Search

EP-4742108-A1 - A METHOD FOR NOISE-REDUCED SIGNAL PROCESSING BY A QUANTUM COMPUTING CIRCUIT AND A QUANTUM COMPUTER SYSTEM

EP4742108A1EP 4742108 A1EP4742108 A1EP 4742108A1EP-4742108-A1

Abstract

A method for noise-reduced signal processing by a quantum computing circuit and a quantum computer system The invention relates to a method for noise-reduced signal processing by a quantum circuit having at least two quantum gates ( ,), comprising the steps of, a) determining a fused inverse noise channel by propagating selected or all predetermined gate-specific inverse noise channels ( Λ 1 − 1 , Λ 2 − 1 , … , Λ L − 1 ) to a predetermined circuit section of the quantum computing circuit (1) as a function of each noisy gate operation of the gates ( ,) between the gate-specific inverse noise channel ( Λ 1 − 1 , Λ 2 − 1 , … , Λ L − 1 ) and the predetermined circuit section, b) modifying the signal processing by the quantum computing circuit (1) by adding an additional quantum computing operation at the predetermined circuit section according to the fused inverse noise channel and a quantum computer system.

Inventors

  • Scheiber, Timon Florian
  • HELLER, MATTHIAS
  • Mueller-Roemer, Johannes S.

Assignees

  • Fraunhofer-Gesellschaft zur Förderung der angewandten Forschung e.V.

Dates

Publication Date
20260513
Application Date
20241108

Claims (11)

  1. A method for noise-reduced signal processing by a quantum computing circuit (1) having at least two quantum gates ( ,), comprising the steps of, a) determining a fused inverse noise channel by propagating selected or all predetermined gate-specific inverse noise channels ( Λ 1 − 1 , Λ 2 − 1 , … , Λ L − 1 ) to a predetermined circuit section of the quantum computing circuit (1) as a function of each noisy gate operation of the gates ( ,) between the gate-specific inverse noise channel ( Λ 1 − 1 , Λ 2 − 1 , … , Λ L − 1 ) and the predetermined circuit section, b) modifying the signal processing by the quantum computing circuit (1) by adding an additional quantum computing operation at the predetermined circuit section according to the fused inverse noise channel.
  2. The method according to claim 1, characterized in that the predetermined section is the start or end of the quantum computing circuit (1).
  3. The method according to one of the preceding claims, characterized in that a gate-specific noise channel ( Λ 1 − 1 , Λ 2 − 1 , … , Λ L − 1 ) is modelled as Pauli noise channel.
  4. The method according to one of the preceding claims, characterized in that propagating comprises a) determining a gate-specific part of the fused inverse noise channel by applying a sequence of gate-specific conjugation operations for each gate arranged between the respective gate-specific inverse noise channel ( Λ 1 − 1 , Λ 2 − 1 , … , Λ L − 1 ) and the predetermined circuit section, b) offsetting the gate-specific parts.
  5. The method according to claim 4, characterized in that an operator reduction is performed for the fused inverse noise channel.
  6. The method according to one of the preceding claims, characterized in that the fused inverse noise channel is determined by additional considering a read-out error.
  7. The method according to claim 6, characterized in that a measurement error channel is constructed and its inverse ( Λ e − 1 ) is propagated.
  8. The method according to claim 7, characterized in that constructing the measurement error channel comprises a) determining an assignment matrix which correlates ideal measurements with noisy measurements, b) symmetrizing the assignment matrix,
  9. The method according to one of the preceding claims, characterized in that a Monte-Carlo-simulation is performed to determine the fused inverse noise channel.
  10. The method according to one of the preceding claims, characterized in that the gate-specific noise channels (Λ 1 , Λ 2 , ..., Λ L ) are modelled according to a Sparse-Pauli-Lindbladian model.
  11. A quantum computer system comprising a quantum computing circuit (1) with at least two gates ( ,) and means for modifying the quantum computing circuit at a predetermined circuit section according to a fused inverse noise channel.

