Decoherence & Noise Simulator
Real-time T1/T2 decay on the Bloch sphere with density matrix evolution.
Unit ILO2
Parameters
Bloch Sphere
⟨X⟩1.000
⟨Y⟩0.000
⟨Z⟩0.000
Purity1.000
Time0.0 us
Density Matrix rho(t)
| 0.500 | 0.500 |
| 0.500 | 0.500 |
Tr(rho)=1.000
Tr(rho^2)=1.000
S(rho)=0.000 bits
Expectation Values vs Time
Physics Reference
Lindblad Master Equation:
d rho/dt = -i[H,rho] + Sum_k (L_k rho L_k^dag - 1/2 {L_k^dag L_k, rho})
Amplitude Damping (T1):
rho_11(t) = rho_11(0) exp(-t/T1), rho_01(t) = rho_01(0) exp(-t/2T1)
Pure Dephasing:
1/T2 = 1/(2T1) + 1/T_phi. Off-diag: rho_01(t) = rho_01(0) exp(-t/T2)
Constraint:
T2 ≤ 2T1 (always enforced in physical systems)
Transmon Qubit Designer
Diagonalize the Cooper Pair Box Hamiltonian. Tune E_J/E_C to design a transmon.
Unit IILO4
Hamiltonian Parameters
Computed Properties
w_01 (qubit freq)--
w_12--
Anharmonicity alpha--
alpha / w_01--
Charge dispersion--
Energy Spectrum
Energy vs Gate Charge n_g
Energy Levels vs E_J/E_C
Physics Reference
CPB Hamiltonian:
H = 4 E_C (n - n_g)^2 - E_J cos(phi)
Charge basis:
⟨n|H|n⟩ = 4 E_C (n-n_g)^2, ⟨n|H|n+/-1⟩ = -E_J/2
Transmon (E_J/E_C >> 1):
E_m ~ -E_J + sqrt(8 E_J E_C)(m+1/2) - E_C/12 (6m^2+6m+3)
Anharmonicity:
alpha = w_12 - w_01 ~ -E_C
Photonic Quantum Circuit Lab
Beam splitter interference and Hong-Ou-Mandel effect simulation.
Unit IIILO1,LO3
Hong-Ou-Mandel Experiment
0=identical, 1=distinguishable
Output Probabilities
P(2,0)--
P(0,2)--
P(1,1) coincidence--
HOM Visibility--
Mach-Zehnder
P(det 1)--
P(det 2)--
HOM Dip
Beam Splitter
Physics Reference
BS Transform:
(a'1,a'2)^T = U(a1,a2)^T, U=[[sqrt(R),i*sqrt(T)],[i*sqrt(T),sqrt(R)]]
HOM Effect (50:50):
|1,1⟩ -> (i/sqrt(2))(|2,0⟩ + |0,2⟩) -- zero coincidences
Coincidence:
P_11(tau) = 1/2 [1 - exp(-(tau/tau_c)^2)]
Ion Trap Physics Simulator
Paul trap stability diagram, secular frequency, and Rabi oscillations.
Unit IVLO1,LO4
Paul Trap Parameters
Trap Properties
Stability--
Secular freq--
Trap depth (eV)--
Rabi Oscillations
Stability Diagram
Rabi Oscillations
Physics Reference
Mathieu Equation:
d^2 u/d zeta^2 + (a - 2q cos(2 zeta)) u = 0
Secular Frequency:
w_sec = (Omega/2) sqrt(a + q^2/2)
Rabi:
P_up(t) = (Omega_R^2/Omega'^2) sin^2(Omega' t/2), Omega'=sqrt(Omega_R^2 + delta^2)
NV Center Spin Lab
Simulate Zeeman splitting, ODMR spectra in diamond NV centers.
Unit VLO1,LO4
NV Center Parameters
0=along NV axis
Energy Levels (GHz)
E(ms=0)--
E(ms=+1)--
E(ms=-1)--
f+ transition--
f- transition--
Splitting--
Energy vs B Field
ODMR Spectrum
Physics Reference
Spin Hamiltonian (S=1):
H = D*Sz^2 + E(Sx^2 - Sy^2) + ge*muB*B.S
Zero-field splitting:
D ~ 2.87 GHz, lifts |ms=0⟩ vs |ms=+/-1⟩ degeneracy
Zeeman (B || NV):
f+/- = D +/- 28.025 GHz/T * B