# In-Depth Analysis: Preparing and Measuring State with Barium Qubits

When we talk about error rate in quantum computing, we usually refer to the quantum quality of a system *doors,* the operations that actually make up the calculation. But there is also another source of error, which every quantum computer must deal with: state preparation and measurement, or SPAM.

By using barium qubits instead of ytterbium qubits in our trapped ion quantum computers, IonQ is now able to report a significant breakthrough in improving our SPAM error rates. Because this is an unfamiliar concept to many readers, this blog post explains exactly what SPAM is, how it can determine if a quantum computer is useful, and how the use of barium qubits exceeds all previous results.

The ingredients of SPAM

Each quantum calculation goes through three steps:

**Preparation of the report**where we put the qubits in their initial state

**Calculation,** where we run an algorithm consisting of a series of quantum gates

**The measure,** where we read the final state of each qubit after the calculation – this is also sometimes called “state sensing” or “reading”.

*A diagram of a simple quantum circuit, with preparation, calculation and measurement highlighted*

By analogy, if you want a calculator to calculate 5^{2} = 25, **state preparation** is when you type “5” into the calculator. the **doors** are the other buttons you press (*“^2”)*which manipulate your starting state in the result, and **the measure** is the calculator displaying the number 25 on the screen after you press the “=” button. If any of these steps don’t go as planned, you’ll get the wrong answer. If you press the wrong button or if the wiring inside the calculator is bad, you may get a bad result. Although we have largely solved these kinds of problems in classical computers, we are still working to perfect them in the quantum realm.

Even if the final “algorithmic” result of a calculation includes both sources of error (and more!), we can understand each of them individually by directly measuring SPAM – we prepare a report |0〉sup id=” fnref1″>1 on a qubit, then measure it immediately without performing any gates, effectively asking “did I read a |0〉” regardless of which gates introduced other errors.

Since this test involves first preparing and then immediately measuring the qubit, it is very difficult to distinguish where the error has occurred – when you get a wrong answer, you don’t know if the error is due poor preparation of the qubit or poor measurement. correctly.

For this reason, report preparation and measurement are usually grouped under a single measure called report preparation and measurement error, or **spam error** to shorten it. We often describe this as SPAM *error rate*the percentage chance that the test will produce the wrong answer, but you’ll also see this described as SPAM *loyalty*which is the percentage probability that it produces the correct one.

Strictly speaking, there is a separate |0〉SPAM error and |1〉SPAM error. To measure the SPAM error |0〉, we prepare the qubit in |0〉and then read its state, repeating this cycle thousands of times. In some fraction of these cycles, we intend to prepare |0〉but actually read |1〉 This fraction is your error |0〉SPAM. The |1〉SPAM error works the same way, but we prepare it in a |1〉before the measurement.

When we present a unique number for the SPAM error, like below, it is the *Medium* of the |0〉 SPAM error and |1〉SPAM error. Because quantum algorithms output both |0〉and |1〉in their response, this gives us an overall idea of the SPAM error in practice.

How state sensing works with ions

With trapped ion qubits like those in IonQ, state detection (measurement) is done via *fluorescence,* orlight emission. A specially tuned laser beam illuminates the ions, making any ion in the |1〉 state “glow”, scattering many photons. However, any ion in the |0〉 state will remain dark, scattering very few photons, if at all.

This effect, known as *state-dependent fluorescence*, gives us a simple way to distinguish |0〉and |1〉 We simply count how many photons are emitted by each ion when illuminated by our tuned laser beam. A number of photons is chosen as the dividing line, known as the *threshold value*. If we detect a number of photons greater than this threshold value, we conclude that the ion was in the |1〉 state. Otherwise, we conclude that it was in state |0〉.

To set this threshold, we try to prepare |0〉and then measure the qubit several times, normally thousands. We then construct a histogram of the number of times we have measured a given number of photons. We repeat this process for the state |1〉. We can then draw a line between the histograms, and that’s our threshold. Anything we thought was a |0〉but falls above the threshold line is an error in our preparation and measurement of the state, and the same goes for |1〉

Barium ions

IonQ has worked with ytterbium ions for most of the company’s history. We are now also exploring barium ions as qubits, as barium ions have a number of intrinsic characteristics that we believe will improve the performance of our computers.

