diff --git a/data/observable-estimations/circuit-models/su2_lsh_hadron_dynamics/REPLY b/data/observable-estimations/circuit-models/su2_lsh_hadron_dynamics/REPLY new file mode 100644 index 0000000..f23f63b --- /dev/null +++ b/data/observable-estimations/circuit-models/su2_lsh_hadron_dynamics/REPLY @@ -0,0 +1,839 @@ +README.txt + +Quantum Advantage Tracker submission update +Instance: su2_lsh_hadron_dynamics_N60_x100_dt0p0015_t20 + +This README is an updated submission note prepared in response to the tracker +review comments. It supplements the earlier summary with: +(1) the qubit Hamiltonian used in the submitted quantum simulation, +(2) explicit computational-basis initial states, +(3) observables written in Pauli/Z language, +(4) the IBM Boston observable value for the submitted instance, +(5) the comparative error-bar prescription actually used in the work, and +(6) a reproducibility manifest for circuit files and raw data. + +======================================================================== +SHORT RESPONSE SUMMARY TO THE TRACKER REVIEW POINTS +======================================================================== + +(1) Hamiltonian in qubit/Pauli form: + Added in Section 2. + +(2) Explicit computational-basis initial states: + Added in Section 3. + +(3) Observables in Pauli/Z language: + Added in Section 4. + +(4) IBM Boston observable values and error-bar clarification for the submitted + instances t = 5, 10, 15, 20: + Added in Sections 5, 6, and 7. The README now explicitly states that the + quoted error bars are inter-method comparative estimates combined with an + exactly known symmetry-violation diagnostic, not shot-noise bars. + +(5) Copies of circuits, raw data, and a circuit figure from the methods section: + Submission-package manifest added in Sections 8 and 11. + +======================================================================== +0. HOW ERROR BARS ARE TREATED IN THIS SUBMISSION +======================================================================== + +The quoted error bars in this submission are NOT statistical shot-noise error +bars. + +For the dynamical observable n_f(t), the exact noiseless value is not known at +the scale of the 60-site / 120-qubit experiment. Therefore, within the present +study, the only principled uncertainty estimate available is a comparative +inter-method estimate, supplemented by an error diagnostic from violation of an +exactly conserved quantity. + +Concretely: +- the observable n_f(t) is computed independently using four methods: + TN, PP_CPU, PP_GPU, and QPU; +- the spread across these four values measures inter-method uncertainty; +- the conserved global charge Q is exactly known in the chosen sector; +- deviation of the measured/simulated Q from its exact value gives a direct + diagnostic of error in that measurement; +- the final quoted error estimate combines the two in quadrature. + +Thus, the uncertainty quoted here is a comparative cross-method error estimate +with symmetry-violation diagnosis built in. It is not a shot-noise bar. + +======================================================================== +1. PROBLEM INSTANCE +======================================================================== + +We study real-time dynamics in a (1+1)-dimensional SU(2) lattice gauge theory +with staggered fermions, encoded in the gauge-invariant Loop-String-Hadron +(LSH) basis and implemented on IBM Boston. + +Submitted instance: +- system size: N = 60 lattice sites +- qubits: 120 (2 qubits per site) +- coupling: x = 100 +- mass ratio: m/g = 1 +- Trotter step size: dt = 0.0015 +- number of Trotter steps in the original submitted instance: 20 + (this reply includes instances for time steps 5, 10, 15 in addition to 