Supercomputer simulations of crosstalk in transmon quantum computers Dennis Willsch1,2, Madita Willsch1,2, Fengping Jin1, Hans De Raedt3, Kristel Michielsen1,2 1 Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich, D-5 !25 Jülich, "erman# 2 $%&' Aachen Universit#, D-5 )5* Aachen, "erman# 3 +erni,e Institute for Advanced -aterials, (niversity of "roningen, .i/en0orgh !, .L-23!3 A" "roningen, &he .etherlands Simulation method "enchmark t t ;he simulator determines the state of the de&ice .<( 3 at time )y sol&in! the time+dependent Dun times on the EFDECA cluster for moderate system sizes: Schr=din!er e7uation (;>SE # (a (a Strong scalin! () Wea* scaling 'here the hard'are model has transmons and resonators [,]# () V Breakdown of computation: transformation is the bottleneck: ?l!orithm: Su@u*i+;rotter product+formula al!orithm [1#"]: Basis: 2 coefficients for each resonator sin!le+threaded multi-threaded and each transmon: V Implementation: exponentials are Transmon NISQ device Quantum !ates: implemented )y optimi@ed# ibmqx4 time+dependent pulses [2] 'ith the same shape dia!onalCuint64_t inc is a= 1; as those used on the IBM Q Experience [5]( four+componentfor(int i = NTr- 1; i >= 0; --i, inc <<= 2) { Sin!le+7u)it !ates ha&e Aaussian en&elopes# transformation: uint64_t incl = inc << 2; We use the processor on the IBM Q Experience [5]: and t'o+7u)it !ates use the echoed cross+ #pragma omp for collapse(2) for(uint64_t K = 0; K < dim; K += incl) resonance scheme [B]: for(uint64_t M = 0; M < inc; ++M) mul4x4(&Vn[16*i], &psi[K | M], inc); } for(int r = NRes-1; r >= 0; --r, inc <<= 2) { uint64_t incl = inc << 2; #pragma omp for collapse(2) for(uint64_t K = 0; K < dim; K += incl) for(uint64_t M = 0; M < inc; ++M) mul4x4(&Va[16*r], &psi[K | M], inc); } Jay M. Gambetta, Jerry M. Chow & Matthias Steffen / CC BY (https://creativecommons.org/licenses/by/4.0) Quantum circuit: !rosstalk experiment ,( prepare Q0 in ./0 1( prepare Q1 to Q2 in ./3 or .-3 or .,3 .-0 "( 'ait for some “idle” time → ideally: nothin! happens → in practice: crosstalk moves qubits! 2( rotate Q0 around y axis by 9:1 → ideally: ./3 6 .,3 → in practice: depends on “idle” time8 .,0 5. measure Q- Time evolution of Q0 to Q4: (from left to right .-0 !onclusions: References: ● [1] Koch et al. Ph#s5 $ev5 A 76, 042319 (200#$ [2] De Raedt. Comp5 Ph#s5 $ep5 7, 1 "19%#$ ● [3] Willsch, PhD thesis, RWTH (achen (2020) ● Simulation and experiment match excellently [4] Willsch et al. 4h#s5 $ev5 A 96, 0)2302 "201#$ [5] +,M -, https.//000.research.ib2.co2/ib234 Both are far from the ideal result (diamonds) [6] 5heldon et al. Ph#s5 $ev5 A 93, 060302 "201)$ Errors are generic for transmon processors [3,7] [7] Willsch et al., 4h#s5 $ev5 A 98, 0*23 % "201%$ .,0 We conclude that the simulation model captures the errors in the NISQ device very well..