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arXiv:2203.10018 · Physical review. D/Physical review. D.

Improving quantum simulation efficiency of final state radiation with dynamic quantum circuits

Plato Deliyannis, James Sud, Diana Chamaki, Zoë Webb-Mack, C. Bauer, Benjamin Philip Nachman

Published Aug 10, 2022• 10 citations
arXivHTMLPDF

Abstract

B. Nachman et al. [Phys. Rev. Lett. 126, 062001 (2021)] recently introduced an algorithm (QPS) for simulating parton showers with intermediate flavor states using polynomial resources on a digital quantum computer. We make use of a new quantum hardware capability called dynamical quantum computing to improve the scaling of this algorithm, which significantly improves the method precision. In particular, we modify the quantum parton shower circuit to incorporate midcircuit qubit measurements, resets, and quantum operations conditioned on classical information. This reduces the computational depth from $\mathcal{O}({N}^{5}{\mathrm{log}}_{2}(N{)}^{2})$ to $\mathcal{O}({N}^{3}{\mathrm{log}}_{2}(N{)}^{2})$ and the qubit requirements from $\mathcal{O}(N{\mathrm{log}}_{2}(N))$ to $\mathcal{O}(N)$. Using ``matrix product state'' state vector simulators, we demonstrate that the improved algorithm yields expected results for 2, 3, 4, and 5-steps of the algorithm. We compare absolute costs with the original QPS algorithm, and show that dynamical quantum computing can significantly reduce costs in the class of digital quantum algorithms representing quantum walks (which includes the QPS). Python code that implements QPS, both with and without dynamic gates, is publicly available on Github.

DOI
10.1103/physrevd.106.036007

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This paper presents a novel quantum walk approach to simulating parton showers on a quantum computer. We demonstrate that the quantum walk paradigm offers a natural and more efficient approach to simulating parton showers on quantum devices, with the emission probabilities implemented as the coin flip for the walker, and the particle emissions to either gluons or quark pairs corresponding to the movement of the walker in two dimensions. A quantum algorithm is proposed for a simplified, toy model of a 31-step, collinear parton shower, hence significantly increasing the number of steps of the parton shower that can be simulated compared to previous quantum algorithms. Furthermore, it scales efficiently: the number of possible shower steps increases exponentially with the number of qubits, and the circuit depth grows linearly with the number of steps. Reframing the parton shower in the context of a quantum walk therefore brings dramatic improvements, and is a step towards extending the current quantum algorithms to simulate more realistic parton showers.
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The interpretation of measurements of high-energy particle collisions relies heavily on the performance of full event generators, which include the calculation of the hard process and the subsequent parton shower step. With the continuous improvement of quantum devices, dedicated algorithms are needed to exploit the potential quantum that computers can provide. We propose general and extendable algorithms for quantum gate computers to facilitate calculations of helicity amplitudes and the parton shower process. The helicity amplitude calculation exploits the equivalence between spinors and qubits and the unique features of a quantum computer to compute the helicities of each particle involved simultaneously, thus fully utilizing the quantum nature of the computation. This advantage over classical computers is further exploited by the simultaneous computation of s- and t-channel amplitudes for a $2\ensuremath{\rightarrow}2$ process. The parton shower algorithm simulates collinear emission for a two-step, discrete parton shower. In contrast to classical implementations, the quantum algorithm constructs a wave function with a superposition of all shower histories for the whole parton shower process, thus removing the need to explicitly keep track of individual shower histories. Both algorithms utilize the quantum computers ability to remain in a quantum state throughout the computation and represent a first step towards a quantum computing algorithm describing the full collision event at the LHC.
In dynamic quantum circuits, classical information from midcircuit measurements is fed forward during circuit execution. This emerging capability of quantum computers confers numerous advantages that can enable more efficient and powerful protocols by drastically reducing the resource requirements for certain core algorithmic primitives. In particular, in the case of the n-qubit quantum Fourier transform followed immediately by measurement, the scaling of resource requirements is reduced from O(n^{2}) two-qubit gates in an all-to-all connectivity in the standard unitary formulation to O(n) midcircuit measurements in its dynamic counterpart without any connectivity constraints. Here, we demonstrate the advantage of dynamic quantum circuits for the quantum Fourier transform on IBM's superconducting quantum hardware with certified process fidelities of >50% on up to 16 qubits and >1% on up to 37 qubits, exceeding previous reports across all quantum computing platforms. These results are enabled by our contribution of an efficient method for certifying the process fidelity, as well as of a dynamical decoupling protocol for error suppression during midcircuit measurements and feed forward within a dynamic quantum circuit that we call "feed-forward-compensated dynamical decoupling." Our results demonstrate the advantages of leveraging dynamic circuits in optimizing the compilation of quantum algorithms.
The real-time simulation of large many-body quantum systems is a formidable task, that may only be achievable with a genuine quantum computational platform. Currently, quantum hardware with a number of qubits sufficient to make classical emulation challenging is available. This condition is necessary for the pursuit of a so-called quantum advantage, but it also makes verifying the results very difficult. In this paper, we flip the perspective and utilize known theoretical results about many-body quantum critical dynamics to qualitatively benchmark digital quantum hardware and various error mitigation techniques. In particular, we benchmark against known universal scaling laws in the Hamiltonian simulation of a time-dependent transverse-field Ising Hamiltonian of up to 133 qubits. Incorporating only basic error mitigation and suppression methods, our study shows reliable control up to a two-qubit gate depth of 28, featuring a maximum of 1396 two-qubit gates, before noise becomes prevalent. These results are transferable to applications such as Hamiltonian simulation, variational algorithms, optimization, or quantum machine learning. We demonstrate this on the example of digitized quantum annealing for optimization and identify an optimal working point in terms of both circuit depth and time step on a 133-site optimization problem. Published by the American Physical Society 2024
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