20) +- hardware backend: IBM Boston (156-qubit Heron processor) +- shot budget: 10,000 shots per Trotter step +- readout mitigation: measurement-error mitigation only + +The main reported dynamical observable is built from a differential protocol: +one run evolves the strong-coupling vacuum (SCV), a second run evolves a +centered meson in the same background, and the reported signal is the +difference of the corresponding observables. + +======================================================================== +2. HAMILTONIAN AND QUBIT MAPPING +======================================================================== + +2.1 Dimensionless Hamiltonian + +The scaled SU(2) Kogut-Susskind Hamiltonian is written as + + W = H_E + mu H_M + x H_I + +with + x = 1 / (g^2 a^2) + mu = 2 (m/g) sqrt(x) + +For the submitted instance x = 100 and m/g = 1, so + + mu = 20(sqrt(x)) + +The quantum circuit uses the large-x / weak-coupling LSH approximation discussed +in the paper and methods supplement. + +2.2 LSH variables and qubit encoding + +At each site r there are two binary LSH string-end occupations: + n_i(r) in {0,1} + n_o(r) in {0,1} + +These are encoded directly in qubits. In operator form, + + n_i(r) = (I - Z_i(r)) / 2 + n_o(r) = (I - Z_o(r)) / 2 + +where Z_i(r) and Z_o(r) are Pauli-Z operators on the two qubits associated with +site r. + +The loop variable n_l(r) is not stored as a separate qubit in this 1D setup; in +the weak-coupling approximation it is replaced by a large incoming boundary flux +l_i and treated analytically. + +2.3 Approximate Hamiltonian used for the quantum circuit + +The approximate electric term is + + H_E^(approx) = const + A sum_r P_01(r), + +where + A = l_i / 2 + 3/4 + +and P_01(r) is the projector onto the local two-qubit basis state +|n_i(r), n_o(r)> = |0,1>. + +In Pauli form, + + P_01(r) = [(I + Z_i(r)) (I - Z_o(r))] / 4 + = [I - Z_o(r) + Z_i(r) - Z_i(r) Z_o(r)] / 4. + +So, up to an irrelevant global constant, + + H_E^(approx) = (A/4) sum_r [I - Z_o(r) + Z_i(r) - Z_i(r) Z_o(r)]. + +The approximate mass term is + + H_M^(approx) = sum_r (-1)^r [n_i(r) + n_o(r)]. + +Since n = (I - Z)/2 and N = 60 is even, this is equivalently + + H_M^(approx) = -(1/2) sum_r (-1)^r [Z_i(r) + Z_o(r)]. + +The approximate interaction term is + + H_I^(approx) + = sum_r [ chi_o^+(r) chi_o^-(r+1) + chi_o^+(r+1) chi_o^-(r) + + chi_i^+(r) chi_i^-(r+1) + chi_i^+(r+1) chi_i^-(r) ]. + +After Jordan-Wigner mapping this becomes an XY hopping Hamiltonian on the i and +o chains. In Pauli form, + + H_I^(approx) + = - sum_{r=0}^{N-2} [ X_i(r) X_i(r+1) + Y_i(r) Y_i(r+1) ] + - sum_{r=0}^{N-2} [ X_o(r) X_o(r+1) + Y_o(r) Y_o(r+1) ]. + +Equivalently, in the logical ordering where the first N qubits are the i chain +and the next N qubits are the o chain, + + H_I^(approx) + = - sum_{r != N-1} [ X_r X_{r+1} + Y_r Y_{r+1} ]. + +This is the Pauli Hamiltonian implemented by the digital circuit up to the +large-x approximation and the omission of global phases. + +2.4 Numerical couplings used in the submitted x = 100 simulation + +For the first-order Trotter step, + dt = 0.0015 + +The interaction block uses + c = dt * x = 0.0015 * 100 = 0.15. + +The mass block uses + m_tilde = dt * mu = 0.0015 * 20 = 0.03. + +The electric block uses a site-pair phase + theta = -dt * (l_i/2 + 3/4), +with the exact numerical theta fixed by the chosen large-flux approximation and +encoded directly in the submitted circuit files. + +The Trotter step is applied in the order + + exp[-i m_tilde H_M] exp[-i dt H_E] exp[-i c H_I] + +using first-order Lie-Trotter decomposition. + +======================================================================== +3. INITIAL STATES (COMPUTATIONAL BASIS