Reversible circuits with Janus

Run a circuit forward. Then watch it unwind.

call emits a circuit gate by gate. uncall walks the same Janus procedure backward, reversing both the gate order and each operation.

Quantum Fourier Transform

A number becomes phase.
Reverse it to get the number back.

QFT spreads one basis value across eight equal magnitudes. The arrows reveal where the value went: it is now stored in their relative phases.

Computational basis input Phase pattern · editable after call |101⟩

Gate sequence

ready · 0 / 7

q0 · LSBq1q2 · MSB

Forward circuit appears gate by gate.

Ready. Call QFT and watch the value move into relative phase.

|000⟩ 0.000 0.000 rad
|001⟩ 0.000 0.000 rad
|010⟩ 0.000 0.000 rad
|011⟩ 0.000 0.000 rad
|100⟩ 0.000 0.000 rad
|101⟩ 0.000 0.000 rad
|110⟩ 0.000 0.000 rad
|111⟩ 0.000 0.000 rad

Call · QFT

Uncall · inverse QFT

qft.janus · width-generic

one algorithm · variable width

Specialized to three qubits by the host adapter before execution

length target control swap_index

procedure qft()
    if length > 0 then
        target += length - 1
        from target = (length - 1) do
            call h(target)
            if target > 0 then
                control += target
                control -= 1
                from control = (target - 1) do
                    call cp_pi(control, target, 1, 2 ** (target - control))
                loop
                    control -= 1
                until control = 0
            else skip
            fi target > 0
        loop
            target -= 1
        until target = 0
        call reverse_qubit_order()
    else skip
    fi length > 0

procedure reverse_qubit_order()
    if length > 1 then
        from swap_index = 0 do
            call swap(swap_index, length - swap_index - 1)
        loop
            swap_index += 1
        until swap_index = (length / 2 - 1)
        swap_index -= length / 2
        swap_index += 1
    else skip
    fi length > 1

Reversible adder

Add forward.
Subtract backward.

The gate sequence adds register a into b. Uncall reverses that exact sequence, turning the same procedure into subtraction.

a · unchanged0101 · 5

b · sum · editable after call

carry · starts and ends at 00

Gate sequence

ready · 0 / 24

a0a1a2a3b0b1b2b3c0 · |0⟩

Forward addition circuit appears gate by gate.

Ready. Call add to compute b = a + b mod 16.

Run a circuit forward. Then watch it unwind.

A number becomes phase.
Reverse it to get the number back.

Gate sequence

Call · QFT

Uncall · inverse QFT

Add forward.
Subtract backward.

Gate sequence

Call · addition

Uncall · subtraction