# Adjusting for Mistakes: Achieving Imperative Error Correction in Quantum Computers

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Image courtesy of Google AI blog.

Just a couple of decades ago, a functional quantum computer lay firmly in the realm of fantasy; the prospect of creating one was rife with challenges both theoretical and practical. Yet, given its unbounded potential to solve problems that are unsolvable by conventional computers, scientists have persevered, tirelessly chipping away at the barriers that lay in their way. A recent paper in *Nature* from a team at Yale University sees us inch even closer towards this goal. They have successfully implemented a critical technique to extend the lifetime of quantum data that could be used in a quantum computer.

**Quantum Computing: What is it?**

All the hype (and troubles) surrounding quantum computers stems from the fundamentally different manner in which a quantum computer operates. While your laptop (a ‘classical’ computer) uses the principles of classical physics to operate, a quantum computer exploits seemingly unintuitive quantum phenomena to perform its computations. Investigating how these quantum phenomena can be leveraged in a quantum computer is at the heart of the mission of Yale’s Quantronics Laboratory (QLab). “The laws of quantum physics are radically different from the laws of classical physics, so quantum computers pose new challenges that one does not encounter with classical computers,” said Michel Devoret, F.W. Beinecke Professor of

Applied Physics, QLab principal investigator, and co-author of the research.

Among the most significant of these challenges that the QLab attempts to tackle arises due to the curious phenomenon of quantum decoherence, wherein quantum information is lost. Just as classical computers store information using bits (binary values of 0 and 1), quantum computers utilize qubits (quantum bits). Unintuitively, these qubits can take on a combination (superposition) of binary values which are encoded by their wavefunctions; it is these wavefunctions that are manipulated while performing computations.

‘When a qubit is encoded in a physical system, its wavefunction interacts with the environment, and the information it stores tends to get corrupted in a process known as quantum decoherence,” said Alec Eickbusch, the co-lead author and a graduate student at the QLab. Since it is impossible in practice to completely isolate a qubit, quantum decoherence tends to quickly scramble the qubit, destroying its information in a matter of microseconds. “In a quantum computer, we need to find a way to give a qubit a longer lifetime,” Eickbusch said.

**Error Correction, the Quantum Way**

Unsurprisingly, prolonging a qubit’s lifetime is much easier said than done. This goal is the focus of quantum error correction (QEC), which seeks to correct for errors stemming from quantum decoherence and other sources. In classical computers, error correction, in the very unlikely circumstance that it is required, is relatively simple: all one needs is redundant copies of bits. Any error causing a bit to change value is easily detected and rectified by observing the values of its copies.

Alas, quantum physics does not allow for such a straightforward solution. The aptly named ‘no-cloning theorem’ disallows the creation of independent, identical copies of quantum states. Even more frustratingly, checking whether the encoded information in a qubit has changed requires one to measure that state of the qubit, which itself alters the qubit. With such enormous roadblocks, QEC seemed an impossible feat, until MIT professor Peter Shor developed a roundabout technique (a “code”), which corrected errors in a “logical qubit” that was made of a collection of ordinary (“physical”) qubits. Since then, a number of different such QEC codes have been theorized, but not all have been practically implemented.

**The Ingenious GKP Code**

The QLab team chose to focus on a particular code devised in 2001 called the GKP code, rather creatively named after the initials of its theorists: Daniel Gottesman, Alexei Kitaev and John Preskill. “The GKP algorithm was a very ingenious form of error correction, developed ahead of its time,” Devoret said. It relies on the principle that quantum noise – the cause of errors in a qubit – is local: it affects different parts of a system differently. Therefore, if information is stored non-locally, it can be recovered in spite of noise.

Devoret uses an analogy to explain the basis behind the GKP algorithm: “Suppose you have two boxes put close together, with a hole in them to allow them to ‘communicate.’ If a bit is stored by placing a ball in either the left (0) or the right (1) box, then shaking the system (introducing ‘noise’) may cause the ball to move between boxes, thus changing the bit stored. However, if the boxes are placed far away (‘non-local storage’), then the ball will remain in its box and the bit will be preserved in spite of the system being shaken. Similarly, the GKP code provides a way to put the 0 and 1 of a logical qubit as far apart in ‘phase space’ as possible, therefore preventing errors to as large an extent as possible.”

