--- title: OQC Toshiko Gen-1 Quantum Processor url: https://www.emergentmind.com/topics/oqc-toshiko-gen-1-system type: topic --- # OQC Toshiko Gen-1 Quantum Processor The OQC Toshiko Gen-1 system (“Tokyo” QPU) is a superconducting quantum processor designed and implemented by Oxford Quantum Circuits (OQC) featuring high-fidelity native two-qubit Echo Cross Resonance (ECR) gates optimized via pulse-level error suppression strategies. It comprises a planar lattice of 32 fixed-frequency coaxmon transmons with engineered connectivity, coherence, and readout characteristics. The system demonstrates substantial error reduction for two-qubit operations through integrated pulse shaping and compensation, achieving improved uniformity and reliability critical for near-term quantum circuit execution and informing scalable, fault-tolerant hardware design [2601.20458]. ## 1. Hardware Architecture and Readout The Toshiko Gen-1 quantum processing unit features 35 coaxmon transmons (32 lattice-connected, remainder reserved), fabricated on sapphire to support exceptional coherence. Each transmon operates at a fixed frequency within 4.24–4.53 GHz, with typical anharmonicity α ~ –182 MHz. The median energy relaxation time $T_{1}$ is 69 μs, and Hahn-echo dephasing time $T_{2e}$ is 103 μs, resulting in robust single-qubit operations. Control and readout wiring exploits a 3D “coaxmon” design: all microwave control lines terminate out-of-plane as coaxial pins, minimizing substrate crosstalk and stray coupling (as referenced to Rahamim et al.). Readout resonators are distributed in the 9.63–10.27 GHz range, achieving a median single-shot readout fidelity of 96%. Nearest-neighbor capacitive coupling strengths are $J$ ≈ 2.7 MHz, facilitating the deployment of cross-resonant two-qubit gates. | Parameter | Value | |-------------------------------|----------------| | Qubit frequency range (GHz) | 4.24–4.53 | | Anharmonicity α (MHz) | –182 | | Median T₁ (μs) | 69 | | Median T₂ₑ (μs) | 103 | | Typical J coupling (MHz) | 2.7 | | Readout frequ. range (GHz) | 9.63–10.27 | | Median readout fidelity (%) | 96 | | Single-qubit SX fidelity (%) | 99.9 | The architectural focus is on uniform connectivity and low-control crosstalk, establishing the platform's suitability for error-budgeted, scalable quantum information processing. ## 2. Native Two-Qubit Gate: Echo Cross Resonance (ECR) The primary entangling operation is the ECR(π/4) gate, implemented as an echoed cross-resonant microwave pulse sequence mediated by the control qubit. The logical gate composition is expressed as:   ZX(π/4)₍cr₎ — X(π)₍ctrl₎ — ZX(–π/4)₍cr₎ Each ZX(±π/4) pulse is a cross-resonant excitation (duration τ₁ ≈ 250–460 ns depending on qubit detuning), shaped as a Gaussian envelope with single- or higher-derivative DRAG (Derivative Removal by Adiabatic Gate) to suppress leakage and non-ideal transitions. The intermediate X(π) on the control is realized as two SX (√X) gates with Gaussian DRAG pulses spanning ≈40 ns. This echo protocol cancels leading-order Hamiltonian errors (IX, IY, ZI) and linear ZZ interactions. ## 3. Formal Error-Budgeting and Characterization Gate fidelity analysis decomposes the total error-per-gate (EPG) into five well-defined contributions: $$E_\text{total} = E_\text{incoh} + E_\text{leakage} + E_\text{coherent} + E_\text{crosstalk} + E_\text{unexplained}$$ - **Incoherent (Decoherence) Errors**: Quantified as $E_\text{incoh} ≈ 1 - e^{-t_g/2T_1}\,e^{-t_g/T_ϕ}$, with $T_ϕ$ defined via $1/T_ϕ ≡ 1/T_{2e} - 1/2T_1$. This channel generally sets a lower bound for gate infidelity, typically 0.3–0.8% per ECR operation. - **Control-Qubit Leakage**: Strong off-resonant CR drives induce population transfer to higher transmon levels (01, 12 single-photon, and 02/2 two-photon transitions). Characterization uses a leakage-amplification circuit, revealing $p_\text{leak}$ up to 2% on some pairs pre-suppression, and <0.1% on best pairs. - **Coherent (Unitary) Errors**: The