STATES) +======================================================================== + +The submission uses two product states, both in the same global charge sector. + +3.1 Strong-coupling vacuum (SCV) + +In site language, the SCV is + +- for even sites r: (n_i(r), n_o(r)) = (0,0) +- for odd sites r: (n_i(r), n_o(r)) = (1,1) + +This gives n_f(r) = 0 on every site. + +In per-site-pair notation + [(n_i(1),n_o(1)), (n_i(2),n_o(2)), ...] +the SCV is + + (00,11,00,11,00,11,...,00,11). + +In the initialization ordering used for the first Trotter step, + [n_i(1), n_i(2), n_o(1), n_o(2), n_i(3), n_i(4), n_o(3), n_o(4), ...], +the SCV is the computational-basis bitstring + + 01010101...0101 + +(i.e. repeating "0101"). + +In the simple zigzag ordering + [n_i(1), n_o(1), n_i(2), n_o(2), ...], +the same state is + + 00110011...0011 + +(i.e. repeating "0011"). + +The chosen initial ordering results in one fewer layer of SWAP gates in the time-evolution circuit. + +3.2 Centered hadron (Baryon-anti-baryon) state + +The hadron state is obtained from the SCV by placing hadronic excitations +on the two central staggered sites. + +In site language (1-based site labels), the centered hadron is chosen as + +- site 30 (even): (n_i, n_o) = (1,1) +- site 31 (odd): (n_i, n_o) = (0,0) + +with all other sites identical to the SCV. + +This gives + n_f(30) = 2, + n_f(31) = 2, +and n_f(r) = 0 elsewhere. + +In per-site-pair notation this is + + (00,11,...,00,11, 11,00, 00,11,...,00,11). + +In the initialization ordering + [n_i(1), n_i(2), n_o(1), n_o(2), ...], +the state is again the SCV bitstring except for the central 4-bit block +corresponding to sites 30 and 31: +- SCV central block: 0101 +- Hadron central block: 1100 + +One can also start with a central block 0110. +So the 120-bit initialization string is the same as the SCV except that the +central "0101" is replaced by "0110". + +If one instead uses the charge-conjugate/reflected hadron orientation, the +central block would be "1001". These two choices are symmetry-related. The +exact choice used in the submission is fixed by the supplied circuit files. + +All initial states are computational-basis product states and are prepared using +only X gates on the qubits whose bit value is 1. + +======================================================================== +4. OBSERVABLES IN PAULI FORM +======================================================================== + +4.1 Qubit occupancies + +For each site r, + + n_i(r) = (I - Z_i(r)) / 2 + n_o(r) = (I - Z_o(r)) / 2 + +These are obtained experimentally from + + P(1) = [1 - ] / 2 + +for each qubit. + +4.2 Local staggered fermion number + +The local fermion number is staggered: + +- on even sites: + n_f(r) = n_i(r) + n_o(r) + = 1 - [Z_i(r) + Z_o(r)] / 2 + +- on odd sites: + n_f(r) = 2 - [n_i(r) + n_o(r)] + = 1 + [Z_i(r) + Z_o(r)] / 2 + +Thus n_f(r) is a diagonal Pauli observable built entirely from local Z +expectation values. + +4.3 Differential observable used in the experiment + +The reported site-resolved signal is + + Delta n_f(r,t) = n_f^hadron(r,t) - n_f^SCV(r,t). + +This differential measurement protocol cancels part of the hardware bias and +removes the background dynamical contribution of the vacuum. + +4.4 Scalar observable used in the present tracker instance + +For the present tracker instance, we report the scalar trace + + n_f(t) = sum_{r=1}^{60} Delta n_f(r,t), + +evaluated at Trotter step t = 20. + +4.5 Conserved global charge + +The exactly conserved charge used as a diagnostic is + + Q = sum_r [ n_i(r) + n_o(r) ] = 60 + +for the symmetry sector used here. + +In Pauli form, + + Q = 60 - (1/2) sum_r [ Z_i(r) + Z_o(r) ]. + +======================================================================== +5. IBM BOSTON VALUES FOR THE SUBMITTED