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arXiv:2007.04447 · Physical review. D/Physical review. D.

Algorithm for quantum computation of particle decays

Anthony N. Ciavarella

Published Nov 6, 2020• 33 citations
arXivHTMLPDF

Abstract

A quantum algorithm is developed to calculate decay rates and cross sections using quantum resources that scale polynomially in the system size assuming similar scaling for state preparation and time evolution. This is done by computing finite-volume one- and two-particle Green's functions on the quantum hardware. Particle decay rates and two-particle scattering cross sections are extracted from the imaginary parts of the Green's function. A $0+1$ dimensional implementation of this method is demonstrated on IBM's superconducting quantum hardware for the decay of a heavy scalar particle to a pair of light scalars.

DOI
10.1103/physrevd.102.094505

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A quantum algorithm is developed to calculate decay rates and cross sections using quantum resources that scale polynomially in the system size assuming similar scaling for state preparation and time evolution. This is done by computing finite-volume one- and two-particle Green's functions on the quantum hardware. Particle decay rates and two-particle scattering cross sections are extracted from the imaginary parts of the Green's function. A 0+10+10+1 dimensional implementation of this method is demonstrated on IBM's superconducting quantum hardware for the decay of a heavy scalar particle to a pair of light scalars.
Green’s function methods lead to ab initio, systematically improvable simulations of molecules and materials while providing access to multiple experimentally observable properties such as the density of states and the spectral function. The calculation of the exact one-particle Green’s function remains a significant challenge for classical computers and was attempted only on very small systems. Here, we present a hybrid quantum-classical algorithm to calculate the imaginary-time one-particle Green’s function. The proposed algorithm combines the variational quantum eigensolver and the quantum subspace expansion methods to calculate Green’s function in Lehmann’s representation. We demonstrate the validity of this algorithm by simulating H 2 and H 4 on quantum simulators and on IBM’s quantum devices.
The description of quantum many-body dynamics is extremely challenging on classical computers, as it can involve many degrees of freedom. On the other hand, the time evolution of quantum states is a natural application for quantum computers that are designed to efficiently perform unitary transformations. In this paper, we study quantum algorithms for response functions, relevant for describing different reactions governed by linear response. We focus on nuclear-physics applications and consider a qubit-efficient mapping on the lattice, which can efficiently represent the large volumes required for realistic scattering simulations. For the case of a contact interaction, we develop an algorithm for time evolution based on the Trotter approximation that scales logarithmically with the lattice size, and is combined with quantum phase estimation. We eventually focus on the nuclear two-body system and a typical response function relevant for electron scattering as an example. We also investigate ground-state preparation and examine the total circuit depth required for a realistic calculation and the hardware noise level required to interpret the signal.
We describe a method for obtaining the scattering matrix for nuclear or chemical reactions on a finite lattice. Aside from the preparation of the initial and final states as wave packets, the only other operation required is unitary time evolution, making this approach ideal for simulations on quantum hardware. The central quantity is a time-dependent overlap between incoming and outgoing wave packets whose Fourier transform corresponds to the scattering matrix at fixed energy, from which one can calculate elastic and inelastic cross sections for reactions involving two interacting clusters. Working in Cartesian coordinates enables an efficient encoding of the problem on quantum hardware via the first quantization mapping, with favorable qubit scaling for describing asymptotic scattering states. Within this framework, we describe a quantum algorithm for probing the scattering amplitude through different angles, including the forward direction, which provides access to the total cross section via the optical theorem. We demonstrate our methods through a series of numerical examples, for both elastic and inelastic processes, comparing against exact calculations. The techniques we describe can more readily be extended to a large number of constituent particles than other existing approaches, once fault-tolerant quantum hardware becomes available.
Simulations of collisions of fundamental particles on a quantum computer are expected to have an exponential advantage over classical methods and promise to enhance searches for new physics. Furthermore, scattering in scalar field theory has been shown to be BQP-complete, making it a representative problem for which quantum computation is efficient. As a step toward large-scale quantum simulations of collision processes, scattering of wavepackets in one-dimensional scalar field theory is simulated using 120 qubits of IBM's Heron superconducting quantum computer ibm_fez. Variational circuits compressing vacuum preparation, wavepacket initialization, and time evolution are determined using classical resources. By leveraging physical properties of states in the theory, such as symmetries and locality, the variational quantum algorithm constructs scalable circuits that can be used to simulate arbitrarily-large system sizes. A new strategy is introduced to mitigate errors in quantum simulations, which enables the extraction of meaningful results from circuits with up to 4924 two-qubit gates and two-qubit gate depths of 103. The effect of interactions is clearly seen, and is found to be in agreement with classical Matrix Product State simulations. The developments that will be necessary to simulate high-energy inelastic collisions on a quantum computer are discussed.