Enhancing dissipative cat qubit protection by squeezing

Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: We're looking at the paper: "Enhancing dissipative cat qubit protection by squeezing".

Mira: Here's the gist of the paper. The gist Dissipative cat-qubits are a promising architecture for quantum processors due to their built-in quantum error correction, and this work implements a squeezing deformation of the cat qubit basis states to further extend bit-flip time while minimally affecting the phase-flip rate How it works The paper introduces a scheme to dissipatively stabilize squeezed cat qubits that does not require any design change compared to previous implementations of standard cat qubits By deforming the states, the authors are able to reach a scaling exponent γ = 4.3, largely exceeding the attainable bound of non-squeezed dissipative cats This results in a steep reduction in the bit-flip error rate with increasing mean photon number, characterized by a scaling exponent γ = 4.3, rising by a factor of 74 per added photon Specifically, they measure bit-flip times of 22 seconds for a phaseflip time of 1.3 µs in a squeezed cat qubit with an average photon number n¯ = 4.1, a 160-fold improvement in bit-flip time compared to a standard cat The method involves engineering a loss operator whose dark states are squeezed states, specifically the dissipator L2(α,λ) = p κ 23a2 −α2 +λ(a†a −α2)´ (1) This dissipator is engineered using an ancillary buffer mode mediating the coupling between the memory and the environment The system is implemented on a superconducting circuit platform featuring a lumped-element memory mode at ωa/2π = 1.1 GHz with intrinsic loss rate κ1/2π = 2.3 kHz and mean thermal photon number nth = 0.93, alongside a buffer mode at ωb/2π = 7.9 GHz with loss rate κb/2π = 18.2 MHz The two-photon exchange between the memory and the buffer modes is mediated by a pump at frequency ωb − 2ωa, resulting in a rate g2/2π = 1.3 MHz and an estimated κ2/2π = 0.37 MHz The deformation parameter λ controls the deviation from coherent states, and the moon cat states become equivalent to squeezed cat states in the limit of small λ, with numerical simulations confirming that for λ ≤ 1, the moon cat qubit performs comparably to an ideal squeezed cat qubit The deformation parameter λ is a complex quantity whose phase determines the squeezing direction, where λ real and positive (resp.

Kai: negative) yields squeezed (resp.

Mira: anti-squeezed) cat states How it works The paper demonstrates that the moon cat qubit bit-flip time is 160 times larger than of the standard cat qubit, with the same phaseflip time This improvement is achieved by leveraging this bias and correcting the remaining phase-flip error by redundantly encoding the information in several cat qubits The Z-gate benefits from the extended bit-flip time, along with a reduction of non-adiabatic phase-flip errors due to the extra confinement that squeezing provides How it works The Zeno gate is realized by applying a drive at ωa orthogonal to the cat qubit axis, HZ/ħ = ξZ a + ξZ a†, where ξZ is the displacement rate During the Z gate, qubit coherences are susceptible to both idle processes captured by κeff1 and non-adiabatic errors Applying a squeezing deformation increases the overlap between the displaced states and the basis states, thereby dividing nonadiabatic errors by a factor 1+λ Consequently, to first-order, the total phase-flip rate during a Z rotation is well approximated by ΓX = 2κeff1 n¯ + 2ξZ2 / (4κ2n¯(1+λ))2 How it works The paper details the calibration of the longitudinal pump for Moon cats stabilization, where the measured signal S(Vatt,Vφ) = υ(Vatt,Vφ)n¯(Vatt,Vφ) is proportional to the number of photons By observing this measurement signal as a function of the compensation module voltages, two zeros of S can be seen: one with a 2π-winding around it and one without (Fig.

Kai: C7B) Since n¯(Vatt,Vφ): R2 → R, the compensation module setting cancelling ξ1 corresponds to the zero without the 2π-winding, with the other being a zero of the complex-valued function υ(Vatt,Vφ) How it works The Zeno gate calibration involves applying a drive to the memory mode while the cat is stabilized, and by fitting these oscillations, they extract the gate parameters as a function of the drive strength Optimizing the parameters for the lowest phase-flip error rate yields an optimal pigate parameters The bit-flip gate error is measured using the Bayesian adaptive bit-flip measurement, as described in Section E 1 How it works The paper compares the standard and moon cat qubits concatenated in a repetition code, demonstrating that using moon cat qubits can lead to several orders of magnitude improvement in the logical error rate for a given physical error rate thanks to a higher threshold This is due to the combination of two effects: first, moon cat qubits have a lower photon number for the same bit-flip error, which results in a lower phase-flip error Second, moon cat qubits have lower non-adiabatic errors, resulting in lower phaseflip errors on ancilla cat qubits How it works The paper concludes that the phase-space distribution of cat qubits can be tailored to significantly improve performances, bringing them closer to practical use in fault-tolerant quantum computing This is achieved by introducing a particular squeezing deformation which gives the moon cat qubit its shape, controlled by the parameter λ The authors report an increase in the bit-flip exponential scaling factor up to γ = 4.3, surpassing the limit γ = 2 holding for coherent state-based dissipative cats qubits For a moon cat with a phase flip time TX = 1.3 µs, they measure a bit-flip time TZ = 22 s compared to 138 ms for a standard cat with same phaseflip time, achieving a 160-fold improvement How it works The authors fixed the thermal population in their fits of the phase-flip lifetimes, leaving the loss rate κ1 as the sole free parameter for each phase-flip scaling fit across different deformation strengths The results from these three methods are shown in Fig.