INSTANCES +======================================================================== + +The tracker-facing scalar observable is reported for four explicit circuit +instances at x = 100 and dt = 0.0015, corresponding to Trotter steps +t = 5, 10, 15, and 20. For each instance, the measured QPU value is listed +together with the TN, PP_CPU, and PP_GPU benchmark values and the +charge-violation diagnostics from the exactly known conserved quantity Q = 60. + +======================================================================== +5A. IBM BOSTON VALUE AND BENCHMARK DATA FOR t = 5 +======================================================================== + +Submitted scalar observable: +- instance: x = 100, dt = 0.0015, Trotter step = 5 +- backend: IBM Boston +- measured value: + n_f(5) = -0.3550984939 + +Independent benchmark values for the same observable at step 5: +- TN = -0.4957689977 +- PP_CPU = -0.4510787869 +- PP_GPU = -0.47774275 +- QPU = -0.3550984939 + +Because the exact value of n_f(5) is not known at this scale, the uncertainty +assigned to this observable is obtained by comparing the four independent method +estimates above, together with a diagnostic based on violation of the exactly +known conserved charge Q. + +For the same step, the conserved-charge values are: +- TN = 60.00000000 +- PP_CPU = 59.99991818 +- PP_GPU = 60.00016050 +- QPU = 59.95749581 + +The exact conserved value in this sector is + + Q = 60. + +Hence the corresponding charge-violation diagnostics are: +- Delta Q_TN(5) = 0.00000000 +- Delta Q_PP_CPU(5) = -0.00008182 +- Delta Q_PP_GPU(5) = 0.00016050 +- Delta Q_QPU(5) = -0.04250419 + +Equivalently, for the IBM Boston data, + + |Delta Q_QPU(5)| = |59.95749581 - 60| = 0.04250419. + +This quantity is not itself the quoted error bar on n_f(5). Rather, it is the +symmetry-violation component used in the full comparative error estimate. + +Comparative error estimate for t = 5: +- inter-method spread: + sigma_std(5) = 0.062633290079 +- charge-diagnostic aggregation: + Delta Q_rms(5) = 0.021252285891 + Delta Q_rms(5)/sqrt(60) = 0.002743658311 +- final shared comparative error estimate: + sigma_shared(5) = 0.062693354409 + +======================================================================== +5B. IBM BOSTON VALUE AND BENCHMARK DATA FOR t = 10 +======================================================================== + +Submitted scalar observable: +- instance: x = 100, dt = 0.0015, Trotter step = 10 +- backend: IBM Boston +- measured value: + n_f(10) = 0.1431540203 + +Independent benchmark values for the same observable at step 10: +- TN = 0.3744026048 +- PP_CPU = 0.4805343441 +- PP_GPU = 0.394226 +- QPU = 0.1431540203 + +Because the exact value of n_f(10) is not known at this scale, the uncertainty +assigned to this observable is obtained by comparing the four independent method +estimates above, together with a diagnostic based on violation of the exactly +known conserved charge Q. + +For the same step, the conserved-charge values are: +- TN = 60.00000000 +- PP_CPU = 59.99959358 +- PP_GPU = 59.99729810 +- QPU = 60.02942661 + +The exact conserved value in this sector is + + Q = 60. + +Hence the corresponding charge-violation diagnostics are: +- Delta Q_TN(10) = 0.00000000 +- Delta Q_PP_CPU(10) = -0.00040642 +- Delta Q_PP_GPU(10) = -0.00270190 +- Delta Q_QPU(10) = 0.02942661 + +Equivalently, for the IBM Boston data, + + |Delta Q_QPU(10)| = |60.02942661 - 60| = 0.02942661. + +This quantity is not itself the quoted error bar on n_f(10). Rather, it is the +symmetry-violation component used in the full comparative error estimate. + +Comparative error estimate for t = 10: +- inter-method spread: + sigma_std(10) = 0.144177140195 +- charge-diagnostic aggregation: + Delta Q_rms(10) = 0.014776593120 + Delta Q_rms(10)/sqrt(60) = 0.001907649969 +- final shared comparative error estimate: + sigma_shared(10) = 0.144189759980 + +======================================================================== +5C. IBM BOSTON VALUE AND BENCHMARK DATA FOR t = 15 +======================================================================== + +Submitted scalar observable: +- instance: x = 100, dt = 0.0015, Trotter step = 15 +- backend: IBM Boston +- measured value: + n_f(15) = 0.00494274374 + +Independent benchmark values for the same observable at step 15: +- TN = -0.1131674269 +- PP_CPU = -0.03107728475 +- PP_GPU = -0.096355725 +- QPU = 0.00494274374 + +Because the exact value of n_f(15) is not known at this scale, the uncertainty +assigned to this observable is obtained by comparing the four independent method +estimates above, together with a diagnostic based on violation of the exactly +known conserved charge Q. + +For the same step, the conserved-charge values are: +- TN = 60.00000000 +- PP_CPU = 60.01033665 +- PP_GPU = 60.00620690 +- QPU = 59.91796245 + +The exact conserved value in this sector is + + Q = 60. + +Hence the corresponding charge-violation diagnostics are: +- Delta Q_TN(15) = 0.00000000 +- Delta Q_PP_CPU(15) = 0.01033665 +- Delta Q_PP_GPU(15) = 0.00620690 +- Delta Q_QPU(15) = -0.08203755 + +Equivalently, for the IBM Boston data, + + |Delta Q_QPU(15)| = |59.91796245 - 60| = 0.08203755. + +This quantity is not itself the quoted error bar on n_f(15). Rather, it is the +symmetry-violation component used in the full comparative error estimate. + +Comparative error estimate for t = 15: +- inter-method spread: + sigma_std(15) = 0.055371122250 +- charge-diagnostic aggregation: + Delta Q_rms(15) = 0.041459412535 + Delta Q_rms(15)/sqrt(60) = 0.005352387143 +- final shared comparative error estimate: + sigma_shared(15) = 0.055629211996 + +======================================================================== +5D. IBM BOSTON VALUE AND BENCHMARK DATA FOR t = 20 +======================================================================== + +Submitted scalar observable: +- instance: x = 100, dt = 0.0015, Trotter step = 20 +- backend: IBM Boston +- measured value: + n_f(20) = -0.07723426024 + +Independent benchmark values for the same observable at step 20: +- TN = 0.2778348725 +- PP_CPU = 0.4081775866 +- PP_GPU = 0.2456276125 +- QPU = -0.07723426024 + +Because the exact value of n_f(20) is not known at this scale, the uncertainty +assigned to this observable is obtained by comparing the four independent method +estimates above, together with a diagnostic based on violation of the exactly +known conserved charge Q. + +For the same step, the conserved-charge values are: +- TN = 60.00000000 +- PP_CPU = 60.00538161 +- PP_GPU = 59.99313828 +- QPU = 59.99402699 + +The exact conserved value in this sector is + + Q = 60. + +Hence the corresponding charge-violation diagnostics are: +- Delta Q_TN(20) = 0.00000000 +- Delta Q_PP_CPU(20) = 0.00538161 +- Delta Q_PP_GPU(20) = -0.00686172 +- Delta Q_QPU(20) = -0.00597301 + +Equivalently, for the IBM Boston data, + + |Delta Q_QPU(20)| = |59.99402699 - 60| = 0.00597301. + +This quantity is not itself the quoted error bar on n_f(20). Rather, it is the +symmetry-violation component used in the full comparative error estimate. + +Comparative error estimate for t = 20: +- inter-method spread: + sigma_std(20) = 0.206233598084 +- charge-diagnostic aggregation: + Delta Q_rms(20) = 0.005284926111 + Delta Q_rms(20)/sqrt(60) = 0.000682281027 +- final shared comparative error estimate: + sigma_shared(20) = 0.206234726673 + +======================================================================== +6. ERROR-BAR PRESCRIPTION USED