effective two-qubit drive Hamiltonian is expressed as: $$H/\hbar = \frac{1}{2} (\Omega_{IX}\,IX + \Omega_{IY}\,IY + \Omega_{IZ}\,IZ + \Omega_{ZI}\,ZI + \Omega_{ZX}\,ZX + \Omega_{ZY}\,ZY + \Omega_{ZZ}\,ZZ)$$  Only ZX is required for ideal CZ(π/4). Before correction, residual Ω_{IZ} and Ω_{ZZ} terms may contribute up to ∼10% and ∼1.8% EPG, respectively, notably on poorly detuned pairs. Other terms are negligible after calibration. A plausible implication is that comprehensive process tomography is necessary for continuous gate performance assessment, especially as device size and complexity grow. ## 4. Error Suppression Procedures All error suppression is implemented via pulse-level software with minimal calibration overhead: - **DRAG Pulse Shaping for Leakage**: Adapts the drive envelope, $F(t) \to [1 + i\alpha\,d/dt]\,F(t)$, selecting α from measured frequency differences. α is set as $1/[2\pi(f_x - f_{CR})]$ for single-photon, $1/[4\pi(f_x - f_{CR})]$ for two-photon leakage. Most pairs achieve $p_\text{leak} \lesssim 10^{-4}$ post-suppression. - **Virtual-Z Compensation for IZ Terms**: Corrective virtual Z-rotations, $R_Z(\theta_c)$, are added on the target after each ZX, with θ_c chosen to null residual Ω_{IZ}. These do not incur additional latency or decoherence. - **Compensating RY Rotations for ZZ Terms**: For affected pairs, ZX pulses are sandwiched with $R_Y(\theta)$ and $R_Y(-\theta)$, where $\theta = \arctan(\Omega_{ZZ}/\Omega_{ZX})$, rotating residual ZZ into the ZX interaction and renormalizing the overall gate via reduced CR amplitude. Calibration of pulse parameters requires only minutes per pair, with virtual-Z pulses and phase corrections incorporated into existing gate calibration flows. No hardware changes or additional gate depth are required. ## 5. Benchmarking Methodology and Results Gate fidelity evaluation utilizes interleaved randomized benchmarking (IRB) according to Magesan et al. Random Clifford sequences are interleaved with the ECR gate. Survival probability $P(m)$ is fit to $A\,p^m + B$, extracting depolarizing parameter $p_\text{interleaved}$, compared to reference RB $p_\text{ref}$. ECR gate fidelity is $$F_\text{ECR} = 1 - \frac{1 - p_\text{interleaved}/p_\text{ref}}{2}$$ Thirty random sequences are averaged per sequence length (up to $m\sim50$). Uncertainty arises from curve fitting and statistical sampling. Key quantitative outcomes: | Pair ID | EPG_before (%) | EPG_after (%) | Reduction (×) | |---------|---------------|--------------|--------------| | 3 | 7.9 | 2.0 | 4.0 | | 7 | 5.2 | 1.0 | 5.2 | | 12 | 2.3 | 0.7 | 3.3 | | 15 | 1.5 | 0.6 | 2.5 | For a 16-qubit chain, median EPG improves from 4.6% to 1.2%, mean EPG from 6.75% to 1.6%, the best pair from 1.5% to 0.6%, averaging a 3.7× error reduction. ## 6. Implications and Device Scaling Outlook Suppression of two-qubit errors via pulse optimization and software increments shifts the dominant residual error to incoherent processes (decoherence) and unexplained terms, possibly related to spectator-qubit interactions (spectator ZZ during control X(π)), or higher-order Hamiltonian components. This suggests investigation into context-aware spectator decoupling and further advances in substrate and materials science to reduce TLS noise. Uniform error improvement across qubit chains enhances overall circuit reliability by eliminating “weak links,” a necessary predicate for quantum circuit scaling and progression toward fault-tolerant thresholds (<0.5% error rates). Achieving such fidelity will require gate durations $τ_g \lesssim 100$ ns compared to T₁, optimized device layout, and improved fabrication to control frequency collisions and coupling strengths. A plausible implication is that hardware-aware error budgeting and integrated process tomography will become routine in future device generations, with post-fabrication tuning to further optimize operational envelopes. Source: https://www.emergentmind.com/topics/oqc-toshiko-gen-1-system