Optimal and robust error filtration for quantum information processing

TL;DR

This work tackles noise mitigation in quantum information processing by optimizing error filtration, a probabilistic scheme that encodes a signal with $n$ ancillas via a universal unitary $U$ and decodes with post-selection. The authors perform an ansatz-free optimization over $U\in\mathrm{SU}(2^{n+1})$ using gradient-based and stochastic methods, and analyze performance under realistic noise models (dephasing and depolarizing) as well as imperfect encodings and cross-talk. They derive analytic results for small ancilla counts, connect filtration to error-detection codes, and demonstrate improved entanglement fidelity, CHSH violations, and quantum Fisher information relative to deterministic error correction and the SQEM scheme, across one to three ancillas. The findings show robust error filtration as a practical, scalable tool for near-term quantum devices, with clear implications for metrology, cryptography, and quantum communication.

Abstract

Error filtration is a hardware scheme that mitigates noise by exploiting auxiliary qubits and entangling gates. Although both signal and ancillas are subject to local noise, constructive interference(and in some cases post-selection) allows us to reduce the noise level in the signal qubit. Here we determine the optimal entangling unitary gates that make the qubits interfere most effectively,starting from a set of universal gates and proceeding by optimizing suitable functionals by gradient-descent or stochastic approximation. We examine how our optimized scheme behaves under imperfect implementation, where ancillary qubits may be noisy or subject to cross-talk. Even with these imperfections, we find that adding more ancillary qubits helps in protecting quantum information . We benchmark our approach against figures of merit that correspond to different applications, including entanglement fidelity, quantum Fisher information (for applications in quantum sensing),and CHSH value (for cryptographic applications), with one, two, and three ancillary qubits. With one and two ancillas we also provide analytical explicit expressions from an ansatz for the optimal unitary. We also compare our method with the recently introduced Superposed Quantum Error Mitigation (SQEM) scheme based on superposition of causal orders, and show that, for a wide range of noise strengths, our approach may outperform SQEM in terms of effectiveness and robustness.

Figures (19)

• Figure 1: General scheme of error filtration. On the left, one signal qubit $|\psi\rangle$, and $n$ ancillary qubits $|0\rangle^{\otimes n}$. After the encoding $U$ on the signal and ancillas, the information is transmitted through a memoryless noisy channel $\mathcal{E}$. The inverse unitary $U^\dag$ is applied for the decoding, followed by a measurement of the ancillary qubits. The effects of noise on the signal qubit are reduced conditioned on the ancillary qubits being found in the state $|0\rangle^{\otimes n}$.
• Figure 2: Construction of a two-qubit unitary gate from four single-qubit gates $U_1, U_2, U_3, U_4 \in \mathrm{SU}(2)$, three CNOT gates, two rotations along the $y$-axis, and one along the $z$-axis shende2004minimal.
• Figure 3: Quantum Shannon Decomposition for constructing $U\in\mathrm{U}(2^{n+1})$ involving recursive application of $V_1, V_2, V_3, V_4\in\mathrm{U}(2^{n})$ and multiplexed rotations shende2005. The recursive definition of the multiplexed rotation is shown in Fig. \ref{['fig:nesting']}.
• Figure 4: By recursively applying the decomposition shown in the picture, one can decompose any multiplexed rotation into elementary gates shende2005.
• Figure 5: For $n=1$, the multiplexed rotation is defined by combining two C-NOT gates and two single-qubit rotations. Note that in general the two single-qubit rotations have different angles shende2005.