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Understanding Generic Features of Quantum Algorithms

Window glass has a strange mix of properties. Similar to a liquid, its atoms have been disordered, but like a solid, its atoms are firm, so a force employed on one atom makes all of them move. This is an analogy that physicists used to explain a quantum state known as a “quantum spin-glass,” in which quantum mechanical bits (qubits) in a quantum computer illustrate both rigidity (when one qubit flips, so do all the others) and disorder (taking on smoothly random values).

A strange mix of properties has been displayed by the window glass. Similar to a liquid, its atoms have been disordered, but like a solid, its atoms are firm, so a force employed on one atom makes all of them move.

Image Credit: Zapp2Photo/

A research group from Cornell University unexpectedly discovered the existence of this quantum state while performing a research project developed to learn more about quantum algorithms and, relevantly, new policies 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 which change one another when they are measured. We find that certain random sequences of these incompatible measurements lead to the formation of a quantum spin-glass.

Erich Mueller, Professor of Physics, College of Arts and Sciences, Cornell University

Mueller added, “One implication of our work is that some types of information are automatically protected in quantum algorithms which share the features of our model.”

“Subsystem Symmetry, Spin-glass Order, and Criticality from Random Measurements in a Two-dimensional Bacon-Shor Circuit” published on July 31st in Physical Review B. The study's lead author is Vaibhav Sharma, a doctoral student in physics.

Assistant professor of physics Chao-Ming Jian (A&S) and Mueller are co-authors. All three conduct their research at Cornell’s Laboratory of Atomic and Solid-State Physics (LASSP). The study received financial support from a College of Arts and Sciences New Frontier Grant.

We are trying to understand generic features of quantum algorithms—features which transcend any particular algorithm,” stated Sharma.

Sharma added, “Our strategy for revealing these universal features was to study random algorithms. We discovered that certain classes of algorithms lead to hidden ‘spin-glass’ order. We are now searching for other forms of hidden order and think that this will lead us to a new taxonomy of quantum states.”

Random algorithms are known to be those that integrate a degree of randomness as part of the algorithm—for example, random numbers could decide what to do next.

Mueller’s proposal for the 2021 New Frontier Grant “Autonomous Quantum Subsystem Error Correction” aimed to clarify quantum computer architectures by coming up with a new strategy to correct for quantum processor errors that have been made by environmental noise—that is, any factor, like cosmic rays or magnetic fields, that would intervene with a quantum computer’s qubits, thereby corrupting data.

The bits of classical computer systems have been safeguarded by error-correcting codes, Mueller said; information is replicated so that if one bit “flips,” users could detect it and fix the error.

For quantum computing to be workable now and in the future, we need to come up with ways to protect qubits in the same way.

Erich Mueller, Professor of Physics, College of Arts and Sciences, Cornell University

Mueller stated, “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 with one another. We borrow language from cryptography for talking about such strategies and refer to the repeated set of bits as a ‘codeword.’”

When they made their breakthrough regarding spin-glass order, Mueller and his team observed a generalization, where several codewords are utilized to depict the same information. For instance, in a subsystem code, the bit “1” might be stored in 4 various ways: 111; 100; 101; and 001.

The extra freedom that one has in quantum subsystem codes simplifies the process of detecting and correcting errors.

Erich Mueller, Professor of Physics, College of Arts and Sciences, Cornell University

The scientists stressed that they were not just trying to generate an improved error safety scheme when they started this research. Instead, they were learning random algorithms to learn the general properties of all such algorithms.

Mueller stated, “Interestingly, we found nontrivial structure. The most dramatic was the existence of this spin-glass order, which points toward there being some extra hidden information floating around, which should be useable in some way for computing, though we don’t know how yet.”

Journal Reference

Sharma,V.,et al. (2023) Subsystem symmetry, spin-glass order, and criticality from random measurements in a two-dimensional Bacon-Shor circuit. Physical Review B.

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