Dynamical Magic Transitions in Monitored Clifford+T Circuits

• URL: http://arxiv.org/abs/2312.00132v3
• Date: Sat, 29 Jun 2024 13:44:05 GMT
• Title: Dynamical Magic Transitions in Monitored Clifford+T Circuits
• Authors: Mircea Bejan, Campbell McLauchlan, Benjamin Béri,
• Abstract summary: We study simulability transitions beyond entanglement. We focus on random monitored Clifford circuits doped by T gates. We find cases where transitions in magic and entanglement coincide, but also others with a magic and simulability transition in a highly (volume-law) entangled phase.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The classical simulation of highly-entangling quantum dynamics is conjectured to be generically hard. Thus, recently discovered measurement-induced transitions between highly entangling and low-entanglement dynamics are phase transitions in classical simulability. Here, we study simulability transitions beyond entanglement: noting that some highly-entangling dynamics (e.g., integrable systems or Clifford circuits) are easy to classically simulate, thus requiring "magic"--a subtle form of quantum resource--to achieve computational hardness, we ask how the dynamics of magic competes with measurements. We study the resulting "dynamical magic transitions" focusing on random monitored Clifford circuits doped by T gates (injecting magic). We identify dynamical "stabilizer-purification"--the collapse of a superposition of stabilizer states by measurements--as the mechanism driving this transition. We find cases where transitions in magic and entanglement coincide, but also others with a magic and simulability transition in a highly (volume-law) entangled phase. In establishing our results, we use Pauli-based computation, a scheme distilling the quantum essence of the dynamics to a magic state register subject to mutually commuting measurements. We link stabilizer-purification to "magic fragmentation" wherein these measurements separate into disjoint, O(1)-weight blocks, and relate this to the spread of magic in the original circuit becoming arrested.

Related papers

• Quantum magic dynamics in random circuits [1.9568111750803001]
  Magic refers to the degree of "quantumness" in a system that cannot be fully described by stabilizer states and Clifford operations alone. In quantum computing, stabilizer states and Clifford operations can be efficiently simulated on a classical computer.
  arXiv  Detail & Related papers  (2024-10-28T15:29:21Z)
• Visualizing Dynamics of Charges and Strings in (2+1)D Lattice Gauge Theories [103.95523007319937]
  We study the dynamics of local excitations in a lattice of superconducting qubits. For confined excitations, the magnetic field induces a tension in the string connecting them. Our method allows us to experimentally image string dynamics in a (2+1)D LGT.
  arXiv  Detail & Related papers  (2024-09-25T17:59:05Z)
• Magic transition in measurement-only circuits [0.0]
  We study magic in a measurement-only quantum circuit with competing types of Clifford and non-Clifford measurements. We study the magic transition in this circuit in both one- and two-dimensional lattices using large-scale numerical simulations.
  arXiv  Detail & Related papers  (2024-07-22T18:00:07Z)
• Magic spreading in random quantum circuits [0.0]
  Calderbank-Shor-Steane entropy is a measure of non-stabilizerness. Our main finding is that magic resources equilibrate on timescales logarithmic in system size N. We conjecture that our findings describe the phenomenology of non-stabilizerness growth in a broad class of chaotic many-body systems.
  arXiv  Detail & Related papers  (2024-07-04T13:43:46Z)
• Entanglement-magic separation in hybrid quantum circuits [0.0]
  We study magic, quantified by stabilizer entropy, in a hybrid quantum circuit with projective measurements. We discover a phase transition between a (sub)-extensive and area law scaling of magic controlled by the rate of measurements.
  arXiv  Detail & Related papers  (2023-12-04T16:57:33Z)
• Phase transition in magic with random quantum circuits [1.3551232282678036]
  We observe that a random stabilizer code subject to coherent errors exhibits a phase transition in magic. A better understanding of such rich behavior in the resource theory of magic could shed more light on origins of quantum speedup.
  arXiv  Detail & Related papers  (2023-04-20T17:29:45Z)
• Measurement-induced entanglement and teleportation on a noisy quantum processor [105.44548669906976]
  We investigate measurement-induced quantum information phases on up to 70 superconducting qubits. We use a duality mapping, to avoid mid-circuit measurement and access different manifestations of the underlying phases. Our work demonstrates an approach to realize measurement-induced physics at scales that are at the limits of current NISQ processors.
  arXiv  Detail & Related papers  (2023-03-08T18:41:53Z)
• Reminiscence of classical chaos in driven transmons [117.851325578242]
  We show that even off-resonant drives can cause strong modifications to the structure of the transmon spectrum rendering a large part of it chaotic. Results lead to a photon number threshold characterizing the appearance of chaos-induced quantum demolition effects.
  arXiv  Detail & Related papers  (2022-07-19T16:04:46Z)
• Continuous-time dynamics and error scaling of noisy highly-entangling quantum circuits [58.720142291102135]
  We simulate a noisy quantum Fourier transform processor with up to 21 qubits. We take into account microscopic dissipative processes rather than relying on digital error models. We show that depending on the dissipative mechanisms at play, the choice of input state has a strong impact on the performance of the quantum algorithm.
  arXiv  Detail & Related papers  (2021-02-08T14:55:44Z)
• Universality of entanglement transitions from stroboscopic to continuous measurements [68.8204255655161]
  We show that the entanglement transition at finite coupling persists if the continuously measured system is randomly nonintegrable. This provides a bridge between a wide range of experimental settings and the wealth of knowledge accumulated for the latter systems.
  arXiv  Detail & Related papers  (2020-05-04T21:45:59Z)
• Quantum Zeno effect appears in stages [64.41511459132334]
  In the quantum Zeno effect, quantum measurements can block the coherent oscillation of a two level system by freezing its state to one of the measurement eigenstates. We show that the onset of the Zeno regime is marked by a $textitcascade of transitions$ in the system dynamics as the measurement strength is increased.
  arXiv  Detail & Related papers  (2020-03-23T18:17:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.