IN THIS WORK +======================================================================== + +The error bars quoted for the dynamical observable n_f(t) are defined by a +comparative inter-method prescription together with an exactly known symmetry +diagnostic. This is the prescription used in the methods supplement. + +6.1 Four independent estimates of the observable + +For each time slice t, we obtain four estimates + + n_f^(m)(t), m in {TN, PP_CPU, PP_GPU, QPU}. + +Because the exact value of n_f(t) is not known at this scale, these four values +are treated as independent method estimates of the same quantity. + +6.2 Inter-method spread + +The methods supplement defines the inter-method spread using the mean across the +four estimates: + + mean_n_f(t) = (1/4) sum_m n_f^(m)(t) + + sigma_std(t) = sqrt[ (1/3) sum_m ( n_f^(m)(t) - mean_n_f(t) )^2 ]. + +This term quantifies the method-to-method spread of the observable. + +6.3 Symmetry-violation diagnostic from the exactly known conserved charge + +The global charge is exactly known: + + Q = sum_r [n_i(r) + n_o(r)] = 60. + +For each method m, define the charge violation + + Delta Q^(m)(t) = Q^(m)(t) - 60. + +Since Q is a sum over L = 60 sites, the methods supplement converts this into a +conservative per-site diagnostic scale and then aggregates over methods through + + Delta Q_rms(t) = sqrt[ (1/4) sum_m (Delta Q^(m)(t))^2 ]. + +The corresponding per-site symmetry-violation scale is + + Delta Q_rms(t) / sqrt(60). + +This term is directly grounded in an exactly known physical constraint. + +6.4 Final shared error estimate + +The final shared uncertainty band used in the methods supplement is the +quadrature combination + + sigma_shared(t) + = sqrt[ sigma_std(t)^2 + ( Delta Q_rms(t) / sqrt(60) )^2 ]. + +This is the comparative error estimate quoted for the observable. It combines: +- inter-method spread in the observable itself, and +- diagnosed symmetry violation through the exactly known conserved charge. + +6.5 Method-specific error estimate + +The supplement also defines an individual method-specific error bar + + sigma_m(t) + = sqrt[ sigma_pair,m(t)^2 + ( |Delta Q^(m)(t)| / sqrt(60) )^2 ], + +where + + sigma_pair,m(t) = | n_f^(m)(t) - n_ref(t) |. + +This is the per-method comparative error estimate. + +6.6 Important clarification + +These quoted error bars are NOT statistical shot-noise bars. They are not +derived from repeated sampling around a known exact observable value. Instead, +they are the uncertainty estimates used in this work precisely because: +- the exact value of n_f(t) is not known at the present scale, +- multiple classical/quantum methods are available for comparison, and +- the exactly known conserved quantity Q provides a direct diagnostic of + measurement/simulation error. + +======================================================================== +7. NUMERICAL ERROR-ESTIMATE SUMMARY FOR THE SUBMITTED INSTANCES +======================================================================== + +The table below collects the comparative error-estimate ingredients for the four +explicitly reported circuit instances. + +Step sigma_std(t) DeltaQ_rms/sqrt(60) sigma_shared(t) |DeltaQ_QPU| +5 0.062633290079 0.002743658311 0.062693354409 0.04250419 +10 0.144177140195 0.001907649969 0.144189759980 0.02942661 +15 0.055371122250 0.005352387143 0.055629211996 0.08203755 +20 0.206233598084 0.000682281027 0.206234726673 0.00597301 + +Thus, for all four submitted instances, the quoted uncertainty is dominated by +the inter-method spread among TN / PP_CPU / PP_GPU / QPU values, while the +symmetry-violation term from the exactly known conserved charge provides a +direct additional diagnostic. + +======================================================================== +8. QUANTUM