Q: "What is the reason for suggesting that practical quantum computers cannot be built (as presented by Professor Gil Kalai, and has anything changed since 2013)?".
In an interview titled "Perpetual Motion of The 21st Century?" Prof. Kalai states:
"For quantum systems there are special obstacles, such as the inability to make exact copies of quantum states in general. Nevertheless, much of the theory of error-correction has been carried over, and the famous threshold theorem shows that fault-tolerant quantum computation (FTQC) is possible if certain conditions are met. The most-emphasized condition sets a threshold for the absolute rate of error, one still orders of magnitude more stringent than what current technology achieves but approachable. One issue raised here, however, is whether the errors have sufficient independence for these schemes to work or correlations limited to what they can handle.".
In an earlier paper of his titled "Quantum Computers: Noise Propagation and Adversarial Noise Models" he states:
Page 2: "The feasibility of computationally superior quantum computers is one of the most fascinating scientific problems of our time. The main concern regarding quantum-computer feasibility is that quantum systems are inherently noisy. The theory of quantum error correction and fault-tolerant quantum computation (FTQC) provides strong support for the possibility of building quantum computers. In this paper we will discuss adversarial noise models that may fail quantum computation. This paper presents a critique of quantum error correction and skepticism on the feasibility of quantum computers.".
Page 19: "The main issue is therefore to understand and describe the fresh (or infinitesimal) noise operations. The adversarial models we consider here should be regarded as models for fresh noise. But the behavior of accumulative errors in quantum circuits that allow error propagation is sort of a “role model” for our models of fresh noise.
The common picture of FTQC asserts:
- Fault tolerance will work if we are able to reduce the fresh gate/qubit
errors to below a certain threshold. In this case error propagation will be suppressed.
What we propose is:
- Fault tolerance will not work because the overall error will behave like accumulated errors for standard error propagation (for circuits that allow error propagation), although not necessarily because of error propagation.
Therefore, for an appropriate modeling of noisy quantum computers the fresh errors should behave like accumulated errors for standard error propagation (for circuits that allow error propagation).
(As a result, in the end we will not be able to avoid error propagation.)".
Page 23: "Conjecture B: In any noisy quantum computer in a highly entangled state there will be a strong effect of error synchronization.
We should informally explain already at this point why these conjectures, if true, are damaging. We start with Conjecture B. The states of quantum computers that apply error-correcting codes needed for FTQC are highly entangled (by any formal definition of “high entanglement”). Conjecture B
will imply that at every computer cycle there will be a small but substantial probability that the number of faulty qubits will be much larger than the threshold. This is in contrast to standard assumptions that the probability of the number of faulty qubits being much larger than the threshold decreases exponentially with the number of qubits. Having a small but substantial probability of a large number of qubits to be faulty is enough to fail the quantum error correction codes.".
See also his paper: "How Quantum Computers Fail: Quantum Codes, Correlations in Physical Systems, and Noise Accumulation".
Many people disagee, and much has changed, see this Wikipedia page: "Quantum Threshold Theorem", or this paper "Experimental Quantum Computations on a Topologically Encoded Qubit", there's even this paper on quantum metrology where the authors claim that: "Making use of coherence and entanglement as metrological quantum resources allows to improve the measurement precision from the shot-noise or quantum limit to the Heisenberg limit." in their paper: "Quantum metrology with a transmon qutrit" by utilizing additional dimensions.