Join Curt Jaimungal talks to Harvard physicist Jacob Barandes and Scott Aaronson. Jacob Barandes claims quantum mechanics can be reformulated without wave functions. Barandes has a new formulation of quantum mechanics which is considered a serious proposal by Scott Aaronson.
Quantum computer theoretician Scott Aaronson gives his perspective. Barandes' "indivisible" approach challenges the standard Schrödinger model.
Barandes proposes a new proposal to what physically underlies the quantum world. Is this interpretation an improvement over the current quantum mechanic framework, theories and interpretation. Reduction in vagueness. More predictability. Should have a long list of unprovable assumptions.
His proposal is without multiple worlds. IF there were multiple worlds underlying the power of quantum computer why are the instances of quantum speedup not broadly seen but only for very limited cases?
Scott Aaronson wanted a pithy summary - Quantum interference of complex quantum waves can give the potential power of quantum computing.
Why are classical computers failing to get speedups where quantum systems may not fail to get speedups in some of those cases. Aaronson views quantum systems being able to evade some cases of classical failure. Classical computers are very broadly successful.
They discussed the specific problems that all of the theories still have. There is problem of predicting trajectories.
Major Everett, Deutsch and Barandes Papers and Their Impact
Hugh Everett III
Paper: Relative State' Formulation of Quantum Mechanics, Reviews of Modern Physics, 1957
Many Worlds?
Everett introduced the Many-Worlds Interpretation (MWI), proposing that all possible outcomes of quantum measurements occur in separate, branching universes, eliminating the need for wave function collapse.
Initially met with skepticism from figures like Niels Bohr, MWI was largely overlooked for decades. However, it has since gained significant traction, particularly with advocates like David Deutsch and David Wallace, who praise its simplicity and consistency as a no-collapse interpretation. The development of decoherence theory has bolstered its credibility by explaining the appearance of classical outcomes. Despite its growing acceptance, it remains controversial, with critics arguing it lacks empirical testability and introduces unnecessary complexity.
David Deutsch
Paper: "Quantum Theory, the Church-Turing Principle and the Universal Quantum Computer"
Publication: Proceedings of the Royal Society, 1985
Foundation of Quantum Computing
Deutsch's paper laid the foundation for quantum computing by introducing the concept of a universal quantum computer, demonstrating that quantum systems could outperform classical computers for certain tasks.
This work is widely regarded as a landmark in the field. It inspired subsequent breakthroughs, such as Peter Shor's factoring algorithm and Charles Bennett's contributions to quantum cryptography. Researchers view Deutsch's ideas as visionary, driving the quantum computing revolution and shaping both theoretical and experimental progress. His paper is seen as a catalyst for the modern era of quantum technology development.
Jacob Barandes
Paper: "The Minimal Modal Interpretation of Quantum Theory", arXiv preprint, 2014
Minimal Modal Interpretation
Barandes proposed the Minimal Modal Interpretation, a novel approach to the quantum measurement problem that uses a minimal set of modal principles to explain definite outcomes without invoking hidden variables or many worlds.
As a newer contribution, it has sparked interest in the quantum foundations community. Scholars like Jeffrey Barrett have commended its elegance and consistency with quantum formalism, appreciating its avoidance of the metaphysical complexities found in other interpretations. While still under scrutiny and less established than MWI, it is considered a promising and parsimonious alternative, with ongoing debate about its broader implications.
Summary of Views by Major Researchers and the Field
Everett's MWI: Once dismissed, it is now a respected interpretation, especially among proponents of no-collapse theories. Its influence has grown alongside decoherence research, though it continues to divide opinions due to its bold ontological claims.
Deutsch's Quantum Computing: Universally celebrated as a foundational achievement, it is credited with launching the field of quantum computing and remains a cornerstone for theoretical and practical advancements.
Barandes' Minimal Modal Interpretation: A recent and evolving contribution, it is gaining attention for its simplicity and potential to address quantum mechanics' foundational issues, though its long-term impact is still being assessed.
Aaronson View of Quantum Computing and the Physics Behind It
Aaronson views quantum computing as a natural extension of quantum mechanics, where the key phenomena -- superposition, entanglement, and interference -- enable computational power that classical systems struggle to replicate. He's long argued that quantum computers don't just "try all answers at once" in a simplistic sense (a common misconception); instead, they exploit the mathematical structure of quantum amplitudes to perform computations in ways that can lead to speedups for specific problems, like factoring (Shor's algorithm) or simulating quantum systems.
Regarding exponential speedups, Aaronson remains cautiously optimistic but rigorous. He believes true exponential speedups are possible for certain problems (e.g., Shor's algorithm for factoring or boson sampling for sampling problems), but not universally. He's emphasized that quantum computers are not magic -- they're constrained by the laws of physics and the complexity class BQP (Bounded-Error Quantum Polynomial Time), which defines what they can efficiently compute.
Hard Problem of the Right Quantum Interference - Cancellation of "Wrong" Answers and Amplification of "Correct" Answers
Amplificationof correct answer are at the heart of quantum algorithms like Grover's algorithm. Aaronson has written a lot about the interference process. In quantum mechanics, amplitudes (complex numbers associated with quantum states) can interfere constructively (adding up) or destructively (canceling out). This isn't a physical management" by the computer but a natural consequence of how quantum states evolve under unitary operations.
Cancellation: In algorithms like Grover's or Deutsch-Jozsa, the "wrong" answers (states corresponding to incorrect solutions) have amplitudes that, through carefully designed quantum gates, interfere destructively. This reduces their probability of being measured. Aaronson often explains this as the quantum computer "sculpting" the state space, where the negative and positive amplitudes of unwanted outcomes cancel each other out due to phase differences.
Amplification: Conversely, "correct" answers have their amplitudes reinforced through constructive interference. In Grover's algorithm, for example, the amplitude of the target state is iteratively boosted (via the "Grover diffusion operator") while others diminish, leading to a higher probability of measuring the right answer. Aaronson sees this as a beautiful demonstration of quantum mechanics' counterintuitive power -- unlike classical probability, where you'd need to sample exponentially many possibilities, quantum interference lets you tilt the odds efficiently.