Controlled Gate Networks: Theory and Application to Eigenvalue Estimation

Abstract

We introduce a new scheme for quantum circuit design called controlled gate networks. Rather than trying to reduce the complexity of individual unitary operations, the new strategy is to toggle between all of the unitary operations needed with the fewest number of gates. We present the general theory of controlled gate networks and show that, under quite general conditions, it can significantly reduce the number of two-qubit gates needed to produce linear combinations of unitary operators. The first example we consider is a variational subspace calculation for a two-qubit system. The second example is estimating the eigenvalues of a two-qubit Hamiltonian via the rodeo algorithm using operators that we call controlled reversal gates. We use the Quantinuum H1-2 and IBM Perth devices to realize the quantum circuits. The third example is the application of controlled gate networks to the controlled time evolution of a free nucleon on a three-dimensional lattice. For all of the examples, we show very substantial reductions in the number of two-qubit gates required. Our work demonstrates that controlled gate networks are a useful tool for reducing gate complexity in quantum algorithms for quantum many-body problems such as those relevant to nuclear physics.

Final version to appear in Eur. Phys. J. A (31 pages, 20 figures)

References in corpus (61)

• Hamiltonian Simulation by Qubitization
• Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
• Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
• Quantum-assisted quantum compiling
• Lattice simulations for few- and many-body systems
• Simulating quantum many-body dynamics on a current digital quantum computer
• Non-Empirical Interactions for the Nuclear Shell Model: An Update
• Finding Exponential Product Formulas of Higher Orders
• Ab initio limits of atomic nuclei
• Ab initio no-core full configuration calculations of light nuclei
• Exponential improvement in precision for simulating sparse Hamiltonians
• Ab Initio Treatment of Collective Correlations and the Neutrinoless Double Beta Decay of ${}^{48}$Ca
• Accurate bulk properties of nuclei from $A=2$ to $\infty$ from potentials with $\Delta$ isobars
• Light-nuclei spectra from chiral dynamics
• Eigenvector continuation with subspace learning
• Quantum Simulating Nature's Fundamental Fields
• Symmetry restoration in mean-field approaches
• Efficient quantum circuits for quantum computational chemistry
• Quantum Krylov subspace algorithms for ground and excited state energy estimation
• Quantum circuit optimizations for NISQ architectures
• Physics of nuclei: Key role of an emergent symmetry
• Linear Response on a Quantum Computer
• Auxiliary field diffusion Monte Carlo calculations of light and medium-mass nuclei with local chiral interactions
• Quantum Computing for Neutrino-nucleus Scattering
• Rodeo Algorithm for Quantum Computing
• Essential elements for nuclear binding
• Bogoliubov Many-Body Perturbation Theory for Open-Shell Nuclei
• Ab initio optical potentials and nucleon scattering on medium mass nuclei
• Ab initio predictions for polarized DT thermonuclear fusion
• Quantum Filter Diagonalization: Quantum Eigendecomposition without Full Quantum Phase Estimation
• Improved Error-Scaling for Adiabatic Quantum State Transfer
• A theory of quantum subspace diagonalization
• Emergent geometry and duality in the carbon nucleus
• Wavefunction matching for solving quantum many-body problems
• Ab initio computation of the longitudinal response function in ${}^{40}$Ca
• Shell-model coupled-cluster method for open-shell nuclei
• Accessing ground state and excited states energies in many-body system after symmetry restoration using quantum computers
• Eigenvector Continuation and Projection-Based Emulators
• Alpha clustering and alpha-capture reaction rate from ab initio symmetry-adapted description of ${}^{20}$Ne
• Spectral density estimation with the Gaussian Integral Transform
• Self-consistent Green's function approaches
• Imaginary Time Propagation on a Quantum Chip
• Exact and practical pattern matching for quantum circuit optimization
• A Comprehensive Review of Quantum Circuit Optimization: Current Trends and Future Directions
• Isospin-symmetry restoration within the nuclear density functional theory: formalism and applications
• Hypernuclear No-Core Shell Model
• Effective interactions in the sd shell
• Machine learning-based inversion of nuclear responses
• Bogoliubov many-body perturbation theory under constraint
• Symmetry breaking/symmetry preserving circuits and symmetry restoration on quantum computers: A quantum many-body perspective
• Filtering states with total spin on a quantum computer
• Ab initio study of the beryllium isotopes ${}^7$Be to ${}^{12}$Be
• Clustering of Four-Component Unitary Fermions
• Wigner SU(4) symmetry, clustering, and the spectrum of ${}^{12}$C
• Quantum Monte Carlo in Configuration Space with Three-Nucleon Forces
• Demonstration of the Rodeo Algorithm on a Quantum Computer
• Quantum Eigenvector Continuation for Chemistry Applications
• Floating block method for quantum Monte Carlo simulations
• Subspace Diagonalization on Quantum Computers using Eigenvector Continuation
• Quantum techniques for eigenvalue problems
• Quantum algorithms for optimal effective theory of many-body systems

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