Stabilization of symmetry-protected long-range entanglement in stochastic quantum circuits

• URL: http://arxiv.org/abs/2306.13008v3
• Date: Fri, 26 Jul 2024 20:52:43 GMT
• Title: Stabilization of symmetry-protected long-range entanglement in stochastic quantum circuits
• Authors: Iosifina Angelidi, Marcin Szyniszewski, Arijeet Pal,
• Abstract summary: We consider quantum circuits in one and two dimensions comprising randomly applied unitary gates and local measurements. In the absence of randomness, the protocol generates a symmetry-protected long-range entangled state in a finite-depth circuit. We find two important time scales that we associate with the emergence of certain symmetry generators.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Long-range entangled states are vital for quantum information processing and quantum metrology. Preparing such states by combining measurements with unitary gates opened new possibilities for efficient protocols with finite-depth quantum circuits. The complexity of these algorithms is crucial for the resource requirements on a large-scale noisy quantum device, while their stability to perturbations decides the fate of their implementation. In this work, we consider stochastic quantum circuits in one and two dimensions comprising randomly applied unitary gates and local measurements. These operations preserve a class of discrete local symmetries, which are broken due to the stochasticity arising from timing and gate imperfections. In the absence of randomness, the protocol generates a symmetry-protected long-range entangled state in a finite-depth circuit. In the general case, by studying the time evolution under this hybrid circuit, we analyze the time to reach the target entangled state. We find two important time scales that we associate with the emergence of certain symmetry generators. The quantum trajectories embody the local symmetry with a time scaling logarithmically with system size, while global symmetries require exponentially long times. We devise error-mitigation protocols that significantly lower both time scales and investigate the stability of the algorithm to perturbations that naturally arise in experiments. We also generalize the protocol to realize toric code and Xu-Moore states in two dimensions, opening avenues for future studies of anyonic excitations. Our results unveil a fundamental relationship between symmetries and dynamics across a range of lattice geometries, which contributes to a broad understanding of the stability of preparation algorithms in terms of phase transitions. Our work paves the way for efficient error correction for quantum state preparation.

Related papers

• Geometric Quantum Machine Learning with Horizontal Quantum Gates [41.912613724593875]
  We propose an alternative paradigm for the symmetry-informed construction of variational quantum circuits. We achieve this by introducing horizontal quantum gates, which only transform the state with respect to the directions to those of the symmetry. For a particular subclass of horizontal gates based on symmetric spaces, we can obtain efficient circuit decompositions for our gates through the KAK theorem.
  arXiv  Detail & Related papers  (2024-06-06T18:04:39Z)
• Quantum quench dynamics as a shortcut to adiabaticity [31.114245664719455]
  We develop and test a quantum algorithm in which the incorporation of a quench step serves as a remedy to the diverging adiabatic timescale. Our experiments show that this approach significantly outperforms the adiabatic algorithm.
  arXiv  Detail & Related papers  (2024-05-31T17:07:43Z)
• Characterizing randomness in parameterized quantum circuits through expressibility and average entanglement [39.58317527488534]
  Quantum Circuits (PQCs) are still not fully understood outside the scope of their principal application. We analyse the generation of random states in PQCs under restrictions on the qubits connectivities. We place a connection between how steep is the increase on the uniformity of the distribution of the generated states and the generation of entanglement.
  arXiv  Detail & Related papers  (2024-05-03T17:32:55Z)
• Unraveling the emergence of quantum state designs in systems with symmetry [15.699822139827916]
  We study the emergence of state designs from the random generator states exhibiting symmetries. We find faster convergence of the trace distance during the early time evolution in comparison to the cases when the symmetry is broken. We expect our findings to pave the way for further exploration of deep thermalization and equilibration of closed and open quantum many-body systems.
  arXiv  Detail & Related papers  (2024-02-14T05:35:03Z)
• Edge modes and symmetry-protected topological states in open quantum systems [0.0]
  Topological order offers possibilities for processing quantum information which can be immune to imperfections. We show robustness of certain aspects of $ZZtimes Z$ symmetry-protected trajectory (SPT) order against a wide class of dissipation channels. Our work thus proposes a novel framework to study the dynamics of dissipative SPT phases.
  arXiv  Detail & Related papers  (2023-10-13T21:09:52Z)
• Optimizing one-axis twists for variational Bayesian quantum metrology [0.0]
  In particular, qubit phase estimation, or rotation sensing, appears as a ubiquitous problem with applications to electric field sensing, magnetometry, atomic clocks, and gyroscopes. We propose a new family of parametrized encoding and decoding protocols called arbitrary-axis twist ansatzes. We show that it can lead to a substantial reduction in the number of one-axis twists needed to achieve a target estimation error.
  arXiv  Detail & Related papers  (2022-12-23T16:45:15Z)
• Quantum error mitigation for rotation symmetric bosonic codes with symmetry expansion [0.2770822269241974]
  We propose a class of quantum error mitigation that virtually projects the state onto the noise-free symmetric subspace. We show that symmetry expansion dramatically suppresses the effect of photon loss. Our novel error mitigation method will significantly enhance computation accuracy in the near-term bosonic quantum computing paradigm.
  arXiv  Detail & Related papers  (2022-11-11T12:33:11Z)
• Simulating scalar field theories on quantum computers with limited resources [62.997667081978825]
  We present a quantum algorithm for implementing $phi4$ lattice scalar field theory on qubit computers. The algorithm allows efficient $phi4$ state preparation for a large range of input parameters in both the normal and broken symmetry phases.
  arXiv  Detail & Related papers  (2022-10-14T17:28:15Z)
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics [62.997667081978825]
  We show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality. We show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators.
  arXiv  Detail & Related papers  (2022-06-03T18:00:02Z)
• 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)
• Measurement-induced topological entanglement transitions in symmetric random quantum circuits [0.0]
  We study a class of (1+1)D symmetric random quantum circuits with two competing types of measurements. The circuit exhibits a rich phase diagram involving robust symmetry-protected topological (SPT), trivial, and volume law entangled phases.
  arXiv  Detail & Related papers  (2020-04-15T18:00:00Z)

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.