How Space and Time Could Be a Quantum Error-Correcting Code | Quanta Magazine (2025)

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 (2025)

FAQs

How Space and Time Could Be a Quantum Error-Correcting Code | Quanta Magazine? ›

How Space and Time Could Be a Quantum Error-Correcting Code. The same codes needed to thwart errors in quantum computers may also give the fabric of space-time its intrinsic robustness. In toy “holographic” universes (if not the real universe), the fabric of space and time emerges from a network of quantum particles.

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.

What is the distance of a quantum error-correcting code? ›

A code that corrects w errors is said to have distance 2w + 1, because it takes 2w + 1 single0qubit changes to get from one codeword to another. We can also define distance as the minimum weight of an operator H that violates equation (3.9) (a definition which also allows codes of even distance).

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.

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.

What is the theory of error correcting codes? ›

An error-correcting code is an algorithm for expressing a sequence of numbers such that any errors which are introduced can be detected and corrected (within certain limitations) based on the remaining numbers. The study of error-correcting codes and the associated mathematics is known as coding theory.

What is the minimum distance for error-correcting code? ›

Minimum Hamming distance for error correction

To design a code that can correct d single bit errors, a minimum distance of 2d + 1 is required.

How many qubits for error correction? ›

According to the quantum Hamming bound, encoding a single logical qubit and providing for arbitrary error correction in a single qubit requires a minimum of 5 physical qubits.

What is approximate quantum error correction? ›

That is, approximate quantum error-correcting codes have the capability of correcting errors in a regime where no exact QECC will function. The scheme is also a secret-sharing scheme, in that no t positions reveal any information at all about the message.

What is the main problem with quantum computing? ›

Compared with standard computers, quantum computers are extremely susceptible to noise. The quantum state of qubits is extremely fragile and any disturbance, such as a slight vibration or a change in temperature, can uncontrollably affect the computer, causing information stored to be lost.

What is the argument against quantum computers? ›

A fundamental challenge for today's quantum computers is that they are very prone to errors. Some have suggested that these so-called “noisy intermediate-scale quantum” (NISQ) processors could still be put to useful work.

Can quantum computers solve real world problems? ›

This opens the door to solving many real-world problems that would take a classical computer hundreds – if not thousands – of years to solve. This is why experts believe that quantum computing will find dozens of applications in the future.

What are the different types of quantum errors? ›

There are two fundamental types of quantum errors: bit flips and phase flips. Bit flip errors occur when a qubit changes from $\ket{0}$ to $\ket{1}$ or vice versa. Bit flip errors are also known as $\sigma_x$-errors, because they map the qubit states $\sigma_x \ket{0} = \ket{1}$ and $\sigma_x \ket{1} = \ket{0}$.

What is Google AI quantum error correction? ›

The Google Quantum AI team has made an important step towards the development of a large-scale useful quantum computer. This breakthrough is the first demonstration of a logical qubit prototype, showing that it's possible to reduce errors by increasing the number of qubits in a scheme known as quantum error correction.

What causes quantum errors? ›

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 error correction code notation? ›

Correcting S is equivalent to C having distance d. We use the notation [[n, k, d]] for a code that encodes k logical qubits into n qubits and corrects errors up to distance d. C ⊆ C2n , which means C uses n physical bits.

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 quantum error correction sensing? ›

In error-corrected quantum sensing, the initial state is a logical state of a QEC code, and errors are repeatedly corrected while the signal imprints on the sensor, until the latter is finally read out.

What is error correction in information theory? ›

In information theory and coding theory with applications in computer science and telecommunication, error detection and correction (EDAC) or error control are techniques that enable reliable delivery of digital data over unreliable communication channels.

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