CIRCUITS USED +======================================================================== + +The submission requires two circuit families for each reported Trotter step: +(1) SCV evolution circuits +(2) centered-hadron evolution circuits + +Because the observable is differential, both circuits are required to reproduce +the reported data. + +The explicit submitted circuit instances are: +- t = 5 +- t = 10 +- t = 15 +- t = 20 + +Circuit structure: +- first-order Trotterization +- interaction block for H_I^(approx) +- electric block for H_E^(approx) +- mass block for H_M^(approx) +- SWAP layers to mediate nearest-neighbor interactions in the hardware layout +- measurement of all 120 qubits in the Z basis + +Depth information: +- two-qubit depth for t Trotter steps: 13 t - 1 +- for t = 5: two-qubit depth = 64 +- for t = 10: two-qubit depth = 129 +- for t = 15: two-qubit depth = 194 +- for t = 20: two-qubit depth = 259 +- for reference, at t = 25 the circuit has two-qubit depth 324, + 17,660 two-qubit gates, and 90,955 total gates + +A cropped version of the circuit figure from the methods section is included +with this submission package as: + +- figures/circuit_figure_methods.png + +======================================================================== +9. CLASSICAL BENCHMARK METHODS +======================================================================== + +9.1 Tensor Network (TN) + +The TN benchmark evolves the full LSH Hamiltonian using an MPS/MPO +representation and 2-site TDVP, with maximum bond dimension 200 and bosonic +cutoff j_max = 5/2. + +For x = 100, the maximum reported TN truncation error in the Schmidt spectrum +reaches 1e-4 by Trotter step 20. + +9.2 Pauli Propagation on CPU (PP_CPU) + +The CPU PP benchmark simulates the noiseless circuit in the Heisenberg picture. +For x = 100, the safe upper bound used for the non-truncated PP term count is +12,500 terms. This is treated as effectively exact up to floating-point +tolerances. + +9.3 Pauli Propagation on GPU (PP_GPU) + +The GPU PP benchmark uses NVIDIA cuQuantum / cuPauliProp with +coefficient-based truncation. The coefficient cutoff is + + epsilon = 1e-5. + +This is a controlled circuit-level approximation that substantially reduces +memory and runtime. + +======================================================================== +10. RUNTIME DATA FOR THE SUBMITTED INSTANCES +======================================================================== + +The supplementary runtime table for x = 100 gives the following values for the +explicitly reported instances: + +Step QPU (s) TN (s) PP_CPU (s) PP_GPU (s) +5 20 584.092 477.4471 547.5810 +10 20 4936.112 1111.2079 1186.1290 +15 20 11300.992 1798.2811 1990.1430 +20 20 8949.110 2484.3693 2930.4400 + +======================================================================== +11. REPRODUCIBILITY FILE MANIFEST +======================================================================== + +The tracker review requested: +- a copy of the quantum circuits used to compute the observable +- the raw data from which the observable is computed + +Accordingly, the final submission package should include the following files +(or files with equivalent content and different names): + +11.1 Circuit files + +SCV circuits: +- circuits/scv_N60_x100_dt0p0015_steps05.qasm +- circuits/scv_N60_x100_dt0p0015_steps10.qasm +- circuits/scv_N60_x100_dt0p0015_steps15.qasm +- circuits/scv_N60_x100_dt0p0015_steps20.qasm + +Centered-hadron circuits: +- circuits/hadron_N60_x100_dt0p0015_steps05.qasm +- circuits/hadron_N60_x100_dt0p0015_steps10.qasm +- circuits/hadron_N60_x100_dt0p0015_steps15.qasm +- circuits/hadron_N60_x100_dt0p0015_steps20.qasm + + +11.2 