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arXiv:2004.06052 · Electronic Proceedings in Theoretical Computer Science

Architecture-Aware Synthesis of Phase Polynomials for NISQ Devices

Arianne Meijer-van de Griend, Ross Duncan

Published Nov 14, 2023• 27 citations
arXivHTMLPDF

Abstract

We propose a new algorithm to synthesise quantum circuits for phase polynomials, which takes into account the qubit connectivity of the quantum computer.We focus on the architectures of currently available NISQ devices.Our algorithm generates circuits with a smaller CNOT depth than the algorithms currently used in Staq and t|ket , while improving the runtime with respect the former.

DOI
10.4204/eptcs.394.8

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Physical Review A•Jan 2, 2024•7 citations
We propose a new algorithm to synthesise quantum circuits for phase polynomials, which takes into account the qubit connectivity of the quantum computer.We focus on the architectures of currently available NISQ devices.Our algorithm generates circuits with a smaller CNOT depth than the algorithms currently used in Staq and t|ket , while improving the runtime with respect the former.
Abstract We present a framework for the synthesis of phase polynomials that addresses both cases of full connectivity and partial connectivity for NISQ architectures. In most cases, our algorithms generate circuits with lower CNOT count and CNOT depth than the state of the art or have a significantly smaller running time for similar performances. We also provide methods that can be applied to our algorithms in order to trade an increase in the CNOT count for a decrease in execution time, thereby filling the gap between our algorithms and faster ones.
Abstract Currently available quantum computing hardware platforms have limited 2-qubit connectivity among their addressable qubits. In order to run a generic quantum algorithm on such a platform, one has to transform the initial logical quantum circuit describing the algorithm into an equivalent one that obeys the connectivity restrictions. In this work we construct a circuit synthesis scheme that takes as input the qubit connectivity graph and a quantum circuit over the gate set generated by { CNOT , R Z } and outputs a circuit that respects the connectivity of the device. As a concrete application, we apply our techniques to Google’s Bristlecone 72-qubit quantum chip connectivity, IBM’s Tokyo 20-qubit quantum chip connectivity, and Rigetti’s Acorn 19-qubit quantum chip connectivity. In addition, we also compare the performance of our scheme as a function of sparseness of randomly generated quantum circuits, and discuss how to apply our techniques as a subroutine for the more general mapping problem over universal set of gates (Clifford + T).
NISQ devices have inherent limitations in terms of connectivity and hardware noise. The synthesis of CNOT circuits considers the physical constraints and transforms quantum algorithms into low-level quantum circuits that can execute on physical chips correctly. In the current trend, quantum chip architectures without Hamiltonian paths are gradually replacing architectures with Hamiltonian paths due to their scalability and low-noise characteristics. To this end, this paper addresses the nearest neighbor synthesis of CNOT circuits in the architectures with and without Hamiltonian paths, aiming to enhance the fidelity of the circuits after execution. Firstly, a key-qubit priority mapping model for general quantum architectures is proposed. Secondly, the initial mapping is further improved by using tabu search to reduce the number of CNOT gates after circuit synthesis and enhance its fidelity. Finally, the noise-aware CNOT circuit nearest neighbor synthesis algorithm for the general architecture is proposed based on the key-qubit priority mapping model. The algorithm is demonstrated on several popular cloud quantum computing platforms and simulators, showing that it effectively optimizes the fidelity of CNOT circuits compared with mainstream methods. Moreover, the method can be extended to more general circuits, thereby improving the overall performance of quantum computing on NISQ devices.
Blocks composed of {CNOT, Rz} are ubiquitous in modern quantum applications, notably in circuits such as QAOA ansatzes and quantum adders. After compilation, many of them exhibit large CNOT counts or depths, which lowers fidelity. Therefore, we introduce HOPPS: a SAT-based hardware-aware optimal phase polynomial synthesis algorithm that could generate {CNOT, Rz} blocks with CNOT count or depth optimality. Sometime {CNOT, Rz} blocks are large, such as in QAOA ansatzes, HOPPS's pursuit of optimality limits its scalability. To address this issue, we introduce an iterative blockwise optimization strategy: large circuits are partitioned into smaller blocks, each block is optimally refined, and the process is repeated for several iterations. Empirical results show that HOPPS is more efficient comparing with existing near optimal synthesis tools. Used as a peephole optimizer, HOPPS reduces the CNOT count by up to 50.0% and the CNOT depth by up to 57.1% under OLSQ. For large QAOA circuit, after mapping by Qiskit, circuit can be reduced CNOT count and depth by up to 44.4% and 42.4% by our iterative blockwise optimization. Index Terms-Phase Polynomial, Quantum Circuit Synthesis, Quantum Circuit Optimization.
In the near future of the noisy intermediate-scale quantum (NISQ) era, almost all quantum computing devices will be restricted to a specific fixed qubits connectivity architecture. Thus, the synthesis of quantum circuits with limited connectivity is urgent. We design quantum circuit synthesis algorithms for basic and essential synthesis problems, such as quantum state preparation, general unitary synthesis, and quantum isometries. For any architecture, the controlled not (cnot) count is at most 5/3 times the state-of-the-art result on complete-graph architecture. For some specific architectures, such as square-grid ones, the ratio is reduced to 1.126. The numerical simulation result is confirmatory of theoretical conclusions. Our algorithms significantly reduce by more than 5050%50 additional cnot count compared to mapping algorithms. These algorithms help to implement the larger-scale algorithm in the physics device. Our results illustrate that well-designed synthesis algorithms can mitigate the problem of limited qubit connectivity in the NISQ era and may suggest the design of large-scale quantum devices.