Quantum Advantage Now: Generation of True Random Numbers

Impact of quantum errors and noise

Quantum computing is inherently probabilistic, so even generating random numbers will be probabilistic. Odd to say, but the randomness would be probabilistic.

How exactly equal are the probabilities for a Hadamard gate?

The Hadamard quantum logic gate is supposedly equivalent to two rotations about the axes of the Bloch sphere (or one diagonal rotation), but rotations are expressed as angles in radians or fractions of the irrational number pi, even when they are exactly 90 or 180 degrees, which have a definite but not infinite precision in floating point, or as a unitary matrix involving an approximation of the square root of 2, which is an irrational number having no exact definite value in any programming language. All of this begs the question of whether the quantum state after execution of a Hadamard gate is indeed precisely equal probability (equal quantum amplitude) for the two basis states.

Effects of calibration

Real quantum computers have to be calibrated on a regular basis, but how exact and precise is that calibration process, and how un-calibrated is the quantum computer likely to be between calibrations?

How identical are each of the qubits?

There will be inevitable differences between each qubit due to the nature of the chip fabrication process, such as differing number of atoms in each qubit, so technically a slightly different calibration might be needed for each qubit, although that level of distinction may be beyond the capabilities of current test equipment. Maybe the distinctions might be too small to impact the probabilities for the state of each qubit, or maybe not.

Functional advantage vs. performance or capacity advantage

Generally, most discussions of quantum advantage are focused on performance or capacity advantages of quantum computers, but occasionally functional advantages are discussed. Generation of true random numbers is such a case of a functional advantage.

Quantum simulators

Software running on a classical computer can do a somewhat adequate job of simulating a quantum computer, at least a relatively small quantum computer (say, 20 qubits), but there is the question of how truly random quantum state will be simulated since the simulator may be using a pseudo-random number generator rather than a hardware source of entropy bits.

Statistical analysis of randomness

All of this is strictly theoretical at this stage. I haven’t heard of any serious statistical analyses of random numbers generated by current quantum computers.

Need for reproducibility

Not all applications can deal with absolute randomness. As one particularly important use case, replicating bug scenarios when doing randomized testing generally needs a seed number and a reproducible process for generating seemingly random numbers so that particular failure scenarios can be reliably recreated to facilitate debugging and testing of bug fixes. Pseudo-random number generators usually address this need reasonably well.


For the near-term, true random number generation (TRNG) may remain the most defensible area of quantum advantage. Classical computers retain an advantage when deterministics results are needed, but probability and randomness are the forte of quantum computers.



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