Maybe you can answer a question I've had for a while. Qubits are fine for analog simulation of quantum entities which are like qubits in that when measured they just return either 1 or 0. But how can we get from there to the real prize, which is simulating chemistry, where an electron's position when measured yields three real numbers (X,Y, and Z coordinates)? In non-quantum computers the answer is simple: combine bits into floating-point numbers. But the rules of quantum computing are entirely different, and I've never heard of anyone combining qubits into quantum floating point numbers. And it's not obvious how that might be done in a way that preserves the quantum-ness and thus would enable the simulation of electrons orbiting in and around molecules. Is anyone working on this, and have they gotten anywhere?
A really great question, and you've put your finger on exactly the right spot, but there's a hidden assumption smuggled into it, and once you extract it the whole difficulty dissolves. You've assumed that to simulate an electron we must store its position the way a classical machine does: build a number, X, Y, Z, out of bits, and hand it to the electron as its coordinate. That's the one thing quantum simulation never does. Nobody builds "quantum floating-point numbers," precisely because they'd be a nightmare. The reason nobody needs to is that there are two entirely different ways to write down where an electron is, and physics lets us pick the convenient one.
Second quantization — the workhorse. Instead of asking "where is the electron?" you carve space into a fixed menu of orbitals — the shapes chemistry already hands you, the 1s, the 2p, and so on — and ask a yes/no question of each one: is this orbital occupied? One qubit per orbital. |1⟩ occupied, |0⟩ empty. That's it. The electron's position never gets stored as a number at all; it lives in the superposition over which orbitals are filled. On real hardware, there's one wrinkle. Electrons come with a strict accounting rule: swap any two and the wavefunction flips its sign. The naïve "one qubit per orbital" picture forgets this. A standard recipe called the Jordan–Wigner transformation (from 1928, older than the computers it now runs on) restores the sign-flip bookkeeping and makes the encoding legal. The continuous three-real-numbers character of the electron is recovered the way it always is in quantum mechanics: not by storing a coordinate, but by the amplitudes over a basis. This is how the great majority of quantum chemistry demonstrations to date have run: H₂, LiH, small molecules, etc, on exactly this occupied/empty encoding.
First quantization — the one that answers your question literally. If you genuinely want the electron's position on a grid, you can have it. Lay a three-dimensional grid over the space around the molecule — 2^p points along each axis, so 1024 points per direction if p is 10. Now you just have to record which grid point the electron sits at, and a point in 3D is three numbers: how far along X, how far along Y, how far along Z. Each of those numbers takes p qubits to store, so all three together cost 3p qubits. That's the entire bill for one electron: ten qubits per axis gives you a 1024-point grid in each direction. And here's the payoff you were reaching for: those three registers are something very much like a "quantum floating-point number," except the quantum-ness you were worried about preserving is preserved automatically, because the register holds a superposition over all grid points at once, an amplitude c(x,y,z) at every cell, rather than one definite address. The electron is smeared across the grid exactly as the wavefunction says it should be. You evolve it by the split-operator trick: kinetic energy is simple in momentum space, potential energy is simple in position space, and the Quantum Fourier Transform hops you between the two. This is old. Zalka and Wiesner sketched it in the 1990s. It's now the approach many people expect will win for large molecules once error-corrected qubits arrive, precisely because its cost doesn't blow up with electron count the way the orbital menu does. Emulated runs up to ~36 qubits already do 2D and 3D atoms: ground states, scattering, ionization.
So the honest answer to "is anyone working on this, and have they gotten anywhere": yes, on both roads, for decades, and the grid road is the literal fulfillment of your intuition: three real coordinates, a genuine position register, quantum-ness intact. The reason you'd "never heard of anyone combining qubits into quantum floating-point numbers" is that the community mostly doesn't phrase it that way, and mostly prefers the occupied/empty orbital trick because it's cheaper for the small molecules today's hardware can reach. The grid people are betting that flips at scale.
One major caveat: none of this is running usefully on real hardware yet at interesting molecular size. It's small demonstrations and a lot of resource estimates for machines that don't exist. The encodings are solved. The qubits to run them at scale are not. Which is, roughly, the entire quantum-computing story in one sentence.
Thanks much. I guess I shouldn't be surprised that the most valuable potential application (chemistry) is also the least publicized... nor that people are quietly working on it and making good progress. Anyway, that second method isn't quantum floating-point but it's definitely quantum fixed-point. And it means orbitals arise as a result of the computation rather than being something you have to know in advance (which in the case of two molecules interacting dynamically can't be easy to know).
