How Space and Time Could Be a Quantum Error-Correcting Code | Quanta Magazine (2024)

So, how do quantum error-correcting codes work? The trick to protecting information in jittery qubits is to store it not in individual qubits, but in patterns of entanglement among many.

As a simple example, consider the three-qubit code: It uses three “physical” qubits to protect a single “logical” qubit of information against bit-flips. (The code isn’t really useful for quantum error correction because it can’t protect against phase-flips, but it’s nonetheless instructive.) The |0⟩ state of the logical qubit corresponds to all three physical qubits being in their |0⟩ states, and the |1⟩ state corresponds to all three being |1⟩’s. The system is in a “superposition” of these states, designated |000⟩ + |111⟩. But say one of the qubits bit-flips. How do we detect and correct the error without directly measuring any of the qubits?

The qubits can be fed through two gates in a quantum circuit. One gate checks the “parity” of the first and second physical qubit — whether they’re the same or different — and the other gate checks the parity of the first and third. When there’s no error (meaning the qubits are in the state |000⟩ + |111⟩), the parity-measuring gates determine that both the first and second and the first and third qubits are always the same. However, if the first qubit accidentally bit-flips, producing the state |100⟩ + |011⟩, the gates detect a difference in both of the pairs. For a bit-flip of the second qubit, yielding |010⟩ + |101⟩, the parity-measuring gates detect that the first and second qubits are different and first and third are the same, and if the third qubit flips, the gates indicate: same, different. These unique outcomes reveal which corrective surgery, if any, needs to be performed — an operation that flips back the first, second or third physical qubit without collapsing the logical qubit. “Quantum error correction, to me, it’s like magic,” Almheiri said.

The best error-correcting codes can typically recover all of the encoded information from slightly more than half of your physical qubits, even if the rest are corrupted. This fact is what hinted to Almheiri, Dong and Harlow in 2014 that quantum error correction might be related to the way anti-de Sitter space-time arises from quantum entanglement.

It’s important to note that AdS space is different from the space-time geometry of our “de Sitter” universe. Our universe is infused with positive vacuum energy that causes it to expand without bound, while anti-de Sitter space has negative vacuum energy, which gives it the hyperbolic geometry of one of M.C. Escher’s Circle Limit designs. Escher’s tessellated creatures become smaller and smaller moving outward from the circle’s center, eventually vanishing at the perimeter; similarly, the spatial dimension radiating away from the center of AdS space gradually shrinks and eventually disappears, establishing the universe’s outer boundary. AdS space gained popularity among quantum gravity theorists in 1997 after the renowned physicist Juan Maldacena discovered that the bendy space-time fabric in its interior is “holographically dual” to a quantum theory of particles living on the lower-dimensional, gravity-free boundary.

In exploring how the duality works, as hundreds of physicists have in the past two decades, Almheiri and colleagues noticed that any point in the interior of AdS space could be constructed from slightly more than half of the boundary — just as in an optimal quantum error-correcting code.

In their paper conjecturing that holographic space-time and quantum error correction are one and the same, they described how even a simple code could be understood as a 2D hologram. It consists of three “qutrits” — particles that exist in any of three states — sitting at equidistant points around a circle. The entangled trio of qutrits encode one logical qutrit, corresponding to a single space-time point in the circle’s center. The code protects the point against the erasure of any of the three qutrits.

Of course, one point is not much of a universe. In 2015, Harlow, Preskill, Fernando Pastawski and Beni Yoshida found another holographic code, nicknamed the HaPPY code, that captures more properties of AdS space. The code tiles space in five-sided building blocks — “little Tinkertoys,” said Patrick Hayden of Stanford University, a leader in the research area. Each Tinkertoy represents a single space-time point. “These tiles would be playing the role of the fish in an Escher tiling,” Hayden said.

In the HaPPY code and other holographic error-correcting schemes that have been discovered, everything inside a region of the interior space-time called the “entanglement wedge” can be reconstructed from qubits on an adjacent region of the boundary. Overlapping regions on the boundary will have overlapping entanglement wedges, Hayden said, just as a logical qubit in a quantum computer is reproducible from many different subsets of physical qubits. “That’s where the error-correcting property comes in.”

“Quantum error correction gives us a more general way of thinking about geometry in this code language,” said Preskill, the Caltech physicist. The same language, he said, “ought to be applicable, in my opinion, to more general situations” — in particular, to a de Sitter universe like ours. But de Sitter space, lacking a spatial boundary, has so far proven much harder to understand as a hologram.

For now, researchers like Almheiri, Harlow and Hayden are sticking with AdS space, which shares many key properties with a de Sitter world but is simpler to study. Both space-time geometries abide by Einstein’s theory; they simply curve in different directions. Perhaps most importantly, both kinds of universes contain black holes. “The most fundamental property of gravity is that there are black holes,” said Harlow, who is now an assistant professor of physics at the Massachusetts Institute of Technology. “That’s what makes gravity different from all the other forces. That’s why quantum gravity is hard.”

