Error-detectable Universal Control for High-Gain Bosonic Quantum Error Correction

Abstract

Protecting quantum information through quantum error correction (QEC) is a cornerstone of future fault-tolerant quantum computation. However, current QEC-protected logical qubits have only achieved coherence times about twice those of their best physical constituents. Here, we show that the primary barrier to higher QEC gains is ancilla-induced operational errors rather than intrinsic cavity coherence. To overcome this bottleneck, we introduce error-detectable universal control of bosonic modes, wherein ancilla relaxation events are detected and the corresponding trajectories discarded, thereby suppressing operational errors on logical qubits. For binomial codes, we demonstrate universal gates with fidelities exceeding $99.6\%$ and QEC gains of $8.33\times$ beyond break-even. Our results establish that gains beyond $10\times$ are achievable with state-of-the-art devices, establishing a path toward fault-tolerant bosonic quantum computing.

Figures (4)

• Figure 1: Concept of error-detectable (ED) universal control on bosonic modes. (a) A bosonic mode is coupled with an ED ancilla. (b) The ED process of a bosonic mode is realized by error-detecting the ED ancilla and post-selecting the no-error trajectories.
• Figure 2: Performance of an ED universal gate set of logical qubits. (a-b) Differences between simulated and ideal Pauli transfer matrices for a Hadmard (a) and T (b) gate of a binomial code, respectively. The left and right matrices of each sub figures represent situations without (left) and with (right) error-detection and PS of the ED ancilla. (c) Numerical optimized waveform of a logical Hadmard gate. (d) Differences between simulated and ideal Pauli transfer matrices for a logical controlled-phase gate for two binomial codes with (right) and without (left) error-detection and PS of the ED ancilla.
• Figure 3: Performance of ED QEC processes of a logical qubit. (a) Process fidelity as a function of time for a physical qubit (gray squares) and a binomial code (blue stars and green circles) with repetitive ED-A QEC (error detection on ancilla only). The solid lines represent the fitting curves of the physical qubit (black) and the binomial code (red and green). (b) Success probability as a function of time for the binomial code with repetitive ED QEC processes. The blue stars and the green circles represent ED QEC cycle times of $t=0.046/\kappa$ and $t=0.081/\kappa$, respectively. (c) Process infidelity ratio vs time. The blue curve is the ratio between the physical qubit and an ED-A QEC protected binomial code. The red curve is the ratio between the physical qubit and the binomial code protected by the ED-AB QEC (error detection on both the ancilla and the bosonic mode). (d) Process infidelities corresponding to (c) at 2375 $\mu$s. (e) Process fidelity vs time for an ED-AB QEC protected binomial code.
• Figure 4: Performance of ED QEC processes. (a) Schematic diagram of a single ED QEC cycle. (b) ED QEC gain $G_{\mathrm{break}}$ versus ancilla lifetime $1/\kappa_{\mathrm{e}}$. The blue and red dotted lines represent post-selecting both the ancilla and the bosonic mode (AB) and only post-selecting the bosonic mode (B), respectively. Each point represents the maximum QEC gain $G_{\mathrm{break}}$ for a given lifetime of the ancilla, obtained by optimizing over the interval time $t_{\mathrm{int}}$ and the number of parity measurements $N_{\mathrm{PM}}$.