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IEEE International Symposium on Parallel & Distributed Processing, Workshops and Phd Forum

Quantifying Performance of Wire-Based Quantum Circuit Cutting with Entanglements

Shiplu Sarker, Wenyang Qian, Soham Pal, Robert Basili, Mary Mehrnoosh Eshaghian‐Wilner, Ashfaq Khokhar, Glenn R. Luecke, James P. Vary

Published May 27, 2024• 1 citation
Publisher

Abstract

Circuit cutting is a promising technique for mapping a quantum circuit requiring many qubits to a series of circuits requiring fewer qubits. At the cost of a longer runtime, such a strategy can reduce qubit requirements and mitigate noise in currently available Noisy Intermediate-Scale Quantum (NISQ) devices where noise scales poorly with greater levels of entanglement. In this work, we investigate the performance of wire-based circuit cutting in cases of different levels of entanglement and forms of noise. As a broadly applicable starting point, we focus on cutting Hamiltonian-inspired quantum circuits with various entanglement strategies and circuit depths. We provide model calculations of these circuits before and after cutting, both in the ideal case and in the presence of noise, using quantum simulators with quantum noise models. We present a numerical analysis of the performance of circuit cutting using various metrics for comparing ideal and noisy model calculations. Our results indicate that the efficacy of circuit cutting is sensitive to the level of entanglements and is affected differently by incoherent quantum noises.

