Randomly Monitored Quantum Codes

• URL: http://arxiv.org/abs/2402.00145v1
• Date: Wed, 31 Jan 2024 19:53:06 GMT
• Title: Randomly Monitored Quantum Codes
• Authors: Dongjin Lee and Beni Yoshida
• Abstract summary: Recent studies have shown that quantum measurement itself can induce novel quantum phenomena. One example is a monitored random circuit, which can generate long-range entanglement faster than a random unitary circuit. In particular, we demonstrate that for a large class of quantum error-correcitng codes, it is impossible to destroy the encoded information through random single-qubit Pauli measurements.
• Score: 8.557392136621894
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum measurement has conventionally been regarded as the final step in quantum information processing, which is essential for reading out the processed information but collapses the quantum state into a classical state. However, recent studies have shown that quantum measurement itself can induce novel quantum phenomena. One seminal example is a monitored random circuit, which can generate long-range entanglement faster than a random unitary circuit. Inspired by these results, in this paper, we address the following question: When quantum information is encoded in a quantum error-correcting code, how many physical qubits should be randomly measured to destroy the encoded information? We investigate this question for various quantum error-correcting codes and derive the necessary and sufficient conditions for destroying the information through measurements. In particular, we demonstrate that for a large class of quantum error-correcitng codes, it is impossible to destroy the encoded information through random single-qubit Pauli measurements when a tiny portion of physical qubits is still unmeasured. Our results not only reveal the extraordinary robustness of quantum codes under measurement decoherence, but also suggest potential applications in quantum information processing tasks.

Related papers

• The curse of random quantum data [62.24825255497622]
  We quantify the performances of quantum machine learning in the landscape of quantum data. We find that the training efficiency and generalization capabilities in quantum machine learning will be exponentially suppressed with the increase in qubits. Our findings apply to both the quantum kernel method and the large-width limit of quantum neural networks.
  arXiv  Detail & Related papers  (2024-08-19T12:18:07Z)
• Quantum Information Processing with Molecular Nanomagnets: an introduction [49.89725935672549]
  We provide an introduction to Quantum Information Processing, focusing on a promising setup for its implementation. We introduce the basic tools to understand and design quantum algorithms, always referring to their actual realization on a molecular spin architecture. We present some examples of quantum algorithms proposed and implemented on a molecular spin qudit hardware.
  arXiv  Detail & Related papers  (2024-05-31T16:43:20Z)
• Simple Tests of Quantumness Also Certify Qubits [69.96668065491183]
  A test of quantumness is a protocol that allows a classical verifier to certify (only) that a prover is not classical. We show that tests of quantumness that follow a certain template, which captures recent proposals such as (Kalai et al., 2022) can in fact do much more. Namely, the same protocols can be used for certifying a qubit, a building-block that stands at the heart of applications such as certifiable randomness and classical delegation of quantum computation.
  arXiv  Detail & Related papers  (2023-03-02T14:18:17Z)
• Sample-size-reduction of quantum states for the noisy linear problem [0.0]
  We show that it is possible to reduce a quantum sample size in a quantum random access memory (QRAM) to the linearithmic order. We achieve a shorter run-time for the noisy linear problem.
  arXiv  Detail & Related papers  (2023-01-08T05:53:17Z)
• Quantum Anomaly Detection with a Spin Processor in Diamond [10.0891240648429]
  We experimentally demonstrate the anomaly detection of quantum states encoding audio samples with a three-qubit quantum processor. By training the quantum machine with a few normal samples, the quantum machine can detect the anomaly samples with a minimum error rate of 15.4%.
  arXiv  Detail & Related papers  (2022-01-25T12:18:01Z)
• Characterizing quantum instruments: from non-demolition measurements to quantum error correction [48.43720700248091]
  In quantum information processing quantum operations are often processed alongside measurements which result in classical data. Non-unitary dynamical processes can take place on the system, for which common quantum channel descriptions fail to describe the time evolution. Quantum measurements are correctly treated by means of so-called quantum instruments capturing both classical outputs and post-measurement quantum states.
  arXiv  Detail & Related papers  (2021-10-13T18:00:13Z)
• Depth-efficient proofs of quantumness [77.34726150561087]
  A proof of quantumness is a type of challenge-response protocol in which a classical verifier can efficiently certify quantum advantage of an untrusted prover. In this paper, we give two proof of quantumness constructions in which the prover need only perform constant-depth quantum circuits.
  arXiv  Detail & Related papers  (2021-07-05T17:45:41Z)
• Quantum Algorithm for Quantum State Discrimination via Partial Negation and Weak Measurement [1.2691047660244335]
  A quantum algorithm using weak measurement and partial negation will be proposed to solve the quantum state discrimination problem. The proposed algorithm will be able to determine, with high probability of success, the state of the unknown qubit.
  arXiv  Detail & Related papers  (2021-02-23T21:18:19Z)
• Quantum information spreading in a disordered quantum walk [50.591267188664666]
  We design a quantum probing protocol using Quantum Walks to investigate the Quantum Information spreading pattern. We focus on the coherent static and dynamic disorder to investigate anomalous and classical transport. Our results show that a Quantum Walk can be considered as a readout device of information about defects and perturbations occurring in complex networks.
  arXiv  Detail & Related papers  (2020-10-20T20:03:19Z)
• Maximal entropy approach for quantum state tomography [3.6344381605841187]
  Current quantum computing devices are noisy intermediate-scale quantum $($NISQ$)$ devices. Quantum tomography tries to reconstruct a quantum system's density matrix by a complete set of observables. We propose an alternative approach to quantum tomography, based on the maximal information entropy, that can predict the values of unknown observables.
  arXiv  Detail & Related papers  (2020-09-02T04:39:45Z)
• Quantum error-correcting codes and their geometries [0.6445605125467572]
  This article aims to introduce the reader to the underlying mathematics and geometry of quantum error correction. We go on to construct quantum codes: firstly qubit stabilizer codes, then qubit non-stabilizer codes, and finally codes with a higher local dimension. This allows one to deduce the parameters of the code efficiently, deduce the inequivalence between codes that have the same parameters, and presents a useful tool in deducing the feasibility of certain parameters.
  arXiv  Detail & Related papers  (2020-07-12T13:57:39Z)

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.