Although the GKP code has been around for nearly two decades, it was believed to be too impractical to physically realize in a laboratory setting. However, in the decades since, the development of better instrumentation has allowed the QLab team to recognize that implementing the GKP code was “very possible, using tricks of superconducting circuits”—the quantum mechanical apparatus that hosts the qubits they manipulate.

**Bringing the Code to Life**

Eickbusch outlined the two-year research journey by separating it into three rough stages. First, the team set about crafting simulations to determine whether their idea would work in practice. Then, they spent time in the cleanroom, building, tweaking, and debugging their quantum superconducting circuits. Finally, with their system working, they wrote the code to carry out measurements and extract meaningful information from their setup. From start to finish, the team donned the roles of theoretical physicists, electrical engineers and computer scientists to work on the different theoretical and experimental facets that were needed to get their research up-and-running.

To implement these GKP code states in a quantum circuit, the QLab employed state-of-the-art technology, “assembled from scratch and constructed completely in-house.” For example, the experiment collected data by analyzing weak microwave signals that emerged from their setup using extremely sensitive amplifiers. “[These amplifiers are so sensitive that] if you were on the Moon and called home with a telephone, we’d be able to hear you,” Devoret said.

**Challenges and Results**

Employing incredibly precise technology also necessitates equally precise feats of engineering. “The biggest challenge in the research process was engineering the exact parameters of the device that we needed. It took six or seven tries for us to get it right,” Eickbusch said. The superconducting circuits used in the QLab need to be cooled to extremely low temperatures, making this debugging process all the more cumbersome. “It would take two days to cool down the device to test it. Then, we’d realize that a parameter was off, and it would take another two days to warm back up”, Eickbusch said. Malfunctioning apparatus also added to the team’s woes. Co-lead author Philippe Campagne-Ibarcq, now on the faculty of the National Institute for Research in Digital Science and Technology in France, recalled the late nights that these technical difficulties often brought. “In the middle of our experimental work, our cryostat started to die. We were on a race against time, and, after some completely crazy nights, ended up implementing an important variation of our code in just one week,” he said.

Their painstaking efforts were eventually rewarded—using the GKP code, the QLab team was able to extend the lifetime of a logical qubit by a factor of 2, showing that their quantum error correction had successfully mitigated the impact of quantum decoherence on a qubit. “This research is a proof-of-concept that GKP codes can be practically stabilized using quantum superconducting circuits,” Eickbusch said. However, the improvement in qubit lifetime provided by the GKP code could be further extended. “We have not yet attained the ‘break-even point’, in that this GKP state does not last longer than the best possible encoding of quantum information [that does not use GKP codes]. Our goal for the future is to beat the break-even point by orders of magnitude”, Devoret said. In fact, armed with a government grant from the Department of Energy, this is one of the goals towards which the QLab is now working.

**Future Directions**

Even if the lifetime of qubits could be extended by orders of magnitude, according to Devoret, there is still much to be done before a quantum computer could become reality. “What we have shown in this paper is prolonging memory. The next step involves fault-tolerant computation: showing that quantum error correction can be implemented while performing an operation on a qubit,” Devoret and Eichbusch said. Progress also needs to be made on the technological front to improve the superconductors, insulators and electronics that form the physical quantum device. “Our Lego bricks are still not optimum and perfectly functioning. Part of the work in our lab seeks to develop the Lego bricks we need to build more complicated devices in the future,” Devoret said.

With all that remains to tackle ahead, it’s no surprise that Campagne-Ibarcq thinks that this is an exciting time to be active in the field of quantum computing. “There is always room for new ideas,” he said. Teams across the globe are working on different, innovative solutions to similar problems, collaborating and sharing ideas among one another in what Devoret describes as a “highly stimulating environment”. In fact, Campagne-Ibarcq recounts that the QLab was also a direct beneficiary of this kind of collaboration. “Our friendly competitors working with trapped ions (an alternative to superconducting circuits to store qubits) presented their results in a seminar at Yale, describing an easier way to stabilize the GKP code. This prompted fruitful discussion, during which the protocol we used in our research was devised,” Campagne-Ibarcq said.

“In just a decade from now, we should have a good idea of whether a quantum computer can ever be built, what it will look like, and how useful it is,” said Devoret. But for such a machine to be realized, it will need some form of error correction, and how that is implemented will no doubt be, in part, due to this work.

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