Measurement-induced phase transitions in sparse nonlocal scramblers

Abstract

Measurement-induced phase transitions arise due to a competition between the scrambling of quantum information in a many-body system and local measurements. In this work we investigate these transitions in different classes of fast scramblers, systems that scramble quantum information as quickly as is conjectured to be possible -on a timescale proportional to the logarithm of the system size. In particular, we consider sets of deterministic sparse couplings that naturally interpolate between local circuits that slowly scramble information and highly nonlocal circuits that achieve the fast-scrambling limit. We find that circuits featuring sparse nonlocal interactions are able to withstand substantially higher rates of local measurement than circuits with only local interactions, even at comparable gate depths. We also study the quantum error-correcting codes that support the volume-law entangled phase and find that our maximally nonlocal circuits yield codes with nearly extensive contiguous code distance. Use of these sparse, deterministic circuits opens pathways towards the design of noise-resilient quantum circuits and error correcting codes in current and future quantum devices with minimum gate numbers.

Entanglement Transitions from Stochastic Resetting of Non-Hermitian Quasiparticles

“…Recently, a new class of phase transitions characterized by a qualitative change of the entanglement properties has been identified for quantum many-body systems under the effect of stochastic measurements [12][13][14][15]. For hybrid quantum circuits with random unitary gates and projective measurements this protocol leads to an entanglement transition between an error correcting/volume law phase and a Zeno phase with area-law scaling [12][13][14][16][17][18][19][20][21][22][23]. Several aspects of this transition have been discussed, including its critical properties [24][25][26][27][28][29][30][31][32], the role of symmetries [33] and dimensionality [34][35][36][37].…”

Tunable Geometries in Sparse Clifford Circuits

“…During the 'even' block, a gate Q ij is placed between qubits i < j with probability p(|i − j|, s) if and only if mod( i/2 m−1 , 2) = 0. During the subsequent odd block, gates are placed according to the same rules but with the odd-bricklayer condition mod( i/2 m−1 , 2) = 1 [46]. Throughout the paper a single timestep δt corresponds to applying a single even block followed by a single odd block.…”