In our latest experiment, we show early results on how cat qubits can remain stable against bit-flip errors for about one hour: a milestone for Alice & Bob and a record for superconducting qubits. This is an outstanding improvement compared to the 7-minute record established a year ago on our Boson 4 chip, and a very encouraging result given that it already far surpasses the target of 13 minutes for our 2030 device, Graphene. *
Before deep-diving into the nitty gritty details of the data analysis, we show the main results in Figure 2. This figure shows a measurement of the state of the cat qubit over 61 hours. When the signal is high, the qubit is in the 
state ( 
in the language of cat qubits). When the signal is low, the state is 
( 
in the language of cat qubits). When the signal jumps, there is a bit-flip. We count a total of 41 bit-flips over 61 hours, which implies an average bit-flip time of 44 minutes.
Like all experimental results, this quantity carries some uncertainty.
As we will explain below, we find that within a confidence interval of 95%, the cat bit-flip time is between 33 and 60 minutes.
Interestingly, this timescale is significantly longer than the occurrence of cosmic ray impacts (literally how often an a high-energy particle from outer space hits the chip), which are commonly thought to be a source of errors in other superconducting quantum computers. As shown in this 2021 paper from Google.
Why is it Important to Make Bit-flips so Rare?
If you are a regular reader of Alice & Bob’s blog, you may have already heard this story. But in a nutshell, the idea is this.
A quantum computer, like an everyday laptop, works with 0s and 1s. But unlike its classical counterpart, it also uses the quantum superposition of these states, meaning the simultaneous coexistence of 0 and 1. This is one of the key ingredients of any quantum computer. Two errors can happen in such a system: bit-flips, as in classical computers flipping 
, and phase-flips, which flip the phase of the superposition—for example, 
turning into 
. Both of these errors need to be tackled to reliably run quantum algorithms.
For reference, typical superconducting qubits achieve bit-flip times in the millisecond range, millions of times shorter than our latest result.
The cat qubit bit-flip advantage comes at the price of a shorter phase-flip time.
Running useful quantum computations will require preserving quantum states for tens of minutes. But how can we get to these timescales? Error correction does this by redundancy: storing the quantum information in a logical qubit made of many physical qubits makes it more robust.
The catch is that simultaneously correcting bit and phase-flips requires hundreds, if not thousands, of physical qubits given current error rates. Alice & Bob’s cat qubit advantage is based on the reduction of bit-flip errors to the point where we can entirely ignore them when running quantum algorithms, making our quantum computers hundreds of times more hardware-efficient in the process—from a thousand to just tens of physical qubits in each logical one.
If this explanation was your cup of tea, then you should definitely check out our whitepaper Think Inside the Box, where we explain not only the cat qubit but also a few rudiments of quantum computing, error correction, early applications, and we deep dive into Alice & Bob’s roadmap to 2030.
But After All, is Our Bit Still “Quantum”?
So far, we have shown you a chip with very long bit-flip times. But this is not enough to call that a qubit!
All classical bits, like the normal transistors in your laptop, have excellent bit-flip error rates. What would make them quantum is the capability of storing and manipulating quantum superpositions between the 0 and 1 states. But a transistor cannot do that. That’s why we need to demonstrate our bit still holds quantum superposition.
One of the “knobs” we use to make our devices more resistant to bit-flips is to drive energy into our system in a smart way. The more energy we pump in, the more photons the device hosts, with each photon carrying a quantum of energy. For this experiment, we calibrated our cat to host 11 photons.
But the more energy you put into a quantum system, the more challenging it becomes for it to hold quantum superposition states. This begs the question: does this cat qubit still display “quantum” properties when it hosts this many photons? In other words, can we prepare a superposition state?
Yes, we can. We show that in figure 4 below, where we prepare a state in superposition of 0 and 1 and measure how the superposition decays over time. To give some context about this measurement, and why it is so cool, what we are measuring is whether the device contains an even or odd number of photons—a quantity known as parity. It maps directly to the Pauli operator X of the cat qubit.
But this is not yet enough.
