[Paper Review] A proposal of noise suppression for quantum annealing

Takayuki Suzuki, Hiromichi Nakazato|arXiv (Cornell University)|Jun 24, 2020

Quantum Computing Algorithms and Architecture21 references4 citations

TL;DR

This paper proposes a noise suppression method for quantum annealing by introducing ancillary qubits to modify the Hamiltonian, enabling cancellation of noise effects through symmetry protection. The approach confines dynamics to a noise-resistant subspace, numerically validated for flux qubits, significantly improving robustness against decoherence while preserving adiabatic evolution.

ABSTRACT

A method to suppress noise, which is one of the major obstacles to obtain an optimal solution in quantum annealers, is proposed. We generalize the conventionally used Hamiltonian, i.e., the transverse field Hamiltonian, by introducing an ancillary system, which leads to cancellation of the effect of noise on the system under consideration for some typical cases. We also confirm numerically that the method is effective for a kind of noise usually encountered in the case of flux qubit.

Motivation & Objective

• To address decoherence as a major obstacle in current quantum annealers, particularly in D-Wave's flux qubit architecture.
• To develop a noise suppression mechanism that does not rely on error correction or dynamical decoupling, but instead uses Hamiltonian engineering.
• To enable robust adiabatic evolution by confining the system dynamics to a subspace where noise effects are canceled.
• To demonstrate applicability and effectiveness of the method in realistic superconducting qubit systems, especially under typical noise models.

Proposed method

• Introduces a modified Hamiltonian with paired ancilla and physical qubits, where the ancilla qubits are entangled with physical qubits via a C-NOT-like unitary transformation.
• The Hamiltonian is designed to be invariant under a Z2 symmetry transformation, ensuring the existence of N conserved quantities σ²ⁱ⁻¹ᶻσ²ⁱᶻ.
• Uses a unitary transformation 𝕎 = ⊗ᵢ C₂ᵢ₋₁,₂ᵢ to map the system into a subspace where the dynamics are protected from transverse noise.
• The method leverages the fact that noise terms with only longitudinal components (e.g., σᶻ) cancel out in the effective dynamics due to symmetry, even under non-Markovian or time-dependent coupling.
• Numerical simulations confirm that the method suppresses decoherence in flux qubit systems under typical noise models.
• The approach is extended to Lindblad master equations, showing that noise suppression holds even when coupling is time-dependent, provided the coupling is predominantly longitudinal.

Experimental results

Research questions

• RQ1 Can noise in quantum annealing be suppressed without relying on active error correction or dynamical decoupling?
• RQ2 How can a Hamiltonian be engineered to protect adiabatic evolution from decoherence in superconducting flux qubits?
• RQ3 What role does symmetry play in enabling noise cancellation in open quantum systems?
• RQ4 Can the dynamics be confined to a subspace where noise effects are intrinsically canceled?
• RQ5 Is the proposed method robust under realistic noise models, including time-dependent and non-Markovian couplings?

Key findings

• The proposed Hamiltonian with ancilla qubits ensures that noise terms with only longitudinal components (σᶻ) cancel out due to symmetry, significantly reducing decoherence.
• Numerical simulations confirm effective noise suppression in flux qubit systems under typical noise models, demonstrating improved fidelity of the final state.
• The method preserves adiabatic evolution by confining the dynamics to a subspace defined by the conserved quantities σ²ⁱ⁻¹ᶻσ²ⁱᶻ, which are protected from transverse noise.
• Even under time-dependent coupling, the noise suppression remains effective when the coupling is predominantly longitudinal, as shown in the Lindblad equation analysis.
• The approach is applicable to real-world D-Wave-type devices, requiring only a doubling of qubits, making it experimentally feasible.
• The method achieves noise suppression without requiring additional control pulses or error correction overhead, offering a passive and scalable solution.