Paper summary: Kai: So, we’ve seen the idea that dissipatively stabilizing squeezed cat qubits is a promising architecture because it has built-in quantum error correction. This paper, "Enhancing dissipative cat qubit protection by squeezing," focuses on implementing this idea further.

Mira: The core claim is that they implement a squeezing deformation of the cat qubit basis states to further extend the bit-flip time while minimally affecting the phase-flip rate. This property substantially reduces how many qubits you need for fault-tolerant quantum computation.

Lev: It’s about reaching a scaling exponent gamma equals four point three, which is much higher than what they could get with non-squeezed dissipative cats, and it rises by a factor of seventy four per added photon <ref:2502.07892#pg1>.

Kai: That steep reduction in bit-flip error rate with increasing mean photon number is characterized by that scaling exponent gamma equals four point three <ref:2502.07892#pg1>. The numbers they use are pretty concrete.

Mira: They specifically measured bit-flip times of twenty two seconds for a phase-flip time of one point three microseconds when the average photon number is four point one, which gives them that sixteen zero fold improvement over a standard cat.

Lev: The paper also shows how this deformation parameter lambda controls the deviation from coherent states; small lambda means moon cat states are like squeezed cat states. This is useful because it allows for tailoring the phase-space distribution of these qubits to improve performance.

Kai: So, they’re essentially saying that by controlling the shape of the state using this squeezing, we can significantly enhance protection without needing a completely different physical design for the circuit itself.

Mira: That's right; it enhances cat qubit performances without requiring any design modification, which moves multi-cat architectures closer to fault-tolerant quantum computation.

Lev: The paper also shows how they calibrated the longitudinal pump for moon cats stabilization by observing signal S(Vatt,Vφ) = υ(Vatt,Vφ)n¯(Vatt,Vφ) and finding two zeros of S with a two point pi winding and one without.

Kai: That calibration part is key because it shows how they actually measured the stabilization condition in the lab. It’s not just theory; it’s experimental setup.

Mira: And they also showed that optimizing the parameters for the lowest phase-flip error rate yields optimal pigate parameters, which helps define how to operate this system for best results.

Lev: The method involves using a drive at omega a orthogonal to the cat qubit axis, HZ/hbar = xiZ a + xiZ a† during the Z gate, where xiZ is the displacement rate. Applying squeezing deformation increases overlap between displaced states and basis states by dividing non-adiabatic errors by a factor of one plus lambda.

Kai: So that means for the Z rotation, to first order, the total phase-flip rate is well approximated by gamma X equals two kappa eff one nbar plus two xiZ squared over four kappa b n bar (one plus lambda) squared.

Mira: That formula clearly shows how squeezing helps reduce those non-adiabatic errors during a Z rotation because of that extra confinement.

Lev: The paper also compares standard and moon cat qubits concatenated in a repetition code, demonstrating that using moon cat qubits can lead to several orders of magnitude improvement in the logical error rate for a given physical error rate thanks to a higher threshold.

Kai: So, the overall picture is that tailoring the phase-space distribution of cat qubits can significantly improve performances by introducing this particular squeezing deformation which gives them their shape controlled by lambda.

Conclusion: Kai: So, looking at the paper "Enhancing dissipative cat qubit protection by squeezing," what we've covered is how they use a specific squeezing deformation to enhance dissipative cat qubits. They found that they can reach a scaling exponent gamma equals four point three and a sixteen zero fold improvement in bit-flip time <ref:2502.07892#pg1>.

Mira: And the authors are showing this technique works without requiring design modification, just by deforming the states with parameter lambda controlling the shape of the qubit. This moves us closer to practical use in fault-tolerant quantum computation.

Lev: The implication is that we can tailor these qubits to significantly improve their performance metrics, and they managed a bit-flip time tz equals twenty two seconds compared to one hundred thirty eight milliseconds for a standard cat with the same phase flip time.

Kai: So, in simple terms, this work shows that by engineering the cat qubit's shape using lambda, you get better error protection without changing the underlying hardware architecture.

Mira: It’s about taking these qubits and making them behave in a way that pushes them toward fault-tolerant quantum computation more quickly.

Lev: The paper also points to how moon cat qubits have lower photon numbers for the same bit-flip error, which results in a lower phase-flip error, which is key for logical error rate improvements when using repetition codes.

Kai: So, the overall message from this paper is that tailoring the phase-space distribution of cat qubits can significantly improve performances by introducing this particular squeezing deformation.