Qubit Performance

Qubit Performance Metrics: Coherence times, gate fidelities, and spectral properties derived from EPR loss analysis

1. Coherence Times

Parameter	Symbol	Unit	Description	Optimal / Best Value	Good Range	Acceptable Range	Poor / Worst Value	Physical Significance
Energy Relaxation Time T_1	T_1	µs	Time for qubit to decay from |1⟩ to |0⟩; bounded by all loss channels weighted by EPR participation.	> 500 µs	100 – 500 µs	10 – 99 µs	< 1 µs	T_1 is the hard ceiling on gate fidelity; EPR identifies dominant loss channel for improvement.
Pure Dephasing Time T_f	T_f	µs	Dephasing time due to low-frequency noise (flux, charge, 1/f); not directly from EPR but informed by participation.	> 200 µs	50 – 200 µs	10 – 49 µs	< 5 µs	Limits T2; EPR participation at surfaces informs TLS dephasing contribution.
Coherence Time T2 (Ramsey)	T2*	µs	Total dephasing time including low-frequency noise; T2* = 2T1.	> 300 µs	100 – 300 µs	20 – 99 µs	< 10 µs	Practical coherence limit; T2*/2T1 ≈ 1 indicates pure-dephasing free regime.
Coherence Time T2 (Echo)	T_2^E	µs	Echo coherence time; removes low-frequency noise contributions; T_2^E = 2T1.	> 500 µs	200 – 500 µs	50 – 199 µs	< 20 µs	Ratio T_2^E/T2* quantifies 1/f noise power; EPR participations guide substrate/surface optimization.
Quality Factor Q_qubit	Q_q	dimensionless	Qubit quality factor Q = ω_q·T_1; dimensionless figure of merit across frequencies.	> 10⁷	10⁶ – 10⁷	10⁵ – 10⁶	< 10⁴	Universal metric independent of frequency; Q > 10⁷ represents state-of-the-art performance.

2. Gate Performance

Parameter	Symbol	Unit	Description	Optimal / Best Value	Good Range	Acceptable Range	Poor / Worst Value	Physical Significance
Single-Qubit Gate Fidelity	F_1Q	%	Average fidelity of single-qubit Clifford gates; limited by T_1, T2, leakage (anharmonicity).	> 99.9%	99.5 – 99.9%	99.0 – 99.4%	< 98%	< 99.9% limits surface-code error correction threshold; leakage tied to anharmonicity from EPR.
Two-Qubit Gate Fidelity	F_2Q	%	Average fidelity of two-qubit entangling gates (CZ, iSWAP); limited by ZZ, T_1, T2.	> 99.5%	99.0 – 99.5%	97.0 – 98.9%	< 95%	ZZ coupling (cross-Kerr from EPR) is primary source of two-qubit gate error on fixed-frequency chips.
Leakage Rate	L_1	% per gate	Probability of leaking to non-computational |2⟩ state per gate operation.	< 0.01%	< 0.1%	0.1 – 0.5%	> 1.0%	Leakage non-destructively accumulates; requires active reset. Minimized by maximising anharmonicity.
Readout Fidelity	F_RO	%	Assignment fidelity for single-shot qubit state discrimination.	> 99%	97 – 99%	90 – 96%	< 85%	Limited by chi (must be large), T_1 during readout, photon number. chi extracted directly via EPR.

3. Spectral Properties

Parameter	Symbol	Unit	Description	Optimal / Best Value	Good Range	Acceptable Range	Poor / Worst Value	Physical Significance
Charge Dispersion	varepsilon_q	MHz	Sensitivity of qubit frequency to offset charge; exponentially suppressed in transmon regime.	< 0.01 MHz	< 0.1 MHz	0.1 – 1 MHz	> 5 MHz	Large dispersion → charge noise dephasing. EPR ratio EJ/EC must be > 50 for transmon.
E_J / E_C Ratio	E_J / E_C	dimensionless	Josephson to charging energy ratio; governs charge noise sensitivity vs. anharmonicity trade-off.	50 – 100	40 – 120	20 – 39	< 10	< 20: charge qubit regime with high sensitivity; > 150: anharmonicity too small for fast gates.
Flux Sensitivity (tunable qubits)	domega / dPhi	GHz/F0	Sensitivity of qubit frequency to external flux; relevant for flux-tunable transmons and SQUID qubits.	< 0.1 GHz/F0 at sweet spot	< 0.5 GHz/F0	0.5 – 2 GHz/F0	> 5 GHz/F0	High flux sensitivity amplifies flux noise dephasing; biasing at sweet spot minimizes first-order sensitivity.
Frequency Spread (fabrication)	sigma_omega / 2pi	MHz	Standard deviation of qubit frequencies across a chip due to junction fabrication variation.	< 5 MHz	< 20 MHz	20 – 50 MHz	> 100 MHz	Large spread causes frequency collisions; EPR helps identify geometry sensitivities to dimension variation.