Halving the cost of quantum addition · HackerPapers discussions

Halving the cost of quantum addition — mentioned by Strilanc

Thu, 12 Dec 2024 00:19:16 GMT

There are two major issues with the paper you linked. First, it says if you can't do accurate rotations then you can't factor. But the premise is false. Quantum error correction allows you to do arbitrarily accurate rotations. Specifically, you can achieve arbitrarily accurate 45 degree rotations around the X and Z axes by using state distillation and gate teleportation [1], and all rotations can be approximated by a sequence of these 45 degree rotations with the error decreasing exponentially versus the length of the sequence [2]. The paper's justification for saying you can't do accurate…

Paper and discussion history. A mention is not an endorsement.

Halving the cost of quantum addition — mentioned by Strilanc

Wed, 07 Aug 2024 23:36:24 GMT

No, that's not true at all. For example, a chemistry simulation can be done in first quantization; where the state is a list of superposed 2s-complement integers indicating the positions of the electrons (as opposed to a more direct one-qubit=one-position mapping). And the list is initialized in a way that satisfies the Pauli exclusion principle by using a sorting network [1]. This is presumably not at all how Nature does it. Another example is factoring. Shor's factoring algorithm is not at all like behaving analogous to a physical system. It's about modular exponentiation and Fourier…

Paper and discussion history. A mention is not an endorsement.

Halving the cost of quantum addition — mentioned by Strilanc

Tue, 11 Apr 2023 16:23:14 GMT

> Shor's algorithm requires not only the logical qubit to be stable (the superposition of 1 and 0, but also the phase [..] to be noise free to an extraordinary degree. There are rotations in very small angles many, many times in the computation. This is wrong. Those rotations are not the hard part. When Shor's algorithm is compiled using qubit recycling [0], factoring an n bit number uses 2n rotations that aren't a multiple of 45 degrees. For relevant number-to-factor sizes like 2048 bits, performing these rotations to a precision of ±0.0000000001° is more than sufficient. Rotations smaller…

Paper and discussion history. A mention is not an endorsement.

Halving the cost of quantum addition — mentioned by Strilanc

Sun, 25 Feb 2018 18:52:01 GMT

For superconducting qubits, without error correction, each operation takes tens of nanoseconds. With error correction... it depends how many spare qubits you have. All the non-trivial operations are done by "magic state distillation", where you produce special states in one part of the computer then consume them to perform the operation elsewhere. The more qubits you have, the more space you can allocate to magic state factories. For example, a 32-bit addition can be done with 124 |T> states [1]. If you have N qubits allocated to factories then you can expect to get about 100N magic states…

Paper and discussion history. A mention is not an endorsement.

Halving the cost of quantum addition — mentioned by Strilanc

Fri, 03 Nov 2017 19:48:12 GMT

> An interesting project would be to create a single environment which can be used for both education and research. This does happen sometimes, by accident. I wrote Quirk [1] as an educational tool for learning about quantum circuits. But then I started finding it useful as a tool for optimizing circuits to use fewer gates, just by dragging things around and seeing what happens (there's still enough low-hanging fruit for that to be viable). The paper "Halving the cost of quantum addition" [2] only exists because of a "that's strange..." moment while I was messing around with a decomposition…

Paper and discussion history. A mention is not an endorsement.