Preskill NISQ Article - Student Summaries (Fall 2020) Quantum computing leverages quantum complexity to do calculations that are inaccessible with classical devices - Current quantum computing (QC) technology seeks to (a) capitalize on quantum complexity (arising from quantum correlations of highly entangled states) that could solve problems inaccessible classically, and (b) reduce quantum errors and at the same time make QC less sensitive to said errors (fault-tolerance) to enable large-scale systems that perform reliably. - Due to the intrinsic difference in how information is stored/processed in a QC, there are problems that are theorized to be difficult classically but easy with a QC. - Quantum computers are needed because of the inability of classical computers to efficiently simulate quantum systems. However, this also means that validation of results from quantum computers is hard. - The information content of a system of entangled qubits of moderate size cannot be represented classically - Quantum computing is expected to solve problems and simulate quantum mechanical systems that classical digital computers will likely never be able to handle. - Part of the current field of quantum computing rests on finding useful problems that are easy for quantum computers to solve but difficult for classical computers to solve. - He makes it a point to clarify that the extravagant complexity of the quantum world doesn’t automatically equate to utility in a classical world. But he gives a minimum of three reasons to insinuate quantum complexity will be useful: - Interesting that Laughlin and Pines said no computer now or in the future will ever break the barrier of solving equations describing many entangled particles. And this was after Feynman had popularized the idea that it would be possible. Feynman’s argument is only now appearing to finally be vindicated, possibly. - Quantum entanglement. This is one of the strongest characteristics in a quantum system. It gives us two principles, quantum complexity and quantum error correction to explore a new frontier. - The power of quantum computing. A quantum computer can efficiently simulate any process in Nature, because Nature is quantum - Quantum supremacy. This is an impending milestone for human civilization. No classical device can perform some tasks by quantum computers. Quantum computation presents new challenges due to the nature of quantum mechanics - Developing quantum computers is hard mainly because of the measurement problem: observing a system necessarily involves interacting with that system. As a consequence, measurement uncontrollably disturbs the quantum state of a system, and so we must reliably isolate a quantum system from the outside world. However, we need qubits to interact with each other strongly and we need to be able to control the system reliably form the outside. - The main barrier slowing down progress in quantum computing is the difficulty of designing and making a system that is isolated from the environment, allows qubits to strongly interact, and allows us to probe the internal state accurately - The fundamental tension between isolating a system of qubits from surrounding environment while allowing certain interaction with that system (to perform measurements, perform gate operations etc.) currently inhibits hardware improvements. Even small error rates pose catastrophic for certain classes of algorithms-including algorithms that have been given lots of press and financial investment. Until a sufficiently low error rate is reduced, reality of quantum computation remains a distant dream for certain classes of algorithms. - Difficulty of quantum computing. It’s a contradiction that we want to keep the system perfectly isolated from the outside and at the same time we want to control the system from the outside. Error correction and fault tolerance is vital to the future of Quantum Computing, but requires a large overhead - In order to make quantum states robust, a qubit should be encoded in a highly entangled system so that it will be robust against interaction with the environment - Quantum error correction will be necessary for large QC’s, but it requires significant overhead - Quantum error correction can fix the noise problems with current quantum computers but requires an infeasible overhead cost in physical qubits to do so. Need less noise. - Quantum error correction requires a significant number of extra qubits, forming a huge bottleneck to quantum computation. Because of this, improving fault-tolerance is one of the most important goals towards the development of quantum computers. - Quantum errors are the major challenge (qubits interacting with their environment). Protecting them with entanglement also comes with a large overhead There are exciting opportunities and applications for Quantum Computation - Quantum computation has potentially world-transforming possibilities through things like simulating truly quantum systems (i.e. Nature) - Quantum “supremacy”/”speed-up”: the paper lists several applications --- with varying likelihoods of near-future realization --- that would establish that QC surpasses classical computing in some, not all aspects. For example: Analog quantum simulation, Optimization algorithms, Prime factorization, Linear algebra, Quantum-enhanced deep learning, and possibly more - With the arrival of 50-100 bit quantum computers, a new era of “Noisy Intermediate-Scale Quantum” technology has begun. The goal of the article is to explore the potential of this era. - While Preskill envisions the specialized NISQ devices to have (compared to what is to come) limited functionality, they are anticipated to have functional uses as well. - There exist algorithms which have been found to solve problems easily on quantum computers which are known to be hard on classical computers. - Quantum algorithms exist that provide exponential speedups as compared with the best known classical algorithms; this provides motivation for industrial applications in addition to purely academic applications - One place we’re fairly confident they have an advantage over classical computers is simulating many body quantum systems - Quantum optimizers, though they may not be able to solve NP-hard problems with significant advantage over classical machines, do seem to have an advantage at finding approximate solutions to such problems. There are two classes of such problems: Quantum Approx. Optimization Algorithms (QAOA) which apply QC to classical combinatorial problems; and Variational Quantum Eigensolvers (VQE) which apply QC to quantum combinatorial problems. - He mentions a handful of potential applications: Matrix inversions for solving linear systems, recommendation systems, semidefinite programming, etc., details of which put me well beyond the quota for this report. - There are good reasons to believe the claim that quantum computers will one day be able to do useful computations that we cannot do classically - There are particular problems to which quantum computing is particularly advantageous when compared with classical computing. The NISQ era is an opportunity to enumerate such a list. - Quantum computing is powerful. We know it's effective on factoring algorithms, sampling and simulating the nature of physics. - 50 qubits is a significant milestone because it can simulate things better than most powerful existing digital supercomputers by brute force. But we’ll have imperfect control over qubits which places serious limitations. - Possible speadups using NISQ technology: The field of Quantum Information is rich with many areas of study - Quantum Information Processing is not limited to Quantum Computing but also includes cryptography, key distribution, networks, and sensing. - He says he won’t discuss much about quantum cryptography, networks, repeaters, randomness generation and expansion, or sensing, but he says these are critically intertwined with quantum computing in general. We need more experiments to test the usefulness of quantum computers - Near-term technologies or procedures like quantum annealing or the Variational Quantum Eigensolver provide test beds for the limits of our current quantum computing power. - As in the development of classical computing, there may be “heuristic” advantages to quantum computing which are theoretically hard to predict but experimentally evident. - NISQ technology may shed light on these advantages. - Even though current QC systems are limited, there are realizable applications worth pursuing that can motivate further exploration of Quantum technology (NISQ devices). - NISQ-era computers may or may not be able to do anything useful, but we don’t really know yet so more experiment is needed - He eventually admits that his conclusion early in the paper about NISQ-era QC being limited to ~100 gates might be overly pessimistic, as there are quantum simulation algorithms that don’t require much circuit depth; or where depth is required, errors might decay away on their own faster than they accumulate. - Experimental realizations of quantum algorithms on quantum computers will inevitably come before we have any reasonable grasp of the underlying theory, similar to the current example playing out in deep learning. - A quantum testbed might help us find ways to push the NISQ era to its limits – be it by finding experimental heuristics or by allowing us to accurately assess and probe the current state of the field - The current era of quantum computing (termed NISQ era) is not the era in which we