0.003034656830204855 * IIIYYIIIYY
+ 0.003034656830204855 * IIIXXIIIYY
+ 0.003034656830204855 * IIIYYIIIXX
+ 0.003034656830204855 * IIIXXIIIXX
- 0.008373361424264817 * YZZZYIIIYY
- 0.008373361424264817 * XZZZXIIIYY
- 0.008373361424264817 * YZZZYIIIXX
- 0.008373361424264817 * XZZZXIIIXX
+ 0.00211113766859809 * YZZYIIIIYY
+ 0.00211113766859809 * XZZXIIIIYY
+ 0.00211113766859809 * YZZYIIIIXX
+ 0.00211113766859809 * XZZXIIIIXX
- 0.00491756976241806 * IIIIIIIIYY
- 0.00491756976241806 * IIIIIIIIXX
+ 0.010540187409026488 * ZIIIIIIIYY
+ 0.010540187409026488 * ZIIIIIIIXX
- 0.0011822832324725804 * IZIIIIIIYY
- 0.0011822832324725804 * IZIIIIIIXX
- 0.0011822832324725804 * IIZIIIIIYY
- 0.0011822832324725804 * IIZIIIIIXX
- 0.00154067008970742 * IIIZIIIIYY
- 0.00154067008970742 * IIIZIIIIXX
+ 0.011733623912074194 * IIIIZIIIYY
+ 0.011733623912074194 * IIIIZIIIXX
+ 0.0027757462269049522 * IIIIIZIIYY
+ 0.0027757462269049522 * IIIIIZIIXX
+ 0.0036202487558837123 * IIIIIIZIYY
+ 0.0036202487558837123 * IIIIIIZIXX
+ 0.0036202487558837123 * IIIIIIIZYY
+ 0.0036202487558837123 * IIIIIIIZXX
+ 0.005996760849734561 * IIYZYIIYZY
+ 0.005996760849734561 * IIXZXIIYZY
+ 0.005996760849734561 * IIYZYIIXZX
+ 0.005996760849734561 * IIXZXIIXZX
+ 0.004802531988356293 * IIYYIIIYZY
+ 0.004802531988356293 * IIXXIIIYZY
+ 0.004802531988356293 * IIYYIIIXZX
+ 0.004802531988356293 * IIXXIIIXZX
- 0.004879740484191497 * YZYIIIIYZY
- 0.004879740484191497 * XZXIIIIYZY
- 0.004879740484191497 * YZYIIIIXZX
- 0.004879740484191497 * XZXIIIIXZX
+ 0.005996760849734561 * IYZZYIYZZY
+ 0.005996760849734561 * IXZZXIYZZY
+ 0.005996760849734561 * IYZZYIXZZX
+ 0.005996760849734561 * IXZZXIXZZX
+ 0.004802531988356293 * IYZYIIYZZY
+ 0.004802531988356293 * IXZXIIYZZY
+ 0.004802531988356293 * IYZYIIXZZX
+ 0.004802531988356293 * IXZXIIXZZX
- 0.004879740484191497 * YYIIIIYZZY
- 0.004879740484191497 * XXIIIIYZZY
- 0.004879740484191497 * YYIIIIXZZX
- 0.004879740484191497 * XXIIIIXZZX
- 0.008373361424264817 * IIIYYYZZZY
- 0.008373361424264817 * IIIXXYZZZY
- 0.008373361424264817 * IIIYYXZZZX
- 0.008373361424264817 * IIIXXXZZZX
+ 0.0307383271773138 * YZZZYYZZZY
+ 0.0307383271773138 * XZZZXYZZZY
+ 0.0307383271773138 * YZZZYXZZZX
+ 0.0307383271773138 * XZZZXXZZZX
- 0.0077644411821215335 * YZZYIYZZZY
- 0.0077644411821215335 * XZZXIYZZZY
- 0.0077644411821215335 * YZZYIXZZZX
- 0.0077644411821215335 * XZZXIXZZZX
- 0.005949019975734247 * IIIIIYZZZY
- 0.005949019975734247 * IIIIIXZZZX
- 0.0351167704024114 * ZIIIIYZZZY
- 0.0351167704024114 * ZIIIIXZZZX
+ 0.0027298828353264134 * IZIIIYZZZY
+ 0.0027298828353264134 * IZIIIXZZZX
+ 0.0027298828353264134 * IIZIIYZZZY
+ 0.0027298828353264134 * IIZIIXZZZX
+ 0.0023679368995844726 * IIIZIYZZZY
+ 0.0023679368995844726 * IIIZIXZZZX
- 0.03305872858775587 * IIIIZYZZZY
- 0.03305872858775587 * IIIIZXZZZX
- 0.0021498576488650843 * IIIIIYIZZY
- 0.0021498576488650843 * IIIIIXIZZX
- 0.0021498576488650843 * IIIIIYZIZY