Maybe you can answer a question I've had for a while. Qubits are fine for analog simulation of quantum entities which are like qubits in that when measured they just return either 1 or 0. But how can we get from there to the real prize, which is simulating chemistry, where an electron's position when measured yields three real numbers (X,Y, and Z coordinates)? In non-quantum computers the answer is simple: combine bits into floating-point numbers. But the rules of quantum computing are entirely different, and I've never heard of anyone combining qubits into quantum floating point numbers. And it's not obvious how that might be done in a way that preserves the quantum-ness and thus would enable the simulation of electrons orbiting in and around molecules. Is anyone working on this, and have they gotten anywhere?
A really great question, and you've put your finger on exactly the right spot, but there's a hidden assumption smuggled into it, and once you extract it the whole difficulty dissolves. You've assumed that to simulate an electron we must store its position the way a classical machine does: build a number, X, Y, Z, out of bits, and hand it to the electron as its coordinate. That's the one thing quantum simulation never does. Nobody builds "quantum floating-point numbers," precisely because they'd be a nightmare. The reason nobody needs to is that there are two entirely different ways to write down where an electron is, and physics lets us pick the convenient one.
Second quantization — the workhorse. Instead of asking "where is the electron?" you carve space into a fixed menu of orbitals — the shapes chemistry already hands you, the 1s, the 2p, and so on — and ask a yes/no question of each one: is this orbital occupied? One qubit per orbital. |1⟩ occupied, |0⟩ empty. That's it. The electron's position never gets stored as a number at all; it lives in the superposition over which orbitals are filled. On real hardware, there's one wrinkle. Electrons come with a strict accounting rule: swap any two and the wavefunction flips its sign. The naïve "one qubit per orbital" picture forgets this. A standard recipe called the Jordan–Wigner transformation (from 1928, older than the computers it now runs on) restores the sign-flip bookkeeping and makes the encoding legal. The continuous three-real-numbers character of the electron is recovered the way it always is in quantum mechanics: not by storing a coordinate, but by the amplitudes over a basis. This is how the great majority of quantum chemistry demonstrations to date have run: H₂, LiH, small molecules, etc, on exactly this occupied/empty encoding.
First quantization — the one that answers your question literally. If you genuinely want the electron's position on a grid, you can have it. Lay a three-dimensional grid over the space around the molecule — 2^p points along each axis, so 1024 points per direction if p is 10. Now you just have to record which grid point the electron sits at, and a point in 3D is three numbers: how far along X, how far along Y, how far along Z. Each of those numbers takes p qubits to store, so all three together cost 3p qubits. That's the entire bill for one electron: ten qubits per axis gives you a 1024-point grid in each direction. And here's the payoff you were reaching for: those three registers are something very much like a "quantum floating-point number," except the quantum-ness you were worried about preserving is preserved automatically, because the register holds a superposition over all grid points at once, an amplitude c(x,y,z) at every cell, rather than one definite address. The electron is smeared across the grid exactly as the wavefunction says it should be. You evolve it by the split-operator trick: kinetic energy is simple in momentum space, potential energy is simple in position space, and the Quantum Fourier Transform hops you between the two. This is old. Zalka and Wiesner sketched it in the 1990s. It's now the approach many people expect will win for large molecules once error-corrected qubits arrive, precisely because its cost doesn't blow up with electron count the way the orbital menu does. Emulated runs up to ~36 qubits already do 2D and 3D atoms: ground states, scattering, ionization.
So the honest answer to "is anyone working on this, and have they gotten anywhere": yes, on both roads, for decades, and the grid road is the literal fulfillment of your intuition: three real coordinates, a genuine position register, quantum-ness intact. The reason you'd "never heard of anyone combining qubits into quantum floating-point numbers" is that the community mostly doesn't phrase it that way, and mostly prefers the occupied/empty orbital trick because it's cheaper for the small molecules today's hardware can reach. The grid people are betting that flips at scale.
One major caveat: none of this is running usefully on real hardware yet at interesting molecular size. It's small demonstrations and a lot of resource estimates for machines that don't exist. The encodings are solved. The qubits to run them at scale are not. Which is, roughly, the entire quantum-computing story in one sentence.
Thanks much. I guess I shouldn't be surprised that the most valuable potential application (chemistry) is also the least publicized... nor that people are quietly working on it and making good progress. Anyway, that second method isn't quantum floating-point but it's definitely quantum fixed-point. And it means orbitals arise as a result of the computation rather than being something you have to know in advance (which in the case of two molecules interacting dynamically can't be easy to know).