Testing Quantum Mechanics with Quantum Computers: Qubit Information Capacity

• URL: http://arxiv.org/abs/2510.02877v1
• Date: Fri, 19 Sep 2025 07:12:31 GMT
• Title: Testing Quantum Mechanics with Quantum Computers: Qubit Information Capacity
• Authors: Tim Palmer,
• Abstract summary: Motivated by Wheeler's assertion that Hilbert Space conceals the information-theoretic nature of the quantum wavefunction, a specific discretisation of complex Hilbert Space is proposed.<n>For any $N ge N_mathrmmax$-qubit state, there is insufficient information in the $N$ qubits to allocate even one bit to each of the $2N+1-2$ degrees of freedom demanded by complex Hilbert Space.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Motivated by John Wheeler's assertion that the continuum nature of Hilbert Space conceals the information-theoretic nature of the quantum wavefunction, a specific discretisation of complex Hilbert Space is proposed, leading to the notion of qubit information capacity $N_{\mathrm{max}}$: for any $N \ge N_{\mathrm{max}}$-qubit state, there is insufficient information in the $N$ qubits to allocate even one bit to each of the $2^{N+1}-2$ degrees of freedom demanded by complex Hilbert Space and hence unitary quantum mechanics. Using gravitised quantum mechanics, it is estimated that, for typical qubits in a quantum computer, $N_{\mathrm{max}} \approx 500-1,000$. By contrast, $N_{\mathrm{max}}=\infty$ in quantum mechanics. On this basis, it is predicted that the exponential speed up of algorithms such as Shor's will have saturated in quantum computers which use more than about 1,000 logical qubits. This predicted breakdown of quantum mechanics should be testable within the coming decade. If verified, factoring 2048-RSA integers using quantum computers will for all practical purposes be impossible. The existence of a finite qubit information capacity has profound implications for reimagining the foundations of quantum physics (including the measurement problem, complementarity and nonlocality) and for developing novel theories which synthesise quantum and gravitational physics.

Related papers

• Practical quantum tokens: challenges and perspectives [49.583101345036624]
  The concept of quantum tokens dates back alongside quantum cryptography to Stephen Wiesner's seminal work in 1983.<n>We discuss the current state-of-the-art of quantum tokens in the field of quantum information, as well as their future perspectives.
  arXiv  Detail & Related papers  (2026-02-11T08:11:36Z)
• Estimating quantum relative entropies on quantum computers [4.4539446220650065]
  We use the Kullback-Leibler divergence to estimate quantum relative between two quantum states.<n>We also investigate the superadditivity of quantum computer channels.
  arXiv  Detail & Related papers  (2025-01-13T13:00:24Z)
• More quantum chemistry with fewer qubits [0.9903198600681908]
  We propose a quantum algorithm that improves on the representation of the physical problem by virtue of second-order perturbation theory. In particular, our quantum algorithm evaluates the second-order energy correction through a series of time-evolution steps under the unperturbed Hamiltonian. Our perturbation theory quantum algorithm can also be applied to symmetry-adapted perturbation theory.
  arXiv  Detail & Related papers  (2023-08-31T17:21:17Z)
• Fundamental causal bounds of quantum random access memories [13.19534468575575]
  We study the intrinsic bounds of rapid quantum memories based on causality. We show that QRAM can accommodate up to $mathcalO(107)$ logical qubits in 1 dimension, $mathcalO(1015)$ to $mathcalO(1020)$ in various 2D architectures, and $mathcalO(1024)$ in 3 dimensions.
  arXiv  Detail & Related papers  (2023-07-25T12:40:48Z)
• Quantum data learning for quantum simulations in high-energy physics [55.41644538483948]
  We explore the applicability of quantum-data learning to practical problems in high-energy physics. We make use of ansatz based on quantum convolutional neural networks and numerically show that it is capable of recognizing quantum phases of ground states. The observation of non-trivial learning properties demonstrated in these benchmarks will motivate further exploration of the quantum-data learning architecture in high-energy physics.
  arXiv  Detail & Related papers  (2023-06-29T18:00:01Z)
• 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)
• Is there evidence for exponential quantum advantage in quantum chemistry? [45.33336180477751]
  The idea to use quantum mechanical devices to simulate other quantum systems is commonly ascribed to Feynman. It may be prudent to assume exponential speedups are not generically available for this problem.
  arXiv  Detail & Related papers  (2022-08-03T16:33:57Z)
• Quantum mechanics? It's all fun and games until someone loses an $i$ [0.0]
  QBism regards quantum mechanics as an addition to probability theory. Recent work has demonstrated that reference devices employing symmetric informationally complete POVMs (or SICs) achieve a minimal quantumness. We attempt to identify the optimal reference device in the first real dimension without a SIC.
  arXiv  Detail & Related papers  (2022-06-30T15:15:16Z)
• How much classical information is carried by a quantum state? An approach inspired by Kolmogorov complexity [0.0]
  I give a definition of the (classical) information content of a quantum state. I show that, for some well-known quantum circuits, the information content of the output state is evaluated in the number of qubits. On the other hand, applying known results, it is possible to devise quantum circuits that generate much more complex states.
  arXiv  Detail & Related papers  (2022-04-05T17:22:11Z)
• Exponential separations between learning with and without quantum memory [17.763817187554096]
  We study the power of quantum memory for learning properties of quantum systems and dynamics. Many state-of-the-art learning algorithms require access to an additional external quantum memory. We show that this trade-off is inherent in a wide range of learning problems.
  arXiv  Detail & Related papers  (2021-11-10T19:03:49Z)
• Can Noise on Qubits Be Learned in Quantum Neural Network? A Case Study on QuantumFlow [25.408147000243158]
  This paper aims to tackle the noise issue from another angle. Instead of creating perfect qubits for general quantum algorithms, we investigate the potential to mitigate the noise issue for dedicate algorithms. This paper targets quantum neural network (QNN), and proposes to learn the errors in the training phase, so that the identified QNN model can be resilient to noise.
  arXiv  Detail & Related papers  (2021-09-08T04:43:12Z)
• On quantum neural networks [91.3755431537592]
  We argue that the concept of a quantum neural network should be defined in terms of its most general function. Our reasoning is based on the use of the Feynman path integral formulation in quantum mechanics.
  arXiv  Detail & Related papers  (2021-04-12T18:30:30Z)
• Towards understanding the power of quantum kernels in the NISQ era [79.8341515283403]
  We show that the advantage of quantum kernels is vanished for large size datasets, few number of measurements, and large system noise. Our work provides theoretical guidance of exploring advanced quantum kernels to attain quantum advantages on NISQ devices.
  arXiv  Detail & Related papers  (2021-03-31T02:41:36Z)
• Ruling out real-valued standard formalism of quantum theory [19.015836913247288]
  A quantum game has been developed to distinguish standard quantum theory from its real-number analog. We experimentally implement the quantum game based on entanglement swapping with a state-of-the-art fidelity of 0.952(1). Our results disprove the real-number formulation and establish the indispensable role of complex numbers in the standard quantum theory.
  arXiv  Detail & Related papers  (2021-03-15T03:56:13Z)
• Quantum Information for Particle Theorists [0.0]
  Lectures given at the Theoretical Advanced Study Institute (TASI 2020), 1-26 June 2020. The topics covered include quantum circuits, entanglement, quantum teleportation, Bell inequalities, quantum entropy and decoherence. Links to a Python notebook and Mathematica notebooks will allow the reader to reproduce and extend the calculations, as well as perform five experiments on a quantum simulator.
  arXiv  Detail & Related papers  (2020-10-06T18:00:02Z)

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.