Finally, Alice makes a “combined” measurement on the two qubits she holds. Such a measurement gives access to some combined (or global) information on both qubits, but none on a single qubit, i.e., no distinction between the two qubits can be established. Her measurement will lead the pair to collapse to one of the four possible states |0102〉, |0112〉, |1102〉, or |1112〉, while the third qubit, correspondingly, will immediately collapse to the state α|13〉 – β|03〉, α|03〉 – β|13〉, α|13〉 + β|03〉, or α|03〉 + β|13〉, respectively, since it is also entangled with qubits 1 and 2. Table 13.1 shows the measurement result Alice will get depending upon the instant the measurement actually occurred, along with the post-measurement state of qubit 3 held by Bob.
Alice communicates the classical result of her “combined” measurement (|0102〉, |0112〉, |1102〉, or |1112〉) to Bob (using classical means such as telephone, email, etc.). Bob then uses the decoder (a unitary transformation) listed in Table 13.1 corresponding to the state of qubits 1 & 2 conveyed to him by Alice to bring his qubit to state |Φ〉 = α|03〉 + β|13〉.
14 The future
Quantum mechanics works exceedingly well in all practical applications. No example of conflict between its predictions and experiment is known. Without quantum physics, we could not explain the behavior of the solids, the structure and function of DNA, the color of the stars, the action of lasers, or the properties of super-fluids. Yet nearly a century after its inception, the debate about the relation of quantum physics to the familiar physical world continues. Why is a theory that seems to account with precision for everything we can measure still deemed lacking?21
The dream is that one day we will produce quantum computers and prove their supremacy over classical computers by their super-classical behavior. Such computers may still require quantum error corrections to achieve scalable quantum computing. There are plenty of challenges to be overcome along the way, namely the difficulty of controlling quantum systems accurately. Even small errors caused by imperfect physical quantum gates will eventually corrupt computations. There is the problem of decoherence arising from unintended correlations with the environment. This is not a problem in classical computers but can be lethal for a quantum computer if quantum superposition is irreparably altered. This is where quantum error-correcting codes play a pivotal role. Compared to error correction codes for classical computers which need only protect against bit flips, such codes for quantum computers are much more difficult because they must, in addition, protect against phase errors.
But there are a few fundamental questions that physicists would also like to answer. Two such questions are: “(1) What quantum tasks are feasible? (2) What quantum tasks are hard to simulate classically?”22 Given that we do not yet have a bridge that spans across classical and quantum physics, what if ultimately Nature really admits succinct classical descriptions of quantum states? The fact is that we are reluctant to believe that such a bridge does not exist. But researchers will not wait. Once quantum computers become technologically mature, there will be no dearth of important applications for quantum computing. Waiting in the wings are simulation of highly entangled matter, e.g., quantum antiferromagnets, exotic superconductors, complex biomolecules, bulk nuclear matter, and space-time near singularities.23 There will be plenty of opportunities to discover new and unimagined natural phenomena. Surely, there are new algorithms waiting to be discovered other than those that do no more than quantum versions of classical ones.
14.1 Boosting AI applications
Quantum computing’s ability to boost AI applications are now under active investigation.24 For the future one indeed looks forward to the fusion of quantum computing and machine learning and what such a fusion may lead to. One expects some amazingly disruptive technologies to follow that may finally and convincingly show that it can outdo or at least tenaciously compete with the best of human minds in creativity and problem solving. In mere computing, computers handily outbeat all humans. Vast computing power and algorithm development has also ensured that in such things as chess and data-mining humans are easily overshadowed by classical computers. In matters such as face recognition, language translation, and medical diagnosis they are improving by the day that respective present day human experts are likely to become unemployed within a few years. Quantum computers can not only manipulate vast arrays of data in a single step (one of its principal advantages) but also spot subtle patterns that classical computers cannot because of a natural connection between the statistical nature of computing and machine learning, say, using neural networks which are designed to mimic human brains in pattern recognition.
24See, e.g., Musser (2018). “Neural networks and other machine-learning systems have become the most disruptive technology of the 21st century.”