Conformal field theories have been extremely useful in our quest to understand physical phenomena in many different branches of physics, starting from condensed matter all the way up to high energy. Here we discuss applications of two-dimensional conformal field theories to fault-tolerant quantum computation based on the coset $ SU(2)_1^{\otimes k} / SU(2)_{k}$. We calculate higher-dimensional braiding matrices by considering conformal blocks involving $2N$ anyons, and search for gapped states that can be built from these conformal blocks. We introduce a gapped wavefunction that generalizes the Moore-Read state which is based on the critical Ising model, and show that our generalization leads to universal quantum computing.Conformal field theories have been extremely useful in our quest to understand physical phenomena in many different branches of physics, starting from condensed matter all the way up to high energy. Here we discuss applications of two-dimensional conformal field theories to fault-tolerant quantum computation based on the coset $ SU(2)_1^{\otimes k} / SU(2)_{k}$. We calculate higher-dimensional braiding matrices by considering conformal blocks involving $2N$ anyons, and search for gapped states that can be built from these conformal blocks. We introduce a gapped wavefunction that generalizes the Moore-Read state which is based on the critical Ising model, and show that our generalization leads to universal quantum computing.

arXiv:2112.06144Dec 12, 20210 citations

Of topology and low-dimensionality

Nature PhysicsNov 1, 20161 citation

QUEST: systematically approximating Quantum circuits for higher output fidelity

Tirthak Patel, Ed Younis, Costin Iancu +2 more

We present QUEST, a procedure to systematically generate approximations for quantum circuits to reduce their CNOT gate count. Our approach employs circuit partitioning for scalability with procedures to 1) reduce circuit length using approximate synthesis, 2) improve fidelity by running circuits that represent key samples in the approximation space, and 3) reason about approximation upper bound. Our evaluation results indicate that our approach of "dissimilar" approximations provides close fidelity to the original circuit. Overall, the results indicate that QUEST can reduce CNOT gate count by 30-80% on ideal systems and decrease the impact of noise on existing and near-future quantum systems.We present QUEST, a procedure to systematically generate approximations for quantum circuits to reduce their CNOT gate count. Our approach employs circuit partitioning for scalability with procedures to 1) reduce circuit length using approximate synthesis, 2) improve fidelity by running circuits that represent key samples in the approximation space, and 3) reason about approximation upper bound. Our evaluation results indicate that our approach of "dissimilar" approximations provides close fidelity to the original circuit. Overall, the results indicate that QUEST can reduce CNOT gate count by 30-80% on ideal systems and decrease the impact of noise on existing and near-future quantum systems.

International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS)Feb 22, 202252 citations

On general- n coefficients in series expansions for row spin–spin correlation functions in the two-dimensional Ising model

Robert E. Shrock

Abstract We consider spin–spin correlation functions for spins along a row, R n = ⟨ σ 0,0 σ n ,0 ⟩, in the two-dimensional Ising model. We discuss a method for calculating general- n expressions for coefficients in high-temperature and low-temperature series expansions of R n and apply it to obtain such expressions for several higher-order coefficients. In addition to their intrinsic interest, these results could be useful in the continuing quest for a nonlinear ordinary differential equation whose solution would determine R n , analogous to the known nonlinear ordinary differential equation whose solution determines the diagonal correlation function ⟨ σ 0,0 σ n , n ⟩ in this model.Abstract We consider spin–spin correlation functions for spins along a row, R n = ⟨ σ 0,0 σ n ,0 ⟩, in the two-dimensional Ising model. We discuss a method for calculating general- n expressions for coefficients in high-temperature and low-temperature series expansions of R n and apply it to obtain such expressions for several higher-order coefficients. In addition to their intrinsic interest, these results could be useful in the continuing quest for a nonlinear ordinary differential equation whose solution would determine R n , analogous to the known nonlinear ordinary differential equation whose solution determines the diagonal correlation function ⟨ σ 0,0 σ n , n ⟩ in this model.

arXiv:2207.09268Journal of Physics A Mathematical and TheoreticalSep 29, 20220 citations

Higher dimensions

Noriaki Horiuchi

Nature PhotonicsMay 28, 20140 citations

2N

anyons, and search for gapped states that can be built from these conformal blocks. We introduce a gapped wavefunction that generalizes the Moore-Read state which is based on the critical Ising model, and show that our generalization leads to universal quantum computing.