- 0.0021498576488650843 * IIIIIXZIZX
+ 0.004479074568182561 * IIIIIYZZIY
+ 0.004479074568182561 * IIIIIXZZIX
+ 0.004802531988356293 * IIYZYIIYYI
+ 0.004802531988356293 * IIXZXIIYYI
+ 0.004802531988356293 * IIYZYIIXXI
+ 0.004802531988356293 * IIXZXIIXXI
+ 0.010328819322301622 * IIYYIIIYYI
+ 0.010328819322301622 * IIXXIIIYYI
+ 0.010328819322301622 * IIYYIIIXXI
+ 0.010328819322301622 * IIXXIIIXXI
- 0.003466391848475337 * YZYIIIIYYI
- 0.003466391848475337 * XZXIIIIYYI
- 0.003466391848475337 * YZYIIIIXXI
- 0.003466391848475337 * XZXIIIIXXI
+ 0.004802531988356293 * IYZZYIYZYI
+ 0.004802531988356293 * IXZZXIYZYI
+ 0.004802531988356293 * IYZZYIXZXI
+ 0.004802531988356293 * IXZZXIXZXI
+ 0.010328819322301622 * IYZYIIYZYI
+ 0.010328819322301622 * IXZXIIYZYI
+ 0.010328819322301622 * IYZYIIXZXI
+ 0.010328819322301622 * IXZXIIXZXI
- 0.003466391848475337 * YYIIIIYZYI
- 0.003466391848475337 * XXIIIIYZYI
- 0.003466391848475337 * YYIIIIXZXI
- 0.003466391848475337 * XXIIIIXZXI
+ 0.00211113766859809 * IIIYYYZZYI
+ 0.00211113766859809 * IIIXXYZZYI
+ 0.00211113766859809 * IIIYYXZZXI
+ 0.00211113766859809 * IIIXXXZZXI
- 0.0077644411821215335 * YZZZYYZZYI
- 0.0077644411821215335 * XZZZXYZZYI
- 0.0077644411821215335 * YZZZYXZZXI
- 0.0077644411821215335 * XZZZXXZZXI
+ 0.006575744899182541 * YZZYIYZZYI
+ 0.006575744899182541 * XZZXIYZZYI
+ 0.006575744899182541 * YZZYIXZZXI
+ 0.006575744899182541 * XZZXIXZZXI
+ 0.023557442395837284 * IIIIIYZZYI
+ 0.023557442395837284 * IIIIIXZZXI
+ 0.010889407716094479 * ZIIIIYZZYI
+ 0.010889407716094479 * ZIIIIXZZXI
- 0.0003518893528389501 * IZIIIYZZYI
- 0.0003518893528389501 * IZIIIXZZXI
- 0.0003518893528389501 * IIZIIYZZYI
- 0.0003518893528389501 * IIZIIXZZXI
- 0.00901204279263803 * IIIZIYZZYI
- 0.00901204279263803 * IIIZIXZZXI
+ 0.0127339139792953 * IIIIZYZZYI
+ 0.0127339139792953 * IIIIZXZZXI
- 0.003818281201314288 * IIIIIYIZYI
- 0.003818281201314288 * IIIIIXIZXI
- 0.003818281201314288 * IIIIIYZIYI
- 0.003818281201314288 * IIIIIXZIXI
+ 0.004217284878422759 * IYYIIIYYII
+ 0.004217284878422759 * IXXIIIYYII
+ 0.004217284878422759 * IYYIIIXXII
+ 0.004217284878422759 * IXXIIIXXII
- 0.004879740484191498 * IIYZYYZYII
- 0.004879740484191498 * IIXZXYZYII
- 0.004879740484191498 * IIYZYXZXII
- 0.004879740484191498 * IIXZXXZXII
- 0.003466391848475337 * IIYYIYZYII
- 0.003466391848475337 * IIXXIYZYII
- 0.003466391848475337 * IIYYIXZXII
- 0.003466391848475337 * IIXXIXZXII
+ 0.004868302545087521 * YZYIIYZYII
+ 0.004868302545087521 * XZXIIYZYII
+ 0.004868302545087521 * YZYIIXZXII
+ 0.004868302545087521 * XZXIIXZXII
- 0.004879740484191498 * IYZZYYYIII
- 0.004879740484191498 * IXZZXYYIII
- 0.004879740484191498 * IYZZYXXIII
- 0.004879740484191498 * IXZZXXXIII
- 0.003466391848475337 * IYZYIYYIII
- 0.003466391848475337 * IXZXIYYIII
- 0.003466391848475337 * IYZYIXXIII
- 0.003466391848475337 * IXZXIXXIII
+ 0.004868302545087521 * YYIIIYYIII
+ 0.004868302545087521 * XXIIIYYIII
