Scientists develop method to speed up quantum measurements using space-time trade-off

In an attempt to speed up quantum measurements, a new Physical Review Letters study proposes a space-time trade-off scheme that could be highly beneficial for quantum computing applications.

Quantum computing has several challenges, including error rates, qubit stability, and scalability beyond a few qubits. However, one of the lesser-known challenges quantum computing faces is the fidelity and speed of quantum measurements.

The researchers of the study address this challenge by using additional or ancillary qubits to significantly reduce measurement time while maintaining or improving the quality of measurements.

Led by Christopher Corlett, Professor Noah Linden, and Dr. Paul Skrzypczyk from the University of Bristol, the work was a collaborative effort, including members from the University of Oxford, University of Strathclyde, and Sorbonne Université.

Phys.org spoke to Corlett, Professor Linden, and Dr. Skrzypczyk about their work.

“The measurement process in quantum mechanics is one of its most important and fascinating features. It is also vital for future quantum technologies,” explained Corlett.

“Accurate and fast quantum measurements are crucial for the development of emerging quantum technologies. Recent seminal results in quantum error correction demonstrate the need for fast and accurate measurements in order to facilitate error decoding, without which fault tolerance would be impossible,” added Dr. Skrzypczyk.

The measurement challenge

There are infinitely many measurements that can be performed on a qubit. A particularly important one is probing whether it is one of two natural states: 0 or 1. To perform this measurement accurately typically involves probing the qubit for a long time.

These longer measurements typically yield higher accuracy but introduce significant overhead and delay, particularly problematic for mid-circuit measurements required in quantum error correction. Additionally, longer measurements introduce noise and decoherence that can accumulate during this time.

The researchers explain this with an analogy.

“Imagine you’re shown a picture of two glasses of water, one glass with 100 ml and the other with 90 ml, and you have to determine, by sight, which glass has more water.

“If you’re only shown the picture for one second you might struggle to tell which glass is more full. However, if you’re shown the picture for two seconds, you can be more confident about which glass is more full,” explained Corlett.

The researchers used an ancillary qubit to amplify the amount of information the measurement can gather about the qubit state in a fixed amount of time.

It is like doubling the volume of each glass; a difference of 20 ml would be easier to observe than a difference of 10 ml. It gives more confidence in the answer. If this process is continued and the amount of information continuously increases, the time taken to answer reduces.

“Continuing with the analogy, adding a second auxiliary qubit would triple the volumes to 300 ml and 270 ml, which you would be able to distinguish, with confidence, in 0.66 seconds. In this way, you can achieve a linear increase in readout speed with the number of qubits,” explained Professor Corlett.

Trading time for space

The researchers’ scheme builds on previous protocols that use repetition codes for error correction. This method entangles the target qubit (on which measurement is to be conducted) with ancillary qubits.

More specifically, the target qubit is entangled with N-1 ancillary qubits. The information from the target qubit is then copied to all the ancillary qubits using so-called CNOT gates.

Here is where the innovation lies. Instead of measuring the target qubit for time t, all N qubits (target and ancillary) are measured simultaneously for t/N time. All the measurements are then added for a combined result, which gives the same statistical confidence as a longer single measurement.

The space (the number of qubits used) is being traded for time. The measurement of a single qubit for five seconds is the same as measuring five qubits simultaneously for one second.

“Remarkably, this allows the quality of a measurement to be maintained, or enhanced, even as it is sped up. The scheme is widely applicable to a broad range of leading quantum hardware platforms, including cold atoms, trapped ions, and superconducting qubits,” said Corlett.

Robust against noise

The researchers investigated their scheme first in ideal conditions with no noise and then with realistic noise models. They found that the ideal case showed a perfectly linear speedup with the number of qubits.

The noise models also showed significant speedup and sometimes had better than linear improvement. The researchers showed that their approach can achieve higher maximum measurement quality than previously possible.

“Making sure our scheme is robust to this noise is incredibly important as it ensures it is useful for real-world implementation where noise is unavoidable,” said Professor Linden.

The researchers are eager to see the experimental implementation of their scheme and are working to develop it in more detail for specific systems like superconducting qubits.

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