DOI
10.1109/ipdpsw63119.2024.00178

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Circuit cutting is a promising technique for mapping a quantum circuit requiring many qubits to a series of circuits requiring fewer qubits. At the cost of a longer runtime, such a strategy can reduce qubit requirements and mitigate noise in currently available Noisy Intermediate-Scale Quantum (NISQ) devices where noise scales poorly with greater levels of entanglement. In this work, we investigate the performance of wire-based circuit cutting in cases of different levels of entanglement and forms of noise. As a broadly applicable starting point, we focus on cutting Hamiltonian-inspired quantum circuits with various entanglement strategies and circuit depths. We provide model calculations of these circuits before and after cutting, both in the ideal case and in the presence of noise, using quantum simulators with quantum noise models. We present a numerical analysis of the performance of circuit cutting using various metrics for comparing ideal and noisy model calculations. Our results indicate that the efficacy of circuit cutting is sensitive to the level of entanglements and is affected differently by incoherent quantum noises.
Current quantum computers suffer from a limited number of qubits and high error rates, limiting practical applicability. Different techniques exist to mitigate these effects and run larger algorithms. In this work, we analyze one of these techniques called quantum circuit cutting. With circuit cutting, a quantum circuit is decomposed into smaller sub-circuits, each of which can be run on smaller quantum hardware. We compare the performance of quantum circuit cutting with different cutting strategies, and then apply circuit cutting to a QAOA algorithm. Using simulations, we first show that Randomized Clifford measurements outperform both Pauli and random unitary measurements. Second, we show that circuit cutting has trouble providing correct answers in noisy settings, especially as the number of circuits increases.
Noisy intermediate-scale quantum (NISQ) devices with limited qubit count and connectivity limit the scale of quantum circuits that can be executed. Circuit cutting methods simulate larger quantum computers by decomposing large circuits into small subcircuits that can be executed on NISQ hardware. Existing circuit cutting methods only consider the qubit count of the target hardware for finding the locations of cuts on the circuits. This can result in deeper subcircuits after mapping on the hardware. Fidelity decays exponentially with circuit depth and diminishes the quality of execution. We propose a circuit-cutting framework that reduces variance in the depth of subcircuits after mapping to the hardware. Our method formulates the initial circuit cutting as a multi-objective optimization problem based on an evolutionary search method with the number of cuts and the maximum depth of individual routed subcircuits as fitness objectives. This method is implemented as an extension to the existing Qiskit Circuit Cutting Addon, which allows for integration in existing flows. Our approach achieves reductions in routed subcircuit depth of up to 9.9% across benchmark circuits compared with baseline methods.
Abstract Noisy intermediate-scale quantum (NISQ) devices are restricted by their limited number of qubits and their short decoherence times. An approach addressing these problems is quantum circuit cutting. It decomposes the execution of a large quantum circuit into the execution of multiple smaller quantum circuits with additional classical postprocessing. Since these smaller quantum circuits require fewer qubits and gates, they are more suitable for NISQ devices. To investigate the effect of quantum circuit cutting in a quantum algorithm targeting NISQ devices, we design two experiments using the quantum approximate optimization algorithm (QAOA) for the Maximum Cut (MaxCut) problem and conduct them on state-of-the-art superconducting devices. Our first experiment studies the influence of circuit cutting on the objective function of QAOA, and the second evaluates the quality of results obtained by the whole algorithm with circuit cutting. The results show that circuit cutting can reduce the effects of noise in QAOA, and therefore, the algorithm yields better solutions on NISQ devices.
Distributed quantum computing supports combining the computational power of multiple quantum devices to overcome the limitations of individual devices. Circuit cutting techniques enable the distribution of quantum computations via classical communication. These techniques involve partitioning a quantum circuit into smaller subcircuits, each containing fewer qubits. The original circuit's outcome can be replicated by executing these sub circuits on separate devices and combining their results. However, the number of circuit executions required to achieve a fixed result accuracy with circuit cutting grows exponentially with the number of cuts, posing significant costs. In contrast, quantum teleportation allows the distribution of quantum computations without an exponential increase in circuit executions. Nevertheless, each teleportation requires a pre-shared pair of maximally entangled qubits for transmitting a quantum state, and non-maximally entangled qubits cannot be used for this purpose. Addressing this, our work explores utilizing non-maximally entangled qubit pairs in wire cutting, a specific form of circuit cutting, to mitigate the associated costs. The cost of this cutting procedure reduces with the increasing degree of entanglement in the pre-shared qubit pairs. We derive the optimal sampling overhead in this context and present a wire cutting technique employing pure non-maximally entangled states that achieves this optimal sampling overhead. Hence, this offers a continuum between existing wire cutting and quantum teleportation.
Noisy Intermediate-Scale Quantum (NISQ) computers impose severe architectural constraints that prevent direct execution of logical quantum circuits. As a result, quantum circuit mapping—transforming ideal circuits into hardware-compatible forms—has become a critical task in quantum software toolchains. This paper presents a comparative study of key mapping techniques, focusing on circuit depth, SWAP gate overhead, and fidelity awareness. Through a case analysis on a 5-qubit Quantum Fourier Transform (QFT) circuit, we demonstrate the performance trade-offs of several prominent mapping strategies, including naive greedy routing, Qiskit’s SABRE, and CQC’s t|ket>. Our findings reveal that mapping technique selection has a profound impact on circuit quality and feasibility on real NISQ hardware.
Circuit cutting allows quantum circuits larger than the available hardware to be executed. Cutting techniques split circuits into smaller subcircuits, run them on the hardware, and recombine results through classical post-processing. Circuit cutting techniques have been extensively researched over the last five years and it been adopted by quantum companies, like IBM, as part of their scaling roadmap. We examine whether current circuit cutting techniques are practical for orchestrating executions on fault-tolerant quantum computers. We conduct a resource estimation-based benchmarking of important quantum applications and different types of circuit cutting techniques. Our applications include practically relevant algorithms such as Hamiltonian simulation, kernels such as quantum Fourier transform and more. To cut these applications, we use IBM's Qiskit cutting tool. We estimate resources for subcircuits using Microsoft's Azure Quantum Resource Estimator and develop models to determine qubit counts and the quantum and classical runtime needs of circuit cutting. We demonstrate that while circuit cutting works for small-scale systems, the exponential growth of the quantum excution runtime and the classical post-processing overhead as the qubit count increases renders it impractical for larger quantum systems with current implementation strategies. As we transition from noisy quantum hardware to fault-tolerance, our work provides useful guidance for the design of quantum software and runtime systems.