+ 0.004868302545087521 * YYIIIXXIII
+ 0.004868302545087521 * XXIIIXXIII
- 0.004917569762418068 * IIIYYIIIII
- 0.004917569762418068 * IIIXXIIIII
+ 0.0027757462269049522 * ZIIYYIIIII
+ 0.0027757462269049522 * ZIIXXIIIII
+ 0.0036202487558837123 * IZIYYIIIII
+ 0.0036202487558837123 * IZIXXIIIII
+ 0.0036202487558837123 * IIZYYIIIII
+ 0.0036202487558837123 * IIZXXIIIII
- 0.005949019975734285 * YZZZYIIIII
- 0.005949019975734285 * XZZZXIIIII
- 0.0021498576488650843 * YIZZYIIIII
- 0.0021498576488650843 * XIZZXIIIII
- 0.0021498576488650843 * YZIZYIIIII
- 0.0021498576488650843 * XZIZXIIIII
+ 0.004479074568182561 * YZZIYIIIII
+ 0.004479074568182561 * XZZIXIIIII
+ 0.02355744239583729 * YZZYIIIIII
+ 0.02355744239583729 * XZZXIIIIII
- 0.003818281201314288 * YIZYIIIIII
- 0.003818281201314288 * XIZXIIIIII
- 0.003818281201314288 * YZIYIIIIII
- 0.003818281201314288 * XZIXIIIIII
+ 1.0709274663656798 * IIIIIIIIII
- 0.5772920990654371 * ZIIIIIIIII
- 0.4244817531727133 * IZIIIIIIII
+ 0.06245512523136934 * ZZIIIIIIII
- 0.4244817531727134 * IIZIIIIIII
+ 0.06245512523136934 * ZIZIIIIIII
+ 0.06558452315458405 * IZZIIIIIII
- 0.3899177647415215 * IIIZIIIIII
+ 0.053929860773588405 * ZIIZIIIIII
+ 0.06022550139954594 * IZIZIIIIII
+ 0.06022550139954594 * IIZZIIIIII
+ 0.004360552555030484 * YZZYZIIIII
+ 0.004360552555030484 * XZZXZIIIII
- 0.30101532158947975 * IIIIZIIIII
+ 0.08360121967246183 * ZIIIZIIIII
+ 0.06278876343471208 * IZIIZIIIII
+ 0.06278876343471208 * IIZIZIIIII
+ 0.053621410722614865 * IIIZZIIIII
+ 0.010540187409026488 * IIIYYZIIII
+ 0.010540187409026488 * IIIXXZIIII
- 0.0351167704024114 * YZZZYZIIII
- 0.0351167704024114 * XZZZXZIIII
+ 0.010889407716094479 * YZZYIZIIII
+ 0.010889407716094479 * XZZXIZIIII
- 0.5772920990654372 * IIIIIZIIII
+ 0.11409163501020725 * ZIIIIZIIII
+ 0.06732342777645686 * IZIIIZIIII
+ 0.06732342777645686 * IIZIIZIIII
+ 0.060505605672770954 * IIIZIZIIII
+ 0.11433954684977561 * IIIIZZIIII
- 0.0011822832324725804 * IIIYYIZIII
- 0.0011822832324725804 * IIIXXIZIII
+ 0.0027298828353264134 * YZZZYIZIII
+ 0.0027298828353264134 * XZZZXIZIII
- 0.0003518893528389501 * YZZYIIZIII
- 0.0003518893528389501 * XZZXIIZIII
- 0.42448175317271336 * IIIIIIZIII
+ 0.06732342777645686 * ZIIIIIZIII
+ 0.0782363777898523 * IZIIIIZIII
+ 0.06980180803300681 * IIZIIIZIII
+ 0.07055432072184756 * IIIZIIZIII
+ 0.06878552428444665 * IIIIZIZIII
+ 0.06245512523136934 * IIIIIZZIII
- 0.0011822832324725804 * IIIYYIIZII
- 0.0011822832324725804 * IIIXXIIZII
+ 0.0027298828353264134 * YZZZYIIZII
+ 0.0027298828353264134 * XZZZXIIZII
- 0.0003518893528389501 * YZZYIIIZII
- 0.0003518893528389501 * XZZXIIIZII
- 0.42448175317271336 * IIIIIIIZII
+ 0.06732342777645686 * ZIIIIIIZII
+ 0.06980180803300681 * IZIIIIIZII
+ 0.0782363777898523 * IIZIIIIZII
+ 0.07055432072184756 * IIIZIIIZII
+ 0.06878552428444665 * IIIIZIIZII
+ 0.06245512523136934 * IIIIIZIZII
+ 0.06558452315458405 * IIIIIIZZII
- 0.00154067008970742 * IIIYYIIIZI
