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Quantum simulation of quantum field theory is a flagship application of quantum computers that promises to deliver capabilities beyond classical computing. The realization of quantum advantage will require methods to accurately predict error scaling as a function of the resolution and parameters of the model that can be implemented efficiently on quantum hardware. In this paper, we address the representation of lattice bosonic fields in a discretized field amplitude basis, develop methods to predict error scaling, and present efficient qubit implementation strategies. A low-energy subspace of the bosonic Hilbert space, defined by a boson occupation cutoff, can be represented with exponentially good accuracy by a low-energy subspace of a finite size Hilbert space. The finite representation construction and the associated errors are directly related to the accuracy of the Nyquist-Shannon sampling and the Finite Fourier transforms of the boson number states in the field and the conjugate-field bases. We analyze the relation between the boson mass, the discretization parameters used for wavefunction sampling and the finite representation size. Numerical simulations of small size $Phi^4$ problems demonstrate that the boson mass optimizing the sampling of the ground state wavefunction is a good approximation to the optimal boson mass yielding the minimum low-energy subspace size. However, we find that accurate sampling of general wavefunctions does not necessarily result in accurate representation. We develop methods for validating and adjusting the discretization parameters to achieve more accurate simulations.
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Intermediate-scale quantum technologies provide unprecedented opportunities for scientific discoveries while posing the challenge of identifying important problems that can take advantage of them through algorithmic innovations. A major open problem in quantum many-body physics is the table-top generation and detection of emergent excitations analogous to gravitons -- the elusive mediators of gravitational force in a quantum theory of gravity. In solid-state materials, fractional quantum Hall phases are one of the leading platforms for realizing graviton-like excitations. However, their direct observation remains an experimental challenge. Here, we generate these excitations on the IBM quantum processor. We first identify an effective one-dimensional model that captures the geometric properties and graviton dynamics of fractional quantum Hall states. We then develop an efficient, optimal-control-based variational quantum algorithm to simulate geometric quench and the subsequent graviton dynamics, which we successfully implement on the IBM quantum computer. Our results open a new avenue for studying the emergence of gravitons in a new class of tractable models that lend themselves to direct implementations on the existing quantum hardware.
It is imperative that useful quantum computers be very difficult to simulate classically; otherwise classical computers could be used for the applications envisioned for the quantum ones. Perfect quantum computers are unarguably exponentially difficult to simulate: the classical resources required grow exponentially with the number of qubits $N$ or the depth $D$ of the circuit. Real quantum computing devices, however, are characterized by an exponentially decaying fidelity $mathcal{F} sim (1-epsilon)^{ND}$ with an error rate $epsilon$ per operation as small as $approx 1%$ for current devices. In this work, we demonstrate that real quantum computers can be simulated at a tiny fraction of the cost that would be needed for a perfect quantum computer. Our algorithms compress the representations of quantum wavefunctions using matrix product states (MPS), which capture states with low to moderate entanglement very accurately. This compression introduces a finite error rate $epsilon$ so that the algorithms closely mimic the behavior of real quantum computing devices. The computing time of our algorithm increases only linearly with $N$ and $D$. We illustrate our algorithms with simulations of random circuits for qubits connected in both one and two dimensional lattices. We find that $epsilon$ can be decreased at a polynomial cost in computing power down to a minimum error $epsilon_infty$. Getting below $epsilon_infty$ requires computing resources that increase exponentially with $epsilon_infty/epsilon$. For a two dimensional array of $N=54$ qubits and a circuit with Control-Z gates, error rates better than state-of-the-art devices can be obtained on a laptop in a few hours. For more complex gates such as a swap gate followed by a controlled rotation, the error rate increases by a factor three for similar computing time.
We present a quantum algorithm for simulation of quantum field theory in the light-front formulation and demonstrate how existing quantum devices can be used to study the structure of bound states in relativistic nuclear physics. Specifically, we apply the Variational Quantum Eigensolver algorithm to find the ground state of the light-front Hamiltonian obtained within the Basis Light-Front Quantization framework. As a demonstration, we calculate the mass, mass radius, decay constant, electromagnetic form factor, and charge radius of the pion on the IBMQ Vigo chip. We consider two implementations based on different encodings of physical states, and propose a development that may lead to quantum advantage. This is the first time that the light-front approach to quantum field theory has been used to enable simulation of a real physical system on a quantum computer.
A classical local cellular automaton can describe an interacting quantum field theory for fermions. We construct a simple classical automaton for a particular version of the Thirring model with imaginary coupling. This interacting fermionic quantum field theory obeys a unitary time evolution and shows all properties of quantum mechanics. Classical cellular automata with probabilistic initial conditions admit a description in the formalism of quantum mechanics. Our model exhibits interesting features as spontaneous symmetry breaking or solitons. The same model can be formulated as a generalized Ising model. This euclidean lattice model can be investigated by standard techniques of statistical physics as Monte Carlo simulations. Our model is an example how quantum mechanics emerges from classical statistics.
Quantum field theory (QFT) simulations are a potentially important application for noisy intermediate scale quantum (NISQ) computers. The ability of a quantum computer to emulate a QFT, therefore, constitutes a natural application-centric benchmark. Foundational quantum algorithms to simulate QFT processes rely on fault-tolerant computational resources, but to be useful on NISQ machines, error-resilient algorithms are required. Here we outline and implement a hybrid algorithm to calculate the lowest energy levels of the paradigmatic 1+1--dimensional interacting scalar QFT. We calculate energy splittings and compare results with experimental values obtained on currently available quantum hardware. We show that the accuracy of mass-renormalization calculations represents a useful metric with which near-term hardware may be benchmarked. We also discuss the prospects of scaling the algorithm to full simulation of interacting QFTs on future hardware.
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