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International Symposium on Lattice Field Theory (LATTICE)

Real-time Quantum Calculations of Phase Shifts On NISQ Hardware Platforms Using Wavepacket Time Delay

Patrick Dreher, Erik Gustafson, Yingyue Zhu, Norbert M. Linke, Yannick Meurice

Published May 16, 2022• 4 citations
Publisher

Abstract

We introduce a new method to calculate phase shifts on noisy intermediate scale quantum (NISQ) hardware platforms using a wave packet edge time delay. The method uses the early and intermediate stages of the collision because the standard method based on the asymptotic out-state behavior is unreachable using today’s NISQ platforms. The calculation was implemented on a 4-site transverse Ising model in one spatial dimension with and without a potential interaction. A time evolution operator describing the progression of the system was constructed and transmission and reflection coefficients were calculated based on the identified quantum Fourier transformed momentum states. The detailed analysis of the phase shift calculations on both IBM superconducting transmon and University of Maryland ion trap quantum computers shows the platform independence of the methodology. This successful implementation of this wave packet preparation and projection on momentum eigenstates can now be performed with actual quantum computing hardware platforms. This method provides a procedure for calculating phase shifts and opens the possibility of using noisy intermediate scale quantum devices to perform real-time quantum mechanics and quantum field theory scattering calculations.

DOI
10.22323/1.396.0464

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We introduce a new method to calculate phase shifts on noisy intermediate scale quantum (NISQ) hardware platforms using a wave packet edge time delay. The method uses the early and intermediate stages of the collision because the standard method based on the asymptotic out-state behavior is unreachable using today’s NISQ platforms. The calculation was implemented on a 4-site transverse Ising model in one spatial dimension with and without a potential interaction. A time evolution operator describing the progression of the system was constructed and transmission and reflection coefficients were calculated based on the identified quantum Fourier transformed momentum states. The detailed analysis of the phase shift calculations on both IBM superconducting transmon and University of Maryland ion trap quantum computers shows the platform independence of the methodology. This successful implementation of this wave packet preparation and projection on momentum eigenstates can now be performed with actual quantum computing hardware platforms. This method provides a procedure for calculating phase shifts and opens the possibility of using noisy intermediate scale quantum devices to perform real-time quantum mechanics and quantum field theory scattering calculations.
We present a method to extract the phase shift of a scattering process using the real-time evolution in the early and intermediate stages of the collision in order to estimate the time delay of a wave packet. This procedure is convenient when using noisy quantum computers for which the asymptotic out-state behavior is unreachable. We demonstrate that the challenging Fourier transforms involved in the state preparation and measurements can be implemented in 1+11+11+1 dimensions with current trapped ion devices and IBM quantum computers. We compare quantum computations of the time delays obtained in the one-particle quantum mechanics limit and the scalable quantum field theory formulation with accurate numerical results. We discuss the finite volume effects in the Wigner formula connecting time delays to phase shifts. The results reported involve two- and four-qubit calculations, and we discuss the possibility of larger scale computations in the near future.
Real-time scattering calculations on a noisy intermediate scale quantum (NISQ) quantum computer are disrupted by errors that accumulate throughout the circuits. To improve the accuracy of such physics simulations, one can supplement the application circuits with a recent error mitigation strategy known as noiseless output extrapolation (NOX). We tested these error mitigation protocols on a transverse field Ising model and improved upon previous phase shift calculations. Our proof-of-concept 4-qubit application circuits were run on several IBM quantum computing hardware architectures. We introduce metrics that show between 22% and 73% error reduction for circuit depths ranging from 13 to 37 hard cycles, confirming that the NOX technique applies to circuits with a broad range of failure rates. We also observed an approximate 28% improvement in the accuracy of the time delay calculation of the scattering phase shift. These observations on different cloud-accessible devices confirm that NOX improves performance even when circuits are executed in substantially time-separated batches. Finally, we provide a heuristic method to obtain systematic error bars on the mitigated results, compare them with empirical errors and discuss their effects on phase shift estimates.
Real-time scattering calculations on a Noisy Intermediate Scale Quantum (NISQ) quantum computer are disrupted by errors that accumulate throughout the circuits. To improve the accuracy of such physics simulations, one can supplement the application circuits with a recent error mitigation strategy known as Noisy Output eXtrapolation (NOX). We tested these error mitigation protocols on a Transverse Field Ising model and improved upon previous calculations of the phase shift. Our proof-of-concept 4-qubit application circuits were run on several IBM quantum computing hardware architectures. Metrics were introduced that show between 21\% and 74\% error reduction for circuit depths ranging from 14 to 37 hard cycles, confirming that the NOX technique applies to circuits with a broad range of failure rates. This observation on different cloud-accessible devices further confirms that NOX provides performance improvements even in the advent where circuits are executed in substantially time-separated batches. Finally, we provide a heuristic method to obtain systematic error bars on the mitigated results, compare them with empirical errors and discuss their effects on phase shift estimates.
Quantum phase estimation (QPE) is one of the core algorithms for quantum computing. It has been extensively studied and applied in a variety of quantum applications such as the Shor's factoring algorithm, quantum sampling algorithms and the calculation of the eigenvalues of unitary matrices. The QPE algorithm has been combined with Kitaev's algorithm and the inverse quantum Fourier transform (IQFT) which are utilized as a fundamental component of such quantum algorithms. In this paper, we explore the computational challenges of implementing QPE algorithms on noisy intermediate-scale quantum (NISQ) machines using the IBM Q Experience (e.g., the IBMQX4, 5-qubit quantum computing hardware platform). Our experimental results indicate that the accuracy of finding the phase using these QPE algorithms is severely constrained by the NISQ computer's physical characteristics such as coherence time and error rates. To mitigate these physical limitations, we propose implementing a modified solution by reducing the number of controlled rotation gates and phase shift operations, thereby increasing the accuracy of the finding phase in near-term quantum computers.
This thesis looks at how we can leverage current and near future quantum computers to effectively simulate quantum field theories. The scope of this thesis covers how to simulate the (1+1)-D Transverse Ising model on digital quantum computers and the methods to handle multiple types of machine errors to effectively extract real-time dynamic information. We leverage modifications to the transverse Ising model to study the calculation of phase shifts from scattering a particle off of simple potentials and demonstrate that these calculations are feasible on current quantum hardware. In looking toward the future we demonstrate two different state preparation algorithms. One algorithm projected cooling we show can extract information about the second order phase transition in the Transverse Ising Model and has excellent scaling properties. The second algorithm involves leveraging classical field theory simulations to circumvent quantum state preparation methods on that should prove tractable on near term quantum computing hardware. These tools together highlight the promise of quantum computing to tackle interesting problems in high energy physics.
We investigate one-dimensional quantum wave-packet dynamics using a grid-based encoding of the wave function onto qubit registers. Time evolution is implemented using a split operator approach, with the kinetic energy operator realized via the Quantum Fourier Transform (QFT) and arbitrary discretized potentials represented by commuting Pauli-Z gates. The algorithm is benchmarked against classical grid-based simulations and validated using a noiseless Qiskit Statevector simulator before being implemented on current quantum hardware (IBM Quantum and IonQ) for qubit counts ranging from two to five. Good agreement with benchmark calculations is obtained for two- and three-qubit implementations, while deviations increase at larger qubit counts due to hardware noise and increased circuit depth. Among the devices examined, the algorithm maintains closer agreement with the benchmark on the trapped-ion IonQ Forte processor as the number of qubits increases.