in the quadratics of the QUBO model and the Ising model, when implementing the Quantum Approximate Optimization Algorithm for the Hamiltonian of a linear system. We test the algorithm on IBM quantum computer and IBM simulator to verify the effectiveness of our algorithm for minimizing circuit depths.
Quantum computers utilize the fundamentals of quantum mechanics to solve computational problems more efficiently than traditional computers. Gate-model quantum computers are fundamental to implement near-term quantum computer architectures and quantum devices. Here, a quantum algorithm is defined for the circuit depth reduction of gate-model quantum computers. The proposed solution evaluates the reduced time complexity equivalent of a reference quantum circuit. We prove the complexity of the quantum algorithm and the achievable reduction in circuit depth. The method provides a tractable solution to reduce the time complexity and physical layer costs of quantum computers.
Quantum Approximation Optimization Algorithm (QAOA) is a highly advocated variational algorithm for solving the combinatorial optimization problem. One critical feature in the quantum circuit of QAOA algorithm is that it consists of two-qubit operators that commute. The flexibility in reordering the two-qubit gates allows compiler optimizations to generate circuits with better depths, gate count, and fidelity. However, it also imposes significant challenges due to additional freedom exposed in the compilation. Prior studies lack the following: (1) Performance guarantee, (2) Scalability, and (3) Awareness of regularity in scalable hardware. We propose a structured method that ensures linear depth for any compiled QAOA circuit on multi-dimensional quantum architectures. We also demonstrate how our method runs on Google Sycamore and IBM Non-linear architectures in a scalable manner and in linear time. Overall, we can compile a circuit with up to 1024 qubits in 10 seconds with a 3.8X speedup in depth, 17% reduction in gate count, and 18X improvement for circuit ESP.
Abstract Simulating quantum systems is believed to be one of the most important applications of quantum computers. On noisy intermediate-scale quantum (NISQ) devices, the high-level circuit designed by quantum algorithms for Hamiltonian simulation needs to consider hardware limitations such as gate errors and circuit depth before it can be efficiently executed. In this work, we develop a hardware-agnostic circuit optimization algorithm to reduce the overall circuit cost for Hamiltonian simulation problems. Our method employ a novel sub-circuit synthesis in intermediate representation and propose a greedy ordering scheme for gate cancellation to minimize the gate count and circuit depth. To quantify the benefits of this approach, we benchmark proposed algorithm on different Hamiltonian models. Compared with state-of-the-art generic quantum compilers and specific quantum simulation compiler, the benchmarking results of our algorithm show an average reduction in circuit depth by 16.5× (up to 64.1×) and in gate count by 7.8× (up to 23.7×). This significant improvement helps enhance the performance of Hamiltonian simulation in the NISQ era.
The quantum approximate optimization algorithm (QAOA) is a promising quantum-classical hybrid technique to solve combinatorial optimization problems in near-term gate-based noisy quantum devices. In QAOA, the objective is a function of the quantum state, which itself is a function of the gate parameters of a multi-level parameterized quantum circuit (PQC). A classical optimizer varies the continuous gate parameters to generate distributions (quantum state) with significant support to the optimal solution. Even at the lowest circuit depth, QAOA offers non-trivial provable performance guarantee which is expected to increase with the circuit depth. However, the existing analysis fails to consider non-idealities in the qubit quality i.e., short lifetime and imperfect gate operations in realistic quantum hardware. In this article, we investigate the impact of various noise sources on the performance of QAOA both in simulation and on a real quantum computer from IBM. Our analyses indicate that the optimal number of stages (p-value) for any QAOA instance is limited by the noise characteristics (gate error, coherence time, etc.) of the target hardware as opposed to the current perception that higher-depth QAOA will provide monotonically better performance for a given problem compared to the low-depth implementations.
Quantum circuit depth minimization is critical for practical applications of circuit-based quantum computation. In this work, we present a systematic procedure to decompose multiqubit controlled unitary gates, which is essential in many quantum algorithms, to controlled-not and single-qubit gates with which the quantum circuit depth only increases linearly with the number of control qubits. Our algorithm does not require any ancillary qubits and achieves a quadratic reduction of the circuit depth against known methods. We show the advantage of our algorithm with proof-of-principle demonstrations on the IBM quantum cloud platform.
In recent years, significant progress has been made in building quantum computers by several companies. Despite the progress, these noisy intermediate-scale quantum (NISQ) computers still suffer from several noises and errors such as measurement errors, multi-qubit gate errors, and worse, short decoherence times. Though quantum computer vendors are releasing better quantum computers in terms of Quantum Volume, the quantum device still remains far from quantum supremacy in practical problems. The Quantum Approximate Optimization Algorithm (QAOA) was suggested to potentially demonstrate a computational advantage in combinatorial optimization problems on NISQ computers. In this paper, we optimize the QAOA circuits and to scale the problem size on IBM quantum processors. In addition, we study the effect of the length of the QAOA ansatz on IBM quantum processors and discuss optimal implementation methods for scalable QAOA. We test our implementations on the MaxCut problems.