The entire spiel of quantum computers is that the odd principles of quantum mechanics allow them to exponentially outperform their classical counterparts. But what if the very foundation of this claim is wrong?
In a recent paper published in Proceedings of the National Academy of Sciences, Tim Palmer, a physicist at the University of Oxford in the United Kingdom, proposes a slight tweak to the underlying math of quantum theory. The framework, dubbed “Rational Quantum Mechanics,” would effectively place an upper bound on quantum hardware capacity.
If validated, that means quantum capacity won’t grow infinitely. That subsequently dampens whatever excitement—or fear—we derive from their potential. For instance, they won’t be as much of a threat to RSA cryptosystems, the protective algorithm used to store most data today, despite countless claims that quantum computers can crack them.
Ambitious intentions
But all this is a big “if.” For one, quantum mechanics is one of the most successful theories in the history of science. Sure, there is still much we don’t understand about the quantum world, but it’s an ambitious move to suggest the theory needs some tweaking.
Palmer agrees but still believes that some mathematical aspects can be revised to better represent reality. What’s more, his idea could be testable with existing quantum technologies within the next five years.
Specifically, Palmer focuses on a concept called the Hilbert space—the standard vector space used to calculate most quantum systems. Compared to classical physics, quantum mechanics is “more vitally dependent on the continuum of real numbers…[but] nature abhors a continuum,” Palmer explained in a statement.
Here’s the plan
In conventional quantum mechanics, the number of dimensions in a Hilbert space grows exponentially with the number of qubits. According to a column by the Quantum Insider, this “exponential scaling is critical for the fulfillment of the promise of quantum computing, enabling algorithms such as Shor’s method for factoring large numbers far faster than classical machines.”
Palmer’s suggestion is as follows: For practical purposes, physical space more resembles a collection of discrete, not continuous, elements. “Rational” quantum mechanics subscribes to this view of geometrical space, and as a result the information content in the quantum state grows linearly with the number of qubits.
“Above a critical number of entangled qubits, there simply isn’t enough information in the quantum state to allocate even one bit of information to each dimension of Hilbert space,” Palmer explained. “When this happens, quantum algorithms that utilize all of Hilbert space will stop having a quantum advantage over classical algorithms.”
According to the paper, quantum computers will lose their advantage once the system exceeds approximately 1,000 qubits. One big selling point of quantum computers is that they’ll be able to factor extremely large numbers in ways classical computers cannot. That infinite factoring capacity is relevant to claims that quantum computers could crack the RSA algorithm. Therefore, there’s a limit to how many qubits engineers can cram into the most “powerful” quantum computer—after 1,000 qubits, the system will tap out long before reaching the required scale. In case you’re wondering, that threshold lies way below a common estimate for the number of qubits required to break RSA: 4,099.
The burden of proof
While a fascinating proposition, rational quantum mechanics remains highly speculative. Only time and scrutiny will tell how much—if at all—this proposal could change things for the better or worse. In the paper, Palmer proposes an experimental test to entangle many qubits according to a specific algorithm and check for any signs of degrading performance.
Then again, quantum mechanics remains one of the most empirically tested theories. Palmer is correct that the Hilbert space is more of an “idealization,” as he says in the statement, but there also haven’t been any experiments to indicate the kind of discrete physical space described by Palmer in his proposal.
Personally, I don’t want to discredit the new idea too much. It’s unwise to assume that something is “impossible” when quantum things are involved. But big claims require big evidence, and if something of that sort arises from this theory, I’d be first in line to learn more.
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