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Rational quantum mechanics: Testing quantum theory with quantum computers.

Tim Palmer1

  • 1Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom.

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PubMed
Summary
This summary is machine-generated.

Rational Quantum Mechanics (RaQM) proposes a discretized Hilbert Space, limiting qubit information capacity. This suggests quantum computers may not surpass 1,000 perfect qubits, impacting algorithms like Shor's.

Keywords:
discrete Hilbert Spacefoundations of quantum physicslimit to quantum computingquantum informationtesting quantum mechanics

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Area of Science:

  • Theoretical Physics
  • Quantum Information Theory
  • Quantum Gravity

Background:

  • John Wheeler's "it-from-bit" concept suggests quantum mechanics hides information-theoretic principles.
  • The continuum nature of Hilbert Space may obscure the fundamental digital essence of quantum states.

Purpose of the Study:

  • To propose Rational Quantum Mechanics (RaQM), a theory based on Hilbert Space discretization.
  • To investigate the implications of rational-number constraints on qubit information capacity.
  • To explore the potential limitations of quantum computing due to these constraints.

Main Methods:

  • Developing RaQM by discretizing complex Hilbert Space with rational-number constraints.
  • Analyzing the information capacity of qubits within the RaQM framework.
  • Comparing RaQM predictions with standard quantum mechanics (QM) for varying qubit numbers.

Main Results:

  • RaQM imposes finite information capacity on qubits, limiting the degrees of freedom they can represent.
  • Estimated maximum qubit capacity is between 200-400 for current technology, capped at 1,000.
  • Quantum algorithms requiring maximal entanglement may not achieve exponential speedup beyond this limit.

Conclusions:

  • Quantum mechanics (QM) is proposed as a singular continuum limit of RaQM, possibly linked to gravity.
  • RaQM predicts a saturation point for quantum algorithm advantage, challenging the scalability of quantum computation for tasks like factoring large integers.
  • The predicted breakdown of QM's exponential advantage is potentially testable within five years.