Description

The invention relates to a method for noise-reduced signal processing by a quantum circuit and a quantum computer system. Quantum computing leverages quantum-mechanical principles to carry out computational and information processing tasks. Unlike classical computing, which relies on transistors to manipulate binary values (0 or 1), quantum computing utilizes quantum bits (qubits), which can exist in a superposition of both 0 and 1 simultaneously. This fundamental difference allows quantum computers to tackle problems that are either unsolvable or take an impractically long time to solve on traditional classical computers due to their computational complexity. In particular, quantum computing is expected to outperform classical computing in specific use cases. However, most of the existing algorithms showing a rigorously proven superior scaling compared to classical algorithms are believed to lie beyond the reach of current noisy intermediate scale quantum (NISQ) computers and will probably become relevant only after fault-tolerance is achieved. While recently tremendous progress in the realization of error corrected qubits has been made, both in terms of efficient encodings and real hardware demonstrations, current quantum hardware is not necessarily fault-tolerant. As outlined above, the current generation of quantum hardware can access computational spaces, which might be out of reach even for advanced super computers. Since these devices are still bounded by noise, current NISQ-algorithms require aid by quantum error mitigation (QEM) schemes to be able to compete with classical solutions. QEM methods mostly focus on quantum algorithms that aim to estimate an expectation value (O) of some observable O, by reducing the noise induced bias, at the cost of an increase in the variance of the estimate. This is e.g. described in the document R. Takagi et al., "Fundamental limits of quantum error mitigation", npj Quantum Information (2022)8:114, https://doi.org/10.1038/s41534-022-00619-z. One of such methods is the so-called probabilistic error cancellation (PEC) which is outlined e.g. in the document K. Temme et al. the document "Error mitigation for short-depth quantum circuits" IBM T.J. Watson Research Center, Yorktown Heights NY 10598 (Dated: November 7, 2017). The classical PEC aims to construct an ideal, noiseless circuit operation (ρ) by expanding it into an (over-complete) basis of natively performable, noisy operations i, which can be directly executed by the hardware. This expansion can be achieved in two ways: Either by compensation, where each gate operation of a circuit is directly replaced by the superimposed operation = Σj nj for some real coefficients nj, or alternatively by inversion, where for each noisy operation = Λi ∘ inverse of the noise channel, Λi−1=∑jηj′Oj is implemented directly before or after Λj to cancel the effect of the noise. This is e.g. described in the document Suguru Endo et al. "Practical Quantum Error Mitigation for Near-Future Applications", 1 Department of Materials, University of Oxford, Oxford OX1 3PH 2Graduate School of China Academy of Engineering Physics, Beijing 100193, China . The implementation of this decomposition is performed probabilistically by sampling from the linear combination with a probability respecting the weights nj. This implementation performs the ideal operation on average but it generally comes at the cost of an increase in the variance of the desired result, often denoted by γ. The latter method has recently been demonstrated experimentally on a superconducting quantum chip (see document Ewout van den Berg et al. "Probabilistic error cancellation with sparse Pauli-Lindblad models on noisy quantum processors" Nature Physics | Volume 19 | August 2023 | 1116-1121, https://doi.org/10.1038/s41567-023-02042-2). In this document, a sparse Pauli-Lindblad noise model was considered to efficiently characterize and learn device noise and estimate the inverse noise channels Λi−1 for different layers of noisy two-qubit gates. While the method delivered desired results in terms of retrieving nearly bias-free estimates, the exponentially scaling increase in γ still limits the usefulness of the method to small circuits. US 2024/0152795 A1 discloses systems, computer-implemented methods or computer program products to facilitate mitigating quantum errors associated with one or more quantum gates. A noise modeling component can generate a sparse error model of noise associated with one or more quantum gates; employ the sparse error model; and draw samples from an inverse noise model. An insertion component can insert the samples to mitigate errors associated with the one or more quantum gates. The insertion component can reduce the noise by running circuit instances augmented with samples from the inverse noise model. The noise modeling component includes a noise shaping component that can shape the noise affecting one or more quantum gates by twirling to