This notebook introduces to recent 2WQC enhancement of standard 1WQC - in this moment theoretical, but with many arguments that their hardware implementations should become available in a near future. Their simulation turned out, thanks to communication with Nikolay Murzin, already possible with Wolfram Quantum Framework we will use here. More discussion about 2WQC can be found in arXiv:2308.13522, lecture recording, and slides.
Below are some other examples for potential realizations. In classical electronics we naturally act two-way by connecting to a battery: actively both pushing electrons into a chip, and pulling them with electric field. Also for hydrodynamics replacing battery with a pump. There are mechanical qubits for superfluid ( https://www.nature.com/articles/s41534-021-00393-3 ) - connecting such quantum computer to a pump, we would get 2WQC. Mathematically superfluid hydrodynamics and electrodynamics are nearly the same (table below), suggesting such two-way quantum computer should also work there if only having some analog of pump.
Unidirectional ring laser seems to act as such pump for photonic quantum computers, which use laser impulse as state preparation (e.g. https://www.nature.com/articles/s41467-019-11489-y ), as the below setting in CPT perspective would reverse photon trajectory - performing the same impulse for the end side of photonic chip. While it might seem unintuitive, there are realization of optical pulling with light, also negative radiation pressure is possible - being CPT symmetry analogs of standard pushing with light using its positive radiation pressure. Generally lasers are based on stimulation emission-absorption equations being CPT symmetry analogs - state preparation is a consequence of one of them, suggesting to use the latter for symmetric counterpart.
1WQC and 2WQC in Wolfram Quantum Framework
The following operations allow us to use Wolfram Quantum Framework:
Below are its amplitudes and the measured probability distribution - there are two possibilities due to the Hadamard gate, and they have to be equal due to CNOT gate:
In[]:=
qc[]["Amplitudes"]
Out[]=
ℰ
0
00
1
2
,
ℰ
0
010,
ℰ
0
100,
ℰ
0
110,
ℰ
1
000,
ℰ
1
010,
ℰ
1
100,
ℰ
1
110,
ℰ
2
000,
ℰ
2
010,
ℰ
2
100,
ℰ
2
110,
ℰ
3
000,
ℰ
3
010,
ℰ
3
100,
ℰ
3
11
1
2
In[]:=
qc[]["ProbabilityPlot"]
Out[]=
To make it 2WQC, we need to replace some measurements with
〈0|
or
〈1|
. In Wolfram Quantum Framework it can be obtained by just applying SuperDagger[] operation to the standard state preparation - let us do it to the first qubit above: