Error Control Begins to Shape Quantum Archtectures

Considerable piece.   I understood that error control was important, how this fits in is less clear.  Reliability can be seen as key.  Diving more deeply.  

Error Control Begins to Shape Quantum Architectures  By Chris Edwards

Communications of the ACM, January 2023, Vol. 66 No. 1, Pages 13-15    10.1145/3570518

Sound waves on both sides of a quantum computer, illustration  .... 

Quantum computing has a crucial weakness that may severely delay, if not kill outright, its chances of becoming a way of running algorithms that classical computers cannot handle: its susceptibility to noise.

Conventional electronic circuits face their own problems of how to deal with random changes to values in memory or circuits caused by cosmic rays and other interference. Codes that exploit just a few redundant data bits allow those random errors to be corrected on the fly.

The same core principle works for quantum computers, but with one key difference: the error correction must take account of the subtle changes in state that quantum circuits move through before the final, collapsed state is read out from each quantum bit (qubit). At that point, information that would signal an error is itself destroyed.

While attempts to show practical quantum error correction (QEC) working on actual hardware have come relatively recently, the concept is almost as old as the first algorithm. Less than a year after he presented his seminal algorithm for efficiently factoring large primes in 1995, Peter Shor, now professor of applied mathematics at the Massachusetts Institute of Technology, developed a code to catch and correct errors in qubits.

Shor showed it is possible to spread the information across multiple qubits and stabilizer qubits that are analogous to the parity bits used in digital error correction. Circuitry can analyze the symmetry properties of all the qubits in the code word without affecting the entanglement of the data qubits by just reading the stabilizer qubits.

Because they often rely on fragile properties such as electron orbitals or spin states, qubits are far more susceptible to unwanted changes than conventional electronic bits, which leads to poor performance in practical circuits. Production machines need the effective error rate per qubit to be less than one in a quadrillion; today, the error rate for physical qubits is one in 1,000 at best. Such high error rates call for as many as 30 additional qubits needed to protect just one physical qubit.

Even with high overheads, QEC as it exists today has limitations that increase the difficulty of making quantum computers reliable. Stabilizer codes cannot deal with errors that are generated by quantum-gate manipulations. That calls for additional flag bits that alert the control electronics to errors as they occur.

Stabilizer codes also do not work for all the operations needed for universal quantum computing. They can only work for gates in the Clifford group that apply a restricted set of phase and magnitude operations. Gates outside that group, such as the T-gate, need to be protected by other means.

There are proposals to encode qubits in a way that might make it possible to detect the subtle phase errors that afflict non-Clifford gates. Unfortunately, some recent experiments have questioned whether this encoding will support useful error detection in those gates.... ' 

On the Need for Quantum Error Correction

 The basics.

QUANTUM ERROR CORRECTION: TIME TO MAKE IT WORK

If technologists can’t perfect it, quantum computers will never be big   in Spectrum IEEE

ATES CHISELED INTO an ancient tombstone have more in common with the data in your phone or laptop than you may realize. They both involve conventional, classical information, carried by hardware that is relatively immune to errors. The situation inside a quantum computer is far different: The information itself has its own idiosyncratic properties, and compared with standard digital microelectronics, state-of-the-art quantum-computer hardware is more than a billion trillion times as likely to suffer a fault. This tremendous susceptibility to errors is the single biggest problem holding back quantum computing from realizing its great promise.

Fortunately, an approach known as quantum error correction (QEC) can remedy this problem, at least in principle. A mature body of theory built up over the past quarter century now provides a solid theoretical foundation, and experimentalists have demonstrated dozens of proof-of-principle examples of QEC. But these experiments still have not reached the level of quality and sophistication needed to reduce the overall error rate in a system.

The two of us, along with many other researchers involved in quantum computing, are trying to move definitively beyond these preliminary demos of QEC so that it can be employed to build useful, large-scale quantum computers. But before describing how we think such error correction can be made practical, we need to first review what makes a quantum computer tick.

Information is physical. This was the mantra of the distinguished IBM researcher Rolf Landauer. Abstract though it may seem, information always involves a physical representation, and the physics matters.  ... '

Advances in Quantum Error Correction

 Always heard that error correction is the key challenge of quantum computing,  here what appear to be advances by Google.   Implications, some suggested here.  For specific kinds of problems here.

Quantum Computing with Exponentially Fewer Errors By Arnout Jaspers, Commissioned by CACM Staff, August 19, 2021  

As long as a quantum computation is going on, one cannot actually check the values of the qubits, as that would destroy the complex quantum-state of the qubits, with the result being noise.

In an ideal world, a quantum computer with as few as 100 qubits would suffice to outperform all classical computers on certain classes of computation tasks. Google's Sycamore quantum processor, which has 53 qubits, is nowhere near accomplishing this.

The reason is that existing qubits, the computational building blocks of a quantum computer, are extremely sensitive to outside interference. Any magnetic or thermal disturbance will cause the qubit to change its internal state randomly; the classical analogy would be that all the bit values in the working memory of a microprocessor keep flipping from 0 to 1 and back, unpredictably.

As a result, quantum computing is still limited to computations taking no more than a few microseconds.

However, a team of Google researchers reported in Nature that they have successfully implemented quantum error correction on 21 qubits on the Sycamore chip, with huge potential for extending computation time.

Quantum error correction has been done before on smaller arrays of qubits, and on other types of qubit than the superconducting transmon qubits that Sycamore uses. 

"This is a strong answer to those sceptics who say a quantum computer will never work in real life," says computer scientist Koen Groenland of QuSoft, the Dutch research center for quantum software in Amsterdam, who was not involved in this research. In Groenland's view, the key achievement of the Google team was showing that the probability of errors decreased exponentially when using more qubits. That means even large qubit circuits can be made resilient to error by adding a modest number of extra qubits. Said Groenland, "That is a great perspective, because to keep a quantum computer working for hours, the error frequency must decrease from once per microseconds to a few per day, or even per week."  ... ' 

Quantum Error Correction

Brought back to my attention, with lots of links  to more detail,   From Google Research, Technical.

Demonstrating the Fundamentals of Quantum Error Correction

Wednesday, August 11, 2021

Posted by Jimmy Chen, Quantum Research Scientist and Matt McEwen, Student Researcher, Google Quantum AI

The Google Quantum AI team has been building quantum processors made of superconducting quantum bits (qubits) that have achieved the first beyond-classical computation, as well as the largest quantum chemical simulations to date. However, current generation quantum processors still have high operational error rates — in the range of 10-3 per operation, compared to the 10-12 believed to be necessary for a variety of useful algorithms. Bridging this tremendous gap in error rates will require more than just making better qubits — quantum computers of the future will have to use quantum error correction (QEC).

The core idea of QEC is to make a logical qubit by distributing its quantum state across many physical data qubits. When a physical error occurs, one can detect it by repeatedly checking certain properties of the qubits, allowing it to be corrected, preventing any error from occurring on the logical qubit state. While logical errors may still occur if a series of physical qubits experience an error together, this error rate should exponentially decrease with the addition of more physical qubits (more physical qubits need to be involved to cause a logical error). This exponential scaling behavior relies on physical qubit errors being sufficiently rare and independent. In particular, it’s important to suppress correlated errors, where one physical error simultaneously affects many qubits at once or persists over many cycles of error correction. Such correlated errors produce more complex patterns of error detections that are more difficult to correct and more easily cause logical errors.  ... " 

Error Correction in Quantum Computers

Semi technical look at the question.   If this works could be a major advance.

Google Demonstrates Vital Step towards Large-scale Quantum Computers  By New Scientist

Google has shown that its Sycamore quantum computer can detect and fix computational errors, an essential step for large-scale quantum computing, but its current system generates more errors than it solves.

Error-correction is a standard feature for ordinary, or classical, computers, which store data using bits with two possible states: 0 and 1. Transmitting data with extra "parity bits" that warn if a 0 has flipped to 1, or vice versa, means such errors can be found and fixed.

In quantum computing the problem is far more complex as each quantum bit, or qubit, exists in a mixed state of 0 and 1, and any attempt to measure them directly destroys the data. One longstanding theoretical solution to this has been to cluster many physical qubits into a single "logical qubit". Although such logical qubits have been created previously, they hadn't been used for error correction until now.  .... 

From New Scientist     View Full Article

NIST: Quantum Bits Can be Self Correcting?

Could be a really big thing,  depending on the context and consequences.  

Error-Prone Quantum Bits Could Correct Themselves, NIST Physicists Show

National Institute of Standards and Technology

Physicists at the U.S. National Institute of Standards and Technology (NIST), the University of Maryland, and the California Institute of Technology have developed an approach that could be used to design self-correcting quantum memory switches. The researchers experimented with a photonic cavity resonator and found that constantly refreshing the supply of photons in the cavity enables the qubit's quantum information to withstand certain amounts and types of noise from the surrounding environment. The new approach accounts for the leakage of photons to the environment. Simon Lieu of the Joint Quantum Institute and the Joint Center for Quantum Information and Computer Science said, "It’s like adding fresh water. Any time the information gets contaminated, the fact that you're pushing in water and cleaning out your pipes dynamically keeps it resistant to damage. This overall configuration is what keeps its steady state strong."

Improving Quantum Error Correction

The results in Quantum Computing are statistical, yet the results need to be precise.  How do we correct the results to precision?   A mostly non-technical discussion of the progress in CACM.

Closing In on Quantum Error Correction   By Don Monroe
Communications of the ACM, October 2019, Vol. 62 No. 10, Pages 11-13
10.1145/3355371

After decades of research, quantum computers are approaching the scale at which they could outperform their "classical" counterparts on some problems. They will be truly practical, however, only when they implement quantum error correction, which combines many physical quantum bits, or qubits, into a logical qubit that preserves its quantum information even when its constituents are disrupted. Although this task once seemed impossible, theorists have developed multiple techniques for doing so, including "surface codes" that could be implemented in an integrated-circuit-like planar geometry.

For ordinary binary data, errors can be corrected, for example, using the majority rule: A desired bit, whether 1 or 0, is first triplicated as 111 or 000. Later, even if one of the three bits has been corrupted, the other two "outvote" it and allow recovery of the original data. Unfortunately, the "no-cloning" theorem of quantum mechanics forbids the duplication (or triplication) of a qubit.

Moreover, the power of quantum computing emerges from having arbitrary mixtures of bit values. Since any combination is valid, it would seem impossible to detect a change from the original combination, let alone correct it.

"Most people who were doing quantum information in the '80s and '90s would say we'll never be able to do error correction in these systems, because it's analog error correction," explained Raymond Laflamme of the University of Waterloo and the Perimeter Institute, both in Waterloo, Ontario.

Fortunately, those experts Laflamme spoke of were mistaken.

Unlike a classical bit that has a value of either 0 or 1, a single qubit can encode a weighted "superposition" of both values. A set of N qubits can thus represent 2N different states simultaneously. There is strong mathematical evidence that devices handling qubits could solve some large problems much faster than traditional computers could, even in principle.

In the mid-1990s, mathematician Peter Shor, then at AT&T Bell Laboratories in Murray Hill, NJ, described a powerful example of using such a quantum algorithm to efficiently factor large numbers. Because public-key encryption relies on this task being impractically slow, the result helped transform quantum computing from a physics curiosity to a technology with potential national security implications.

Quantum computations exploit the fact that the ultimate weights assigned to different configurations of qubits are the sum of contributions that can be positive, negative, or even complex numbers. The algorithms combine qubits so that these contributions reinforce one another for the desired solution, but cancel each other out for the many incorrect configurations. A key step in Shor's algorithm, for example, is finding the repetition period of a sequence of numbers generated from the factoring target, essentially by performing a Fourier transform on the entire sequence that produces a peak at the correct periodicity.

The final step is measuring the qubits to see which are 1 and which are 0. The probability of a particular outcome is proportional the square of the corresponding weight. The measurement leaves each qubit unambiguously in the measured state.  .... "