The language of quantum error correction has provided a new way of describing black holes. The presence of a black hole is defined by the breakdown of correctability,” Hayden said: “When there are so many errors that you can no longer keep track of what’s going on in the bulk [space-time] anymore, you get a black hole. It’s like a sink for your ignorance.”

Ignorance invariably abounds when it comes to black hole interiors. Stephen Hawking’s 1974 epiphany that black holes radiate heat, and thus eventually evaporate away, triggered the infamous “black hole information paradox,” which asks what happens to all the information that black holes swallow. Physicists need a quantum theory of gravity to understand how things that fall in black holes also get out. The issue may relate to cosmology and the birth of the universe, since expansion out of a Big Bang singularity is much like gravitational collapse into a black hole in reverse.

How Space and Time Could Be a Quantum Error-Correcting Code | Quanta Magazine (2024)

FAQs

Is spacetime a quantum error correcting code? ›

Ahmed Almheiri, Xi Dong and Daniel Harlow did calculations suggesting that this holographic “emergence” of space-time works just like a quantum error-correcting code. They conjectured in the Journal of High Energy Physics that space-time itself is a code — in anti-de Sitter (AdS) universes, at least.

What is error correcting code in quantum theory? ›

A quantum error-correcting code (QECC) can be viewed as a mapping of k qubits (a Hilbert space of dimension 2k) into n qubits (a Hilbert space of dimension 2n), where n > k. The k qubits are the “logical qubits” or “encoded qubits” that we wish to protect from error.

How will quantum computers correct their errors? ›

Shor modeled his protocol after the classical repeater code, which involves making copies of each bit of information, then periodically checking those copies against each other. If one of the bits is different from the others, the computer can correct the error and continue the calculation.

What are the challenges of quantum error correction? ›

Correcting errors in the qubits poses special challenges.
  • First, a quantum bit is not only subject to bit flip errors (a 0 turning into a 1 or the other way around), but can suffer gradual errors.
  • Second, according to the no-cloning theorem, it is impossible to make perfect copies of qubit state.

What causes quantum error? ›

In contrast, the error rates for quantum computers are typically much higher due to the nature of quantum mechanics and the challenges associated with building and operating quantum systems. Noise, decoherence, and imperfections in quantum gates can cause errors in quantum computations.

What is the quantum spacetime theory? ›

In mathematical physics, the concept of quantum spacetime is a generalization of the usual concept of spacetime in which some variables that ordinarily commute are assumed not to commute and form a different Lie algebra. The choice of that algebra still varies from theory to theory.

What is the biggest problem with quantum computing? ›

Challenges of quantum computing

The three main challenges we'll look at include quantum decoherence, error correction, and scalability. Each is a major hurdle on the road to quantum computing, and must be overcome if the technology is to reach full potential.

Can quantum computers fix their own mistakes without making more? ›

That could soon change, because for the first time, a quantum computer has demonstrated an error-correction strategy that fixes more errors than it creates, which may provide a practical way to scale up to a machine capable of carrying out genuinely useful computations.

Can a quantum computer solve anything? ›

Quantum Computers Could Solve Countless Problems—And Create a Lot of New Ones. One of the secrets to building the world's most powerful computer is probably perched by your bathroom sink. At IBM's Thomas J.

What is the fundamental of quantum error correction? ›

Quantum error correction methods use multiple physical qubits to represent a single logical qubit. Data is preserved by distributing the information across multiple qubits. Quantum decoders can then detect and correct any errors that occur during computation. Surface code is a popular QEC code.

What are the different types of quantum errors? ›

In fact, the difficulty of correcting both bit-flip and phase-flip errors is one reason why error correction is much harder for quantum computers than for classical computers. Figure 1. Three types of errors affecting qubits: (1) bit-flip errors, (2) phase-flip errors, and (3) erasure errors.

What is the difference between quantum error correction and mitigation? ›

Current quantum computing devices have been able to demonstrate quantum error correction only with a very small number of qubits. What is now referred quantum error mitigation is generally a series of techniques that stemmed as more practical quantum error correction solutions [41].

What is quantum error correction for quantum sensing? ›

Quantum error correction (QEC) is a method for reducing noise in quantum channels and quantum proces- sors27–29. In principle, it enables a noisy quantum computer to simulate faithfully an ideal quantum computer, with reasonable overhead cost, if the noise is not too strong or too strongly correlated.

What is the quantum error correcting protocol? ›

Quantum error-correcting (QEC) stabilizer codes enable protection of quantum information against errors during storage and processing. Simulation of noisy QEC codes is used to identify the noise parameters necessary for advantageous operation of logical qubits in realistic quantum computing architectures.

What is memory style error-correcting code? ›

Error-correcting code (ECC) memory is a type of computer data storage specifically designed to detect, correct and monitor most common kinds of interior data corruption. As data is processed, ECC memory equipped with a special algorithm constantly scans and corrects single-bit memory errors.

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