An Exponential Sample-Complexity Advantage for Coherent Quantum Inference

• URL: http://arxiv.org/abs/2605.21457v1
• Date: Wed, 20 May 2026 17:47:33 GMT
• Title: An Exponential Sample-Complexity Advantage for Coherent Quantum Inference
• Abstract summary: We study an alternative inference setting in which the desired output is quantum, preserving coherence.<n>We show that such protocols can achieve exponentially lower sample complexity than incoherent, measurement-mediated protocols.
• Score: 5.480908143128776
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Standard quantum inference converts quantum data into classical outputs. We study an alternative inference setting in which the desired output is quantum, preserving coherence. Such settings include quantum purity amplification (QPA), mixed-state approximate purification or cloning, and density matrix exponentiation. We show that such protocols can achieve exponentially lower sample complexity than incoherent, measurement-mediated protocols. For QPA with principal eigenstate targets and $d$-dimensional inputs, coherent processing achieves error $\varepsilon$ using $O(1/\varepsilon)$ copies, versus the $Ω(d/\varepsilon)$ copies required by any incoherent protocol. Together, these sharp coherent-incoherent separations seed a theory of coherent quantum inference, with an entanglement-breaking limit identifying the optimal incoherent counterpart of each coherent protocol.

Related papers

• Quantum Purity Amplification for Arbitrary Eigenstates and Multiple Outputs [5.480908143128776]
  Quantum purity (QPA) is the task of coherently transforming $n$ copies of a mixed state into high-fidelity copies of a chosen eigenstate.<n>We characterize the optimal channel and derive its all-site and one-site performance laws across output regimes.
  arXiv  Detail & Related papers  (2026-05-20T17:47:32Z)
• Towards End-to-End Quantum Estimation of Non-Hermitian Pseudospectra [7.8040425216185225]
  Non-Hermitian many-body systems can be spectrally unstable, so small perturbations may induce large eigenvalue shifts.<n>The pseudospectrum quantifies this instability and provides a perturbation-robust diagnostic.<n>We show that deciding whether a point $zinmathbbC$ is $$-close to the spectrum is PSPACE-hard for $5$-local operators.
  arXiv  Detail & Related papers  (2026-03-17T07:44:04Z)
• Purest Quantum State Identification [14.22473588576799]
  We introduce the purest quantum state identification, which can be used to improve the accuracy of quantum computation and communication.<n>For incoherent strategies, we derive the first adaptive algorithm achieving error probability $expleft(- Omegaleft(fracN H_1log(K) 2nfracright)$, fundamentally improving quantum property learning.
  arXiv  Detail & Related papers  (2025-02-20T07:42:16Z)
• Constant Overhead Entanglement Distillation via Scrambling [0.6249768559720122]
  High-fidelity quantum entanglement enables key quantum networking capabilities such as secure communication and distributed quantum computing.<n>We introduce protocols that use quantum scrambling - the spreading of quantum information under chaotic dynamics.<n>We show this protocol remains effective even with noisy quantum gates, making it suitable for near-term devices.
  arXiv  Detail & Related papers  (2025-02-13T16:46:15Z)
• Quantum Homogenization as a Quantum Steady State Protocol on NISQ Hardware [42.52549987351643]
  Quantum homogenization is a reservoir-based quantum state approximation protocol.<n>We extend the standard quantum homogenization protocol to the dynamically-equivalent ($mathttSWAP$)$alpha$ formulation.<n>We show that our proposed protocol yields a completely positive, trace preserving (CPTP) map under which the code subspace is correctable.
  arXiv  Detail & Related papers  (2024-12-19T05:50:54Z)
• Single-shot decoding of good quantum LDPC codes [38.12919328528587]
  We prove that quantum Tanner codes facilitate single-shot quantum error correction (QEC) of adversarial noise. We show that in order to suppress errors over multiple repeated rounds of QEC, it suffices to run the parallel decoding algorithm for constant time in each round.
  arXiv  Detail & Related papers  (2023-06-21T18:00:01Z)
• 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)
• Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
  We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees. Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation. We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
  arXiv  Detail & Related papers  (2022-03-30T02:02:16Z)
• Efficient Bipartite Entanglement Detection Scheme with a Quantum Adversarial Solver [89.80359585967642]
  Proposal reformulates the bipartite entanglement detection as a two-player zero-sum game completed by parameterized quantum circuits. We experimentally implement our protocol on a linear optical network and exhibit its effectiveness to accomplish the bipartite entanglement detection for 5-qubit quantum pure states and 2-qubit quantum mixed states.
  arXiv  Detail & Related papers  (2022-03-15T09:46:45Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)
• Computing conditional entropies for quantum correlations [10.549307055348596]
  In particular, we find new upper bounds on the minimal global detection efficiency required to perform device-independent quantum key distribution. We introduce the family of iterated mean quantum R'enyi divergences with parameters $alpha_k = 1+frac12k-1$ for positive integers $k$. We show that the corresponding conditional entropies admit a particularly nice form which, in the context of device-independent optimization, can be relaxed to a semidefinite programming problem.
  arXiv  Detail & Related papers  (2020-07-24T15:27:51Z)
• 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)
• Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms [87.04438831673063]
  We present an efficient read-out protocol that yields the classical vector form of the generated state. Our protocol suits the case that the output state lies in the row space of the input matrix. One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
  arXiv  Detail & Related papers  (2020-04-14T11:05:26Z)

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.