Quantum Imaginary Time Evolution Algorithm for Quantum Field Theories with Continuous Variables

Abstract

We calculate the energy levels and corresponding eigenstates of an interacting scalar quantum field theory on a lattice using a continuous-variable version of the quantum imaginary time evolution algorithm. Only a single qumode is needed for the simulation of the field at each point on the lattice. Our quantum algorithm avoids the use of non-Gaussian quantum gates and relies, instead, on detectors projecting onto eigenstates of the photon-number operator. Using Xanadu's Strawberry Fields simulator, we obtain results on energy levels that are in very good agreement with results from exact calculations. We propose an experimental setup that can be realized with existing technology.

References in corpus (7)

• Quantum computational advantage using photons
• Integrated Photonic Quantum Technologies
• Quantum circuits with many photons on a programmable nanophotonic chip
• Repeat-until-success cubic phase gate for universal continuous-variable quantum computation
• Single-particle digitization strategy for quantum computation of a ${\varphi }^4$ scalar field theory
• A Quantum Approximate Optimization Algorithm for continuous problems
• Toward simulating quantum field theories with controlled phonon-ion dynamics: A hybrid analog-digital approach

Cited by in corpus (21)

• Quantum Simulation for High Energy Physics
• Quantum Machine Learning for Chemistry and Physics
• Preparations for Quantum Simulations of Quantum Chromodynamics in 1+1 Dimensions: (I) Axial Gauge
• Preparations for Quantum Simulations of Quantum Chromodynamics in 1+1 Dimensions: (II) Single-Baryon $\beta$-Decay in Real Time
• Quantum Machine Learning in Drug Discovery: Applications in Academia and Pharmaceutical Industries
• Medium induced jet broadening in a quantum computer
• Simulating quantum field theories on continuous-variable quantum computers
• State Preparation in the Heisenberg Model through Adiabatic Spiraling
• Preparation for Quantum Simulation of the 1+1D O(3) Non-linear σ-Model using Cold Atoms
• Variational quantum iterative power algorithms for global optimization
• Continuous variable quantum computation of the $O(3)$ model in 1+1 dimensions
• Exactly solvable non-unitary time evolution in quantum critical systems I: Effect of complex spacetime metrics
• Toward hybrid quantum simulations with qubits and qumodes on trapped-ion platforms
• Photonic counterdiabatic quantum optimization algorithm
• Imaginary-time Mpemba effect in quantum many-body systems
• Qumode transfer between continuous and discrete variable devices
• Quantum many-body simulation of finite-temperature systems with sampling a series expansion of a quantum imaginary-time evolution
• Modeling Non-Covalent Interatomic Interactions on a Photonic Quantum Computer
• Robust preparation of ground state phases under noisy imaginary time evolution
• Quantum Imaginary-Time Evolution with Polynomial Resources in Evolution Time
• Probabilistic imaginary-time evolution by using forward and backward real-time evolution with a single ancilla: first-quantized eigensolver of quantum chemistry for ground states