- 0.00154067008970742 * IIIXXIIIZI
+ 0.0023679368995844726 * YZZZYIIIZI
+ 0.0023679368995844726 * XZZZXIIIZI
- 0.00901204279263803 * YZZYIIIIZI
- 0.00901204279263803 * XZZXIIIIZI
- 0.38991776474152134 * IIIIIIIIZI
+ 0.060505605672770954 * ZIIIIIIIZI
+ 0.07055432072184756 * IZIIIIIIZI
+ 0.07055432072184756 * IIZIIIIIZI
+ 0.08470391802239534 * IIIZIIIIZI
+ 0.05665606755281972 * IIIIZIIIZI
+ 0.053929860773588405 * IIIIIZIIZI
+ 0.06022550139954594 * IIIIIIZIZI
+ 0.06022550139954594 * IIIIIIIZZI
+ 0.004360552555030484 * IIIIIYZZYZ
+ 0.004360552555030484 * IIIIIXZZXZ
+ 0.011733623912074194 * IIIYYIIIIZ
+ 0.011733623912074194 * IIIXXIIIIZ
- 0.03305872858775587 * YZZZYIIIIZ
- 0.03305872858775587 * XZZZXIIIIZ
+ 0.0127339139792953 * YZZYIIIIIZ
+ 0.0127339139792953 * XZZXIIIIIZ
- 0.30101532158947975 * IIIIIIIIIZ
+ 0.11433954684977561 * ZIIIIIIIIZ
+ 0.06878552428444665 * IZIIIIIIIZ
+ 0.06878552428444665 * IIZIIIIIIZ
+ 0.05665606755281972 * IIIZIIIIIZ
+ 0.12357087224898464 * IIIIZIIIIZ
+ 0.08360121967246183 * IIIIIZIIIZ
+ 0.06278876343471208 * IIIIIIZIIZ
+ 0.06278876343471208 * IIIIIIIZIZ
+ 0.053621410722614865 * IIIIIIIIZZ
I can’t remember seeing a Hamiltonian like this before. Is there another form this could be in? Thanks!
1 Like
These are the Pauli Strings for the Hamiltonian, but let me check with the author of the problem to see if there is another form
1 Like
There are many ways to represent the Hamiltonian, and this is one of the most common forms. May I ask what form you are most familiar with?
mauro
May 12, 2022, 8:06am
5
For this problem what should be the total time of evolution at which the error must be computed?
1 Like
The Hamiltonian evolution is written as e^(iHt).
As the error is e^(-iH), use t=1
2 Likes
Hello and good afternoon! I’m trying to understand the notation of the problem. For example, the string “IIZIIIIIYY” is the Kronecker product of I * I * Z * … * Y * Y?
1 Like
Most of my quantum education has been from Qiskit, and I don’t remember seeing this form. I don’t understand the YZZIYZZYI type things (Kronecker product as per @pp.dirac ?)
1 Like
pp.dirac:
Kronecker product
Yes, it is the Kronecker product.
1 Like
Do we have closed form expressions for the numerical summands?
1 Like
Correct me if I’m misunderstanding you. Are you asking for a simplified way of representing the Hamiltonian? Perhaps this paper will help with understanding the Pauli String representation, as well as the problem itself.
2 Likes
The coefficients of the Hamiltonian terms are floating-point numbers. They stem from the complex computation of integrals between electronic orbitals. We don’t have a nice analytical way to state them (e.g. pi/4, etc.).
If I misunderstood the question, please clarify.
2 Likes
No, just the numerical coefficients. Thanks for the reference though.
1 Like
Hi everyone,Please could you tell what type of mapping LiH Hamiltonian is it? JW? BK? or Parity?
