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Quantum interference device for controlled two-qubit operations

MetadataDetails
Publication Date2020-05-29
Journalnpj Quantum Information
AuthorsNiels Jakob Søe Loft, Morten Kjaergaard, Lasse Bjørn Kristensen, Christian Kraglund Andersen, Thorvald W. Larsen
InstitutionsMicrosoft (Denmark), ETH Zurich
Citations15
AnalysisFull AI Review Included

Analysis of Quantum Interference Device for Controlled Two-Qubit Operations

Section titled “Analysis of Quantum Interference Device for Controlled Two-Qubit Operations”
  • Core Value Proposition: Demonstration of a four-qubit quantum interference device (“diamond gate”) that natively implements four distinct controlled two-qubit unitaries, significantly easing quantum compilation and simulation tasks.
  • Architecture: The device utilizes four capacitively coupled transmon qubits arranged in a diamond geometry (two control qubits C1, C2, and two target qubits T1, T2).
  • Performance: Achieved a simulated average gate fidelity (F) of 0.9923 in a fast operation time of 59.3 ns, using state-of-the-art superconducting qubit parameters (decoherence rate γ = 0.01 MHz).
  • Gate Functionality: The control qubits determine the operation on the target qubits, implementing two entangling swap/phase operations (ZZ CZ SWAP, -CZ SWAP), a parity-distinguishing phase operation, and an identity (idle) operation.
  • Scalability: The architecture is designed as an extensible building block, allowing connection into highly connected two-dimensional lattices for large-scale quantum computers.
  • Leakage Mitigation: Successfully addressed the critical challenge of leakage to higher-energy transmon states (qutrit |2> levels) using a passive technique: crosstalk engineering. Tuning the weak crosstalk coupling (JT) induces destructive interference, canceling unwanted excitation transfer.

The following specifications are based on Parameter Set 1, representing state-of-the-art superconducting qubit performance, unless otherwise noted.

ParameterValueUnitContext
Total Gate Fidelity (F)0.9923N/AAverage fidelity for arbitrary input states
Simulated Gate Time (tg)59.3nsTime required to reach maximum fidelity
Qubit Decoherence Rate (γ)0.01MHzCorresponds to T1, T2* coherence times of ~100 µs
Target-Control Coupling (J/2π)65MHzCoupling strength between C and T qubits
Control-Control Coupling (JC/2π)20MHzCoupling strength between C1 and C2
Qubit Detuning (Δ/2π)2GHzDetuning between target and control qubits
Controlled Gate U00 Fidelity0.9943N/AZZ CZ SWAP operation
Controlled Gate U11 Fidelity0.9931N/A-CZ SWAP operation
Controlled Gate UΨ+ Fidelity0.9881N/APhase operation (most affected by leakage)
Controlled Gate UΨ- Fidelity0.9968N/AIdentity/Idle operation (highest fidelity)
Optimal Crosstalk (JTopt/2π)-3.66MHzRequired coupling for leakage cancellation (qutrit model)
Qubit Anharmonicity (α)-270 to -280MHzTypical values for transmon qubits

The gate operation and performance were analyzed using a combination of theoretical derivation (Floquet theory) and numerical simulation (Lindblad master equation).

  1. Hamiltonian Modeling: The system was modeled as four coupled qubits (transmons) with exchange interactions (capacitive coupling). The Hamiltonian was simplified using the rotating wave approximation, assuming qubit detuning (Δ) is much greater than coupling strengths (J, JC).
  2. Unitary Derivation via Floquet Theory: The effective unitary time-evolution operator U(t) was derived using the Magnus expansion within Floquet theory, demonstrating that the system naturally implements the four-way controlled gate (U) at a specific gate time tg = π|Δ| / (4J2).
  3. Qutrit Spectrum Inclusion: To accurately model transmons, the Hilbert space was extended to include the second excited state (|2>), treating each qubit as a qutrit. This extension introduced leakage pathways due to the small anharmonicity (α/Ω ~ -0.05).
  4. Leakage Mitigation via Crosstalk Engineering: The unavoidable weak crosstalk coupling (JT) between target qubits was actively tuned to an optimal value (JTopt). This tuning creates destructive quantum interference, canceling unwanted excitation transfer (leakage) across the control qubits to the |2> states.
  5. Numerical Simulation and Fidelity Calculation: The dynamics were simulated using the Lindblad master equation (QuTiP toolbox) to incorporate realistic decoherence (relaxation and dephasing, γ). Gate performance was quantified using the average gate fidelity (F), comparing the simulated operation to the ideal target unitary (Utarget).
  6. Extensible Architecture Design: A 2D lattice structure was proposed where multiple diamond gate modules (plaquettes A and B) are connected. Independent operation is achieved by detuning adjacent plaquettes, while entanglement spread is achieved by tuning connecting qubits into resonance for swap operations.

The development of a high-fidelity, natively multi-controlled gate architecture is critical for advancing scalable quantum computing platforms, particularly those based on superconducting circuits.

  • Universal Quantum Computing: The diamond gate provides a universal gate set when supplemented with single-qubit rotations, enabling the construction of general-purpose quantum processors.
  • Quantum Compilation Efficiency: By natively implementing four distinct controlled operations, the diamond gate reduces the complexity (gate count) required to compile complex quantum algorithms compared to synthesizing these operations from simpler two-qubit gates (e.g., CNOT).
  • Scalable Quantum Architectures: The diamond geometry serves as a highly connected, extensible building block for constructing large-scale 2D quantum processors, addressing the connectivity limitations often faced by linear or simple grid architectures.
  • Fault-Tolerant Quantum Computation (FTQC): Achieving fidelities greater than 0.99 is essential for implementing error-correcting codes (like surface codes). The demonstrated fidelity (0.9923) meets this stringent requirement.
  • Quantum Simulation: The ability to perform controlled entangling and phase operations makes the device highly suitable for simulating complex quantum many-body physics and variational quantum eigensolvers (VQE).