Mixed-state Quantum Phases: Renormalization and Quantum Error Correction

• URL: http://arxiv.org/abs/2310.08639v1
• Date: Thu, 12 Oct 2023 18:02:35 GMT
• Title: Mixed-state Quantum Phases: Renormalization and Quantum Error Correction
• Authors: Shengqi Sang, Yijian Zou, Timothy H. Hsieh
• Abstract summary: We establish that two mixed states are in the same phase, as defined by their two-way connectivity via local quantum channels. We also discover a precise relation between mixed state phase and decodability, by proving that local noise acting on toric code cannot destroy logical information.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Open system quantum dynamics can generate a variety of long-range entangled mixed states, yet it has been unclear in what sense they constitute phases of matter. To establish that two mixed states are in the same phase, as defined by their two-way connectivity via local quantum channels, we use the renormalization group (RG) and decoders of quantum error correcting codes. We introduce a real-space RG scheme for mixed states based on local channels which ideally preserve correlations with the complementary system, and we prove this is equivalent to the reversibility of the channel's action. As an application, we demonstrate an exact RG flow of finite temperature toric code in two dimensions to infinite temperature, thus proving it is in the trivial phase. In contrast, for toric code subject to local dephasing, we establish a mixed state toric code phase using local channels obtained by truncating an RG-type decoder and the minimum weight perfect matching decoder. We also discover a precise relation between mixed state phase and decodability, by proving that local noise acting on toric code cannot destroy logical information without bringing the state out of the toric code phase.

Related papers

• Perturbative stability and error correction thresholds of quantum codes [0.029541734875307393]
  Topologically-ordered phases are stable to local perturbations, and topological quantum error-correcting codes enjoy thresholds to local errors. We construct classical statistical mechanics models for decoding general CSS codes and classical linear codes. For CSS codes satisfying the LDPC condition and with a sufficiently large code distance, we prove the existence of a low temperature ordered phase.
  arXiv  Detail & Related papers  (2024-06-22T06:46:41Z)
• Low-overhead non-Clifford fault-tolerant circuits for all non-chiral abelian topological phases [0.7873629568804646]
  We propose a family of explicit geometrically local circuits on a 2-dimensional planar grid of qudits. These circuits are constructed from measuring 1-form symmetries in discrete fixed-point path integrals. We prove fault tolerance under arbitrary local (including non-Pauli) noise for a very general class of topological circuits.
  arXiv  Detail & Related papers  (2024-03-18T18:00:00Z)
• The Stability of Gapped Quantum Matter and Error-Correction with Adiabatic Noise [0.0]
  We argue that a quantum code can recover from adiabatic noise channels, corresponding to random adiabatic drift of code states through the phase. We show examples in which quantum information can be recovered by using stabilizer measurements and Pauli feedback, even up to a phase boundary.
  arXiv  Detail & Related papers  (2024-02-22T19:00:00Z)
• Quantum process tomography of continuous-variable gates using coherent states [49.299443295581064]
  We demonstrate the use of coherent-state quantum process tomography (csQPT) for a bosonic-mode superconducting circuit. We show results for this method by characterizing a logical quantum gate constructed using displacement and SNAP operations on an encoded qubit.
  arXiv  Detail & Related papers  (2023-03-02T18:08:08Z)
• Deep Quantum Error Correction [73.54643419792453]
  Quantum error correction codes (QECC) are a key component for realizing the potential of quantum computing. In this work, we efficiently train novel emphend-to-end deep quantum error decoders. The proposed method demonstrates the power of neural decoders for QECC by achieving state-of-the-art accuracy.
  arXiv  Detail & Related papers  (2023-01-27T08:16:26Z)
• Channeling quantum criticality [0.0]
  We analyze the effect of decoherence, modelled by local quantum channels, on quantum critical states. We find universal properties of the resulting mixed state's entanglement, both between system and environment and within the system. Our results are relevant to quantum critical states realized on noisy quantum simulators.
  arXiv  Detail & Related papers  (2023-01-17T19:12:15Z)
• 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)
• Dense Coding with Locality Restriction for Decoder: Quantum Encoders vs. Super-Quantum Encoders [67.12391801199688]
  We investigate dense coding by imposing various locality restrictions to our decoder. In this task, the sender Alice and the receiver Bob share an entangled state.
  arXiv  Detail & Related papers  (2021-09-26T07:29:54Z)
• Decodable hybrid dynamics of open quantum systems with Z_2 symmetry [0.0]
  We explore a class of "open" quantum circuit models with local decoherence ("noise") and local projective measurements. Within the spin glass phase the circuit dynamics can be interpreted as a quantum repetition code. We devise a novel decoding algorithm for recovering an arbitrary initial qubit state in the code space.
  arXiv  Detail & Related papers  (2021-08-09T18:07:55Z)
• Performance of teleportation-based error correction circuits for bosonic codes with noisy measurements [58.720142291102135]
  We analyze the error-correction capabilities of rotation-symmetric codes using a teleportation-based error-correction circuit. We find that with the currently achievable measurement efficiencies in microwave optics, bosonic rotation codes undergo a substantial decrease in their break-even potential.
  arXiv  Detail & Related papers  (2021-08-02T16:12:13Z)
• Hardware-Encoding Grid States in a Non-Reciprocal Superconducting Circuit [62.997667081978825]
  We present a circuit design composed of a non-reciprocal device and Josephson junctions whose ground space is doubly degenerate and the ground states are approximate codewords of the Gottesman-Kitaev-Preskill (GKP) code. We find that the circuit is naturally protected against the common noise channels in superconducting circuits, such as charge and flux noise, implying that it can be used for passive quantum error correction.
  arXiv  Detail & Related papers  (2020-02-18T16:45:09Z)

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.