Qudit Gate Tests

Validation of single-qubit gate generators

D2_Gates

Single-qubit gate correctness tests for $d=2$.

Test name	Description	Result	Time taken (s)
CX__00	$CX|00⟩=|00⟩$	✓	0.0038
CX__01	$CX|01⟩=|01⟩$	✓	0.0006
CX__10_11	$CX|10⟩=|11⟩$	✓	0.0009
CX__11_10	$CX|11⟩=|10⟩$	✓	0.0005
H__0_sup	$H|0⟩=(|0⟩+|1⟩)/\sqrt{2}$	✓	0.0021
H__1_sup	$H|1⟩=(|0⟩-|1⟩)/\sqrt{2}$	✓	0.0009
H_decomp	$H=X{R}_Y(\pi /2)$	✓	0.0040
I__0_ID	$I|0⟩=|0⟩$	✓	0.0004
I__1_ID	$I|1⟩=|1⟩$	✓	0.0003
RX	$R_X(\pi )|0⟩\approx |1⟩$ (up to global phase $-i$):	✓	0.0004
RY	$R_Y(\pi )|0⟩=|1⟩$:	✓	0.0003
RZ	$R_Z(\pi )|1⟩\approx -|1⟩$ (up to global phase $i$):	✓	0.0251
SWAP__01_10	$SWAP|01⟩=|10⟩$	✓	0.0004
SWAP__10_01	$SWAP|10⟩=|01⟩$	✓	0.0002
X__0_1	$X|0⟩=|1⟩$	✓	0.0004
X__1_0	$X|1⟩=|0⟩$	✓	0.0004
Y__0_i1	$Y|0⟩=i|1⟩$	✓	0.0003
Y__1_mi0	$Y|1⟩=-i|0⟩$	✓	0.0003
Z__0_stays_0	$Z|0⟩=|0⟩$	✓	0.0003
Z__1_m1	$Z|1⟩=-|1⟩$	✓	0.0004

D3_Gates

Single-qubit gate correctness tests for $d=3$.

Test name	Description	Result	Time taken (s)
CX__00	$CX|00⟩=|00⟩$	✓	0.0004
CX__11	$CX|11⟩=|12⟩$	✓	0.0014
CX__21	$CX|21⟩=|20⟩$	✓	0.0004
H__0_sup	$H|0⟩=(|0⟩+|1⟩+|2⟩)/\sqrt{3}$	✓	0.0006
H__1_sup	$H|1⟩=(|0⟩+\omega |1⟩+{\omega }^2|2⟩)/\sqrt{3}$	✓	0.0007
I__0	$I|0⟩=|0⟩$	✓	0.0002
I__1	$I|1⟩=|1⟩$	✓	0.0002
I__2	$I|2⟩=|2⟩$	✓	0.0002
SWAP__12_21	$SWAP|12⟩=|21⟩$	✓	0.0003
X__0_1	$X|0⟩=|1⟩$	✓	0.0002
X__1_2	$X|1⟩=|2⟩$	✓	0.0002
X__2_0	$X|2⟩=|0⟩$	✓	0.0002
Y__0_i1	$Y|0⟩\propto |1⟩$: generalized $Y=ZX/i$ shifts by one level	✓	0.0007
Y__1_i2	$Y|1⟩\propto |2⟩$: generalized $Y=ZX/i$ shifts by one level	✓	0.0002
Y__2_i0	$Y|2⟩\propto |0⟩$: generalized $Y=ZX/i$ shifts cyclically	✓	0.0002
Z__0	$Z|0⟩=|0⟩$	✓	0.0002
Z__1	$Z|1⟩=\omega |1⟩$	✓	0.0002
Z__2	$Z|2⟩={\omega }^2|2⟩$	✓	0.0002

D5_Gates

Single-qubit gate correctness tests for $d=5$.

Test name	Description	Result	Time taken (s)
CX__00	$CX|00⟩=|00⟩$	✓	0.0003
CX__11	$CX|11⟩=|12⟩$	✓	0.0002
CX__34	$CX|34⟩=|32⟩$	✓	0.0002
H__0_sup	$H|0⟩=(|0⟩+|1⟩+|2⟩+|3⟩+|4⟩)/\sqrt{5}$	✓	0.0003
H__1_sup	$H|1⟩=(|0⟩+\omega |1⟩+{\omega }^2|2⟩+{\omega }^3|3⟩+{\omega }^4|4⟩)/\sqrt{5}$	✓	0.0003
I__0	$I|0⟩=|0⟩$	✓	0.0003
I__1	$I|1⟩=|1⟩$	✓	0.0002
I__2	$I|2⟩=|2⟩$	✓	0.0002
I__3	$I|3⟩=|3⟩$	✓	0.0002
I__4	$I|4⟩=|4⟩$	✓	0.0002
SWAP__13_31	$SWAP|13⟩=|31⟩$	✓	0.0005
X__0_1	$X|0⟩=|1⟩$	✓	0.0004
X__1_2	$X|1⟩=|2⟩$	✓	0.0002
X__4_0	$X|4⟩=|0⟩$	✓	0.0002
Y__0_i1	$Y|0⟩\propto |1⟩$: generalized $Y=ZX/i$ shifts by one level	✓	0.0003
Y__2_i3	$Y|2⟩\propto |3⟩$: generalized $Y=ZX/i$ shifts by one level	✓	0.0002
Y__4_i0	$Y|4⟩\propto |0⟩$: generalized $Y=ZX/i$ shifts cyclically	✓	0.0002
Z__0	$Z|0⟩=|0⟩$	✓	0.0003
Z__1	$Z|1⟩=\omega |1⟩$	✓	0.0002
Z__4	$Z|4⟩={\omega }^4|4⟩$	✓	0.0002