What we have just shown is that the qubit holds quantum superpositions over some time.
Quantum computing, however, is based on manipulating qubits to perform logical operations. In figure 5, we show that we can perform Z rotations, a basic qubit operation that continuously shifts the phase of our qubit (oscillating between the states 
and 
) and thus flips the parity of the system from even to odd and back. The alternating red and blue stripes in the figure show that our system coherently oscillates between positive and negative parity states.
And this is the proof that our cat state can still be operated as a qubit.
The Z gate is also one of the essential operations required to perform a quantum error correction code with cat qubits.
Wrapping up
Here is a summary of the results:
- Number of photons = 11
- Bit-flip time = 44 minutes
- Phase-flip time = 420 ns (equivalent to T1 = 9.2 us)
- Z-gate fidelity = 94.2 % in 26.5 ns **
Overall, we show that despite its large size and very long bit-flip time, we still maintain quantum control over the cat qubit.
Enough?
Well, not quite. These are just preliminary results on very new techniques, and now we have to replicate them during an error correction experiment—particularly during the CNOT gate—but we were just too excited not to share this with you.
Below, we show a first step in that direction where we used our latest flagship 12-qubit processor Helium 2 to see if we could replicate these long bit-flip results on a different QPU. We found that we were capable of exceeding our future target of 13 minutes for Graphene.
The figure 6 below shows three different qubits, operated on the same QPU, where we reached bit flip error rates above the hour.
As we discussed in depth above, this measurement alone is not sufficient to claim that all these systems can now be operated as cat qubits, and with the same level of control as the previous device. But, as we are now collecting more data on even more devices, we believe this to be a promising starting point towards reliably making even better cat qubits. It also raises interesting questions, for example, about the impact of rare and catastrophic events such as cosmic rays on the cat qubit.
For Experts: Bit-Flip Statistics
If you got this far, you probably are ready for some more data, aren’t you? In the next section we deep dive on the bit-flip statistics we show in figure 2 of the blog post, and why we can trust them.
So far, we estimated the bit-flip time in a very simple way, by just counting the number of bit-flips happening in a given amount of time. But can we go further? What statistics do these jumps follow? In particular, are the jumps independent from each other? To answer these questions, we are going to analyze directly the raw signal data, not just the jumps extracted from it.
Figure 7 shows the raw trace signal in Figure 2 before applying any data filtering. The data are more noisy than in figure 2 but, as it was pointed out by Landauer, the noise is the signal [Nature 392, 658 (1998)], and it will in fact allow to extract more information.
In figure 8 we plot the autocorrelation function of the raw signal of figure 7. This quantity tells us about the typical timescales of our processes and their statistics. The left panel of figure 8 focuses on “short” times (of the order of 100s), while the right panel focuses on longer times (up to 1 hour – this duration is solely limited by the fact that the measurement was sliced in chunks of 1 hour).
At short time scales, the estimate of the auto-correlation function is very accurate because it has more independent points on which to average. We observe a single exponential decay, which is consistent with a Markovian (memoryless) switching process characterized by a single time scale. The exponential is characterized by a single time scale of 44 minutes, matching the bit-flip estimate from the counting of the jumps. These are indeed the features we expect from independent bit flips.
At longer time scales, the estimation of the autocorrelation function quickly loses accuracy (see the error bars representing the variance of this function as the time 
increases), but remains compatible with a single exponential decay with a rate within the 95% confidence interval of the bit-flip time estimated by counting the jumps (between 33 and 60 minutes).
Summing up, our data show that the quantum jump statistics is compatible with a Markovian process, at least up to times of hundreds of seconds, which are those relevant for near-term quantum computation. The data are also compatible with the expected Poisson statistics of bit-flip jumps in cat states.
* The 2030 bit-flip time target of 13 minutes must also satisfy more stringent requirements than the ones of this experiment, as it needs to be held during two-qubit gates (Controlled NOT).
** In this experiment, the impact of the drive used to perform the Z gate on bit-flip incidence was not measured but should remain small based on previous experiment and current data.
