Quantum Trajectory Approach to Error Mitigation

• URL: http://arxiv.org/abs/2305.19874v1
• Date: Wed, 31 May 2023 14:10:35 GMT
• Title: Quantum Trajectory Approach to Error Mitigation
• Authors: Brecht. I. C Donvil, Rochus Lechler, Joachim Ankerhold and Paolo Muratore-Ginanneschi
• Abstract summary: Quantum Error Mitigation (EM) is a collection of strategies to reduce errors on noisy quantum devices. We show that the inverse of noise maps can be realised by performing classical post-processing. We demonstrate our result on a model relevant for current NISQ devices.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum Error Mitigation (EM) is a collection of strategies to reduce errors on noisy intermediate scale quantum (NISQ) devices on which proper quantum error correction is not feasible. One of such strategies aimed at mitigating noise effects of a known environment is to realise the inverse map of the noise using a set of completely positive maps weighted by a quasi-probability distribution, i.e. a probability distribution with positive and negative values. This quasi-probability distribution is realised using classical post-processing after final measurements of the desired observables have been made. Here we make a connection with quasi-probability EM and recent results from quantum trajectory theory for open quantum systems. We show that the inverse of noise maps can be realised by performing classical post-processing on the quantum trajectories generated by an additional reservoir with a quasi-probability measure called the influence martingale. We demonstrate our result on a model relevant for current NISQ devices. Finally, we show the quantum trajectories required for error correction can themselves be simulated by coupling an ancillary qubit to the system. In this way, we can avoid the introduction of the engineered reservoir.

Related papers

• Normal quantum channels and Markovian correlated two-qubit quantum errors [77.34726150561087]
  We study general normally'' distributed random unitary transformations. On the one hand, a normal distribution induces a unital quantum channel. On the other hand, the diffusive random walk defines a unital quantum process.
  arXiv  Detail & Related papers  (2023-07-25T15:33:28Z)
• Practical limitations of quantum data propagation on noisy quantum processors [0.9362259192191963]
  We show that owing to the noisy nature of current quantum processors, such a quantum algorithm will require single- and two-qubit gates with very low error probability to produce reliable results. Specifically, we provide the upper bounds on how the relative error in variational parameters' propagation scales with the probability of noise in quantum hardware.
  arXiv  Detail & Related papers  (2023-06-22T17:12:52Z)
• Quantum Conformal Prediction for Reliable Uncertainty Quantification in Quantum Machine Learning [47.991114317813555]
  Quantum models implement implicit probabilistic predictors that produce multiple random decisions for each input through measurement shots. This paper proposes to leverage such randomness to define prediction sets for both classification and regression that provably capture the uncertainty of the model.
  arXiv  Detail & Related papers  (2023-04-06T22:05:21Z)
• Error-Mitigated Quantum Simulation of Interacting Fermions with Trapped Ions [17.707261555353682]
  probabilistic error cancellation (PEC) has been proposed as a general and systematic protocol. PEC has been tested in two-qubit systems and a superconducting multi-qubit system. We benchmark PEC using up to four trapped-ion qubits.
  arXiv  Detail & Related papers  (2023-02-21T04:27:30Z)
• Compressed quantum error mitigation [0.0]
  We introduce a quantum error mitigation technique based on probabilistic error cancellation to eliminate errors which have accumulated during the application of a quantum circuit. For a simple noise model, we show that efficient, local denoisers can be found, and we demonstrate their effectiveness for the digital quantum simulation of the time evolution of simple spin chains.
  arXiv  Detail & Related papers  (2023-02-10T19:00:02Z)
• Suppressing Amplitude Damping in Trapped Ions: Discrete Weak Measurements for a Non-unitary Probabilistic Noise Filter [62.997667081978825]
  We introduce a low-overhead protocol to reverse this degradation. We present two trapped-ion schemes for the implementation of a non-unitary probabilistic filter against amplitude damping noise. This filter can be understood as a protocol for single-copy quasi-distillation.
  arXiv  Detail & Related papers  (2022-09-06T18:18:41Z)
• Probabilistic error cancellation with sparse Pauli-Lindblad models on noisy quantum processors [0.7299729677753102]
  We present a protocol for learning and inverting a sparse noise model that is able to capture correlated noise and scales to large quantum devices. These advances allow us to demonstrate PEC on a superconducting quantum processor with crosstalk errors.
  arXiv  Detail & Related papers  (2022-01-24T18:40:43Z)
• Analytical and experimental study of center line miscalibrations in M\o lmer-S\o rensen gates [51.93099889384597]
  We study a systematic perturbative expansion in miscalibrated parameters of the Molmer-Sorensen entangling gate. We compute the gate evolution operator which allows us to obtain relevant key properties. We verify the predictions from our model by benchmarking them against measurements in a trapped-ion quantum processor.
  arXiv  Detail & Related papers  (2021-12-10T10:56:16Z)
• Model-Independent Error Mitigation in Parametric Quantum Circuits and Depolarizing Projection of Quantum Noise [1.5162649964542718]
  Finding ground states and low-lying excitations of a given Hamiltonian is one of the most important problems in many fields of physics. quantum computing on Noisy Intermediate-Scale Quantum (NISQ) devices offers the prospect to efficiently perform such computations. Current quantum devices still suffer from inherent quantum noise.
  arXiv  Detail & Related papers  (2021-11-30T16:08:01Z)
• 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)
• Using Quantum Metrological Bounds in Quantum Error Correction: A Simple Proof of the Approximate Eastin-Knill Theorem [77.34726150561087]
  We present a proof of the approximate Eastin-Knill theorem, which connects the quality of a quantum error-correcting code with its ability to achieve a universal set of logical gates. Our derivation employs powerful bounds on the quantum Fisher information in generic quantum metrological protocols.
  arXiv  Detail & Related papers  (2020-04-24T17:58:10Z)

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.