During the traditional state-dependent fluorescence technique described above, it is possible for the detection laser itself to change the ion from the |0〉state to the |1〉 state, or vice versa. If this happens, the state will be read incorrectly. This error mechanism limits the number of photons that can be emitted per read attempt, which in turn limits the amount of information we can collect about the qubit state per read attempt. Ultimately, this limits our loyalty to SPAM.

With barium ions, it is possible to use a readout technique known as *shelving*. In this technique, the |0〉 state is first transferred to a different atomic level that does not interact with the detection laser at all.

Once done, this common source of error can no longer occur and we can collect much more fluorescence from the |1〉 state. By extracting more information per read attempt, we have greater confidence in the result, which reduces our SPAM error rate.

Recent results with barium

Below is a histogram that represents SPAM data extracted from IonQ Aria, our latest ytterbium-based system. The red corresponds to the data of our |0〉SPAM tests and the blue to the data of our |1〉SPAM tests. The vertical dotted line is the threshold where we distinguish |1〉 from |0〉

Any red to the right of the threshold line and any blue to the left of the line represent errors. We typically see error rates between 30 and 50 errors per 10,000, and in this test we wanted to prepare |0〉10,000 times but measured |1〉27 times. We wanted to prepare |1〉10,000 times but measured |0〉41 times. This gives a SPAM error of (27+41)/2 = **34 errors per 10,000 executions**for 99.66% SPAM loyalty

We can compare this result with the same measurement made using barium qubits. As you can see, in our barium histogram, the gap between |0〉and |1〉is much wider, and the number of errors is also much lower.

Here we wanted to prepare |0〉20,000 times but measure |1〉5 times, and we wanted to prepare |1〉 20,000 times but measure |0〉9 times. **This gives a combined SPAM error of 3.6 + – 0.9 per 10,000 executions, or SPAM loyalty of 99.96%.**

**This SPAM loyalty is better than all other SPAM data published by all other commercial providers.**

Future consequences

SPAM is very important for scaling hundreds or thousands of qubits because these numbers are *by* each *qubit.*

Given a SPAM loyalty of *F* (per qubit), the SPAM fidelity for a qubit register of N qubits is F^{NOT}. With many qubits, our overall loyalty to SPAM declines rapidly. For example, with SPAM fidelity of 99%, a register of 100 qubits has an overall SPAM fidelity of only 0.99^{100} = 37%. This means that there would only be a 37% chance of getting the correct answer, even with perfect doors!

In this scenario, the quantum computer is very unlikely to return the correct answer, even if it calculates that answer perfectly. With 99% per-qubit SPAM fidelity, this hypothetical 100-qubit computer can’t even report the answer it got 63% of the time.

For SPAM fidelity of 99.96%, a register of 100 qubits would have an overall SPAM fidelity of 96% – a much better probability of success.

IonQ’s barium gamble pays off. Reducing SPAM error rates is a critical part of making quantum hardware useful in the near term, and our barium-based systems have already shown dramatic improvement in this critical aspect of computation.

Moreover, our current results are not at the limit of the performances that we believe possible with this system. With continued improvements, we expect to be able to achieve an average SPAM error of less than 1 in 10,000, or 99.99% accuracy using barium.

Of course, SPAM isn’t the only thing to worry about. It takes a wide variety of metrics – or a well-crafted summary metric like the #AQ benchmark – to understand a system’s actual algorithmic performance and usefulness to customers. We look forward to sharing more information about this system, including its Gate Loyalties and #AQ, in the months ahead.

**1** This notation, called bra-ket notation, indicates that we are dealing with quantum states, rather than classical states. While these states can get very complex, SPAM only deals with the two simplest ones a pure zero, |0〉 and a pure one, |1〉↫

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