Relieving the post-selection problem by quantum singular value transformation

• URL: http://arxiv.org/abs/2504.00108v1
• Date: Mon, 31 Mar 2025 18:00:31 GMT
• Title: Relieving the post-selection problem by quantum singular value transformation
• Authors: Hong-Yi Wang,
• Abstract summary: We propose a post-selection-free experimental strategy based on a fully quantum approach.<n>We deterministically simulate the post-selected quantum states by applying quantum singular value transformation algorithms.<n>We also introduce a pseudoinverse decoder for measurement-induced quantum teleportation.
• Score: 9.861807368585373
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum measurement is a fundamental yet experimentally challenging ingredient of quantum information processing. Many recent studies on quantum dynamics focus on expectation values of nonlinear observables; however, their experimental measurement is hindered by the post-selection problem -- namely, the substantial overhead caused by uncontrollable measurement outcomes. In this work, we propose a post-selection--free experimental strategy based on a fully quantum approach. The key idea is to deterministically simulate the post-selected quantum states by applying quantum singular value transformation (QSVT) algorithms. For pure initial state post-selection, our method is a generalization of fixed-point amplitude amplification to arbitrary projective measurements, achieving an optimal quadratic speedup. We further extend this framework to mixed initial state post-selection by applying linear amplitude amplification via QSVT, which significantly enhances the measurement success probability. However, a deterministic quantum algorithm for preparing the post-selected mixed state is generally impossible because of information-theoretic constraints imposed by quantum coding theory. Additionally, we introduce a pseudoinverse decoder for measurement-induced quantum teleportation. This decoder possesses the novel property that, when conditioned on a successful flag measurement, the decoding is nearly perfect even in cases where channel decoders are information-theoretically impossible. Overall, our work establishes a powerful approach for measuring novel quantum dynamical phenomena and presents quantum algorithms as a new perspective for understanding quantum dynamics and quantum chaos.

Related papers

• 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)
• 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)
• Adiabatic quantum learning [0.0]
  This work proposes to execute some quantum learning protocols based entirely on adiabatic quantum evolution. By contrast, the proposed adiabatic quantum learning here may be integrated with future adiabatic weak measurement protocols.
  arXiv  Detail & Related papers  (2023-03-02T07:27:29Z)
• Anticipative measurements in hybrid quantum-classical computation [68.8204255655161]
  We present an approach where the quantum computation is supplemented by a classical result. Taking advantage of its anticipation also leads to a new type of quantum measurements, which we call anticipative. In an anticipative quantum measurement the combination of the results from classical and quantum computations happens only in the end.
  arXiv  Detail & Related papers  (2022-09-12T15:47:44Z)
• An Amplitude-Based Implementation of the Unit Step Function on a Quantum Computer [0.0]
  We introduce an amplitude-based implementation for approximating non-linearity in the form of the unit step function on a quantum computer. We describe two distinct circuit types which receive their input either directly from a classical computer, or as a quantum state when embedded in a more advanced quantum algorithm.
  arXiv  Detail & Related papers  (2022-06-07T07:14:12Z)
• Variational Approach to Quantum State Tomography based on Maximal Entropy Formalism [3.6344381605841187]
  We employ the maximal entropy formalism to construct the least biased mixed quantum state that is consistent with the given set of expectation values. We employ a parameterized quantum circuit and a hybrid quantum-classical variational algorithm to obtain such a target state making our recipe easily implementable on a near-term quantum device.
  arXiv  Detail & Related papers  (2022-06-06T01:16:22Z)
• 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)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Error mitigation and quantum-assisted simulation in the error corrected regime [77.34726150561087]
  A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations. We show how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit.
  arXiv  Detail & Related papers  (2021-03-12T20:58:41Z)
• Direct Quantum Communications in the Presence of Realistic Noisy Entanglement [69.25543534545538]
  We propose a novel quantum communication scheme relying on realistic noisy pre-shared entanglement. Our performance analysis shows that the proposed scheme offers competitive QBER, yield, and goodput.
  arXiv  Detail & Related papers  (2020-12-22T13:06:12Z)
• 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)
• Arbitrary Measurement on Any Real-valued Probability Amplitude in Any Quantum System [0.0]
  One novel quantum measurement scheme is proposed to solve these questions based on the idea of binary searching. The proposed quantum measurement scheme has the performance in quantum information processing with twofold advantages: separable measurement and exponential speed up.
  arXiv  Detail & Related papers  (2020-08-31T09:56:07Z)

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.