Cornell University researchers have discovered a "quantum spin glass" state in quantum computing, providing insights into error correction and revealing hidden instructions in quantum algorithms, potentially leading to new quantum state classifications and advances in quantum computing.

On a microscopic level, window glass exhibits a curious blend of properties. Its atoms are disordered like a liquid, but have the rigidity of a solid; when a force is applied to one atom, it affects all the other atoms. Physicists use this metaphor to describe a quantum state known as "quantum spin glass," in which the quantum mechanical bits (qubits) in quantum computers exhibit both disorder (having seemingly random values) and rigidity (when one qubit flips, so do all the other qubits). A team of researchers at Cornell University accidentally discovered the existence of this quantum state while working on a research project aimed at further understanding quantum algorithms and related new strategies for error correction in quantum computing.

"Measuring the position of a quantum particle changes its momentum, and vice versa. Similarly, for qubits, there are quantities that change each other when measured. We found that certain random sequences of these incompatible measurements can lead to the formation of quantum spin glass," said Erich Mueller, professor of physics in Cornell University's College of Arts and Sciences (A&S). "One implication of our work is that certain types of information are automatically protected in quantum algorithms that share characteristics with our model."

The research was recently published in Physical Review B. The first author is Vaibhav Sharma, a Ph.D. student in physics.

Chaoming Jian, assistant professor of physics, is a co-author with Mueller. All three are engaged in research at Cornell University's Laboratory of Atomic and Solid-State Physics (LASSP). This research was supported by a grant from the College of Arts and Sciences’ New Frontiers Fund.

"We are trying to understand the universal characteristics of quantum algorithms -- characteristics that transcend any particular algorithm," Sharma said. "Our strategy for uncovering these universal characteristics is to study stochastic algorithms. We found that certain classes of algorithms lead to hidden 'spin glass' order. We are now looking for other forms of hidden order and think this will give us a new taxonomy of quantum states."

A randomized algorithm is one that incorporates some degree of randomness as part of the algorithm - for example, using random numbers to decide what to do next.

Advances in quantum error correction

Mueller's 2021 New Frontiers grant proposal, "Autonomous Quantum Subsystem Error Correction," aims to simplify quantum computer architecture by developing a new strategy to correct quantum processor errors caused by environmental noise—anything like cosmic rays or magnetic fields that interferes with a quantum computer's qubits, corrupting information.

Mueller said the bits in classical computer systems are protected by error-correcting codes; the information is copied so that if a bit "flips," you can detect it and fix the error. "For quantum computing to work now and in the future, we need to come up with ways to protect qubits in the same way. The key to error correction is redundancy. If I send three copies of a bit, you can tell if there is an error by comparing the bits to each other. We borrow the language of cryptography to talk about this strategy and call repeated sets of bits 'ciphers.'"

When Muller and his team discovered the spin glass order, they were working on a general approach to using multiple coded words to represent the same information. For example, in one subsystem code, bit "1" may be stored in 4 different ways: 111, 100, 101, and 001. The extra degrees of freedom in the quantum subsystem's code simplify the process of detecting and correcting errors.

The researchers emphasized that when they began this study, they were not simply trying to generate a better error protection scheme. Instead, they are studying stochastic algorithms to understand the general properties of all such algorithms.

"Interestingly, we found extraordinary structures," Müller said. "The most striking thing is the presence of this spin glass order, which suggests there is some additional hidden information floating around that should somehow be used in calculations, although we don't know how yet."

Reference Vaibhav Sharma, Chao-Ming Jian, and Erich J. Mueller, July 31, 2023, Physical Review B, "Subsystem symmetry, spin glass order, and criticality of stochastic measurements in two-dimensional Beken-Shaw circuits."

DOI:10.1103/PhysRevB.108.024205

Compiled source: ScitechDaily