@article {3504, title = {Phase transition in magic with random quantum circuits}, year = {2024}, month = {4/11/2024}, abstract = {

Magic is a property of quantum states that enables universal fault-tolerant quantum computing using simple sets of gate operations. Understanding the mechanisms by which magic is created or destroyed is, therefore, a crucial step towards efficient and practical fault-tolerant computation. We observe that a random stabilizer code subject to coherent errors exhibits a phase transition in magic, which we characterize through analytic, numeric and experimental probes. Below a critical error rate, stabilizer syndrome measurements remove the accumulated magic in the circuit, effectively protecting against coherent errors; above the critical error rate syndrome measurements concentrate magic. A better understanding of such rich behavior in the resource theory of magic could shed more light on origins of quantum speedup and pave pathways for more efficient magic state generation.

}, url = {https://arxiv.org/abs/2304.10481}, author = {Pradeep Niroula and Christopher David White and Qingfeng Wang and Sonika Johri and Daiwei Zhu and Christopher Monroe and Crystal Noel and Michael Gullans} } @article {3148, title = {Mana and thermalization: Probing the feasibility of near-Clifford Hamiltonian simulation}, journal = {Physical Review B}, volume = {106}, year = {2022}, month = {9/28/2022}, abstract = {

Quantum hydrodynamics is the emergent classical dynamics governing transport of conserved quantities in generic strongly-interacting quantum systems. Recent matrix product operator methods have made simulations of quantum hydrodynamics in 1+1d tractable, but they do not naturally generalize to 2+1d or higher, and they offer limited guidance as to the difficulty of simulations on quantum computers. Near-Clifford simulation algorithms are not limited to one dimension, and future error-corrected quantum computers will likely be bottlenecked by non-Clifford operations. We therefore investigate the non-Clifford resource requirements for simulation of quantum hydrodynamics using {\textquoteleft}{\textquoteleft}mana\&$\#$39;\&$\#$39;, a resource theory of non-Clifford operations. For infinite-temperature starting states we find that the mana of subsystems quickly approaches zero, while for starting states with energy above some threshold the mana approaches a nonzero value. Surprisingly, in each case the finite-time mana is governed by the subsystem entropy, not the thermal state mana; we argue that this is because mana is a sensitive diagnostic of finite-time deviations from canonical typicality.

}, doi = {10.1103/physrevb.106.125130}, url = {https://arxiv.org/abs/2201.12367}, author = {Troy J. Sewell and Christopher David White} } @article {2638, title = {Conformal field theories are magical}, journal = {Physical Review B}, volume = {103}, year = {2021}, month = {2/25/2021}, pages = {075145}, abstract = {

\"Magic\" is the degree to which a state cannot be approximated by Clifford gates. We study mana, a measure of magic, in the ground state of the Z3 Potts model, and argue that it is a broadly useful diagnostic for many-body physics. In particular we find that the q=3 ground state has large mana at the model\&$\#$39;s critical point, and that this mana resides in the system\&$\#$39;s correlations. We explain the form of the mana by a simple tensor-counting calculation based on a MERA representation of the state. Because mana is present at all length scales, we conclude that the conformal field theory describing the 3-state Potts model critical point is magical. These results control the difficulty of preparing the Potts ground state on an error-corrected quantum computer, and constrain tensor network models of AdS-CFT.

}, doi = {https://journals.aps.org/prb/pdf/10.1103/PhysRevB.103.075145}, url = {https://arxiv.org/abs/2007.01303}, author = {Christopher David White and ChunJun Cao and Brian Swingle} } @article {2871, title = {Localization crossover and subdiffusive transport in a classical facilitated network model of a disordered, interacting quantum spin chain}, year = {2021}, month = {9/22/2021}, abstract = {

We consider the random-field Heisenberg model, a paradigmatic model for many-body localization (MBL), and add a Markovian dephasing bath coupled to the Anderson orbitals of the model\&$\#$39;s non-interacting limit. We map this system to a classical facilitated hopping model that is computationally tractable for large system sizes, and investigate its dynamics. The classical model exhibits a robust crossover between an ergodic (thermal) phase and a frozen (localized) phase. The frozen phase is destabilized by thermal subregions (bubbles), which thermalize surrounding sites by providing a fluctuating interaction energy and so enable off-resonance particle transport. Investigating steady state transport, we observe that the interplay between thermal and frozen bubbles leads to a clear transition between diffusive and subdiffusive regimes. This phenomenology both describes the MBL system coupled to a bath, and provides a classical analogue for the many-body localization transition in the corresponding quantum model, in that the classical model displays long local memory times. It also highlights the importance of the details of the bath coupling in studies of MBL systems coupled to thermal environments.

}, url = {https://arxiv.org/abs/2109.10926}, author = {Kai Klocke and Christopher David White and Michael Buchhold} }