Raw experimental data + +Raw experimental data is available at: https://github.com/mathew0036/lsh_data + + +11.5 README note on exact observables + +For the current submission observable n_f(r,t), per-qubit Z expectations are +sufficient because the observable is diagonal and linear in the single-site +occupancies. Full bitstring counts are nevertheless preferable because they +allow independent recomputation of additional observables. + +======================================================================== +12. SUBMITTED BENCHMARK TABLES +======================================================================== + +12.1 Scalar observable n_f(t) + +Step TN PP_CPU PP_GPU QPU Median St.dev +1 1.824222901 1.825335615 1.825336 1.77264257 1.824779258 0.02616639397 +2 1.343818565 1.34880517 1.347871 1.234719061 1.345844782 0.05609802779 +3 0.6852977079 0.698419082 0.693895 0.7005505103 0.696157041 0.006757945893 +4 0.01781852652 0.04434743353 0.0317106 0.1125808617 0.03802901676 0.04206360493 +5 -0.4957689977 -0.4510787869 -0.47774275 -0.3550984939 -0.4644107685 0.0626332901 +6 -0.7447406887 -0.6794112084 -0.725069325 -0.4792900767 -0.7022402667 0.1216756278 +7 -0.6994223897 -0.6144203611 -0.68012595 -0.405844541 -0.6472731556 0.1344237824 +8 -0.4149706965 -0.3149685829 -0.3959514 -0.3160420563 -0.3559967282 0.05251500138 +9 -0.009710517986 0.09777330494 0.010149475 -0.01701975315 0.0002194785072 0.05291043151 +10 0.3744026048 0.4805343441 0.394226 0.1431540203 0.3843143024 0.1441771402 +11 0.6163184396 0.7136997525 0.6325666 0.3540697043 0.6244425198 0.1559910262 +12 0.6514199805 0.7369940536 0.6619868 0.4092782333 0.6567033902 0.142288607 +13 0.4873750145 0.5641770138 0.4951614125 0.2630479833 0.4912682135 0.1308944493 +14 0.1962856389 0.2712616284 0.2069994 0.1957298805 0.2016425194 0.0361687867 +15 -0.1131674269 -0.03107728475 -0.096355725 0.00494274374 -0.06371650487 0.05537112224 +16 -0.3336240614 -0.2318235614 -0.314319025 -0.08874021367 -0.2730712932 0.1113808299 +17 -0.3941897866 -0.2691116404 -0.3787042075 -0.1962503187 -0.323907924 0.09384077972 +18 -0.2807460955 -0.1325140013 -0.272586375 -0.1673053457 -0.2199458603 0.07462290823 +19 -0.03330018147 0.1236920782 -0.035842523 -0.1490836294 -0.03457135223 0.1120789393 +20 0.2778348725 0.4081775866 0.2456276125 -0.07723426024 0.2617312425 0.2062335981 + +12.2 Conserved charge Q + +Step TN PP_CPU PP_GPU QPU error_diagnostic +1 60 60 60 60.07076187 0.03538093432 +2 60 60 60 60.01556783 0.007783914764 +3 60 59.99999892 60.0000295 59.97441541 0.01279704071 +4 60 59.99998537 60.000264 59.98574097 0.007172217667 +5 60 59.99991818 60.0001605 59.95749581 0.02126544441 +6 60 59.99985924 59.99994432 59.9228317 0.03855145367 +7 60 59.99978099 60.0001445 59.97723002 0.0113735536 +8 60 60.00033369 59.99693215 60.01516427 0.008182322904 +9 60 60.00063853 59.99640159 60.09153313 0.04629746559 +10 60 59.99959358 59.9972981 60.02942661 0.01527773734 +11 60 60.00017695 60.0023345 59.95262885 0.02412750108 +12 60 59.99506226 60.0064158 59.97553288 0.01331739931 +13 60 59.99594391 60.00947415 59.95853503 0.02236597107 +14 60 60.00326018 60.0093484 60.09813368 0.04712493522 +15 60 60.01033665 60.0062069 59.91796245 0.04398168579 +16 60 60.01345623 59.99751846 59.92227266 0.04129079 +17 60 60.00953873 59.98460915 59.92904491 0.03599839525 +18 60 59.99695801 59.9810714 60.07128097 0.04016899441 +19 60 59.99513071 59.98358415 60.08671777 0.04740887609 +20 60 60.00538161 59.99313828 59.99402699 0.005710650099 + +======================================================================== + + +======================================================================== +END OF README +========================================================================