Quantum Computing. Melanie Swan

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СКАЧАТЬ systems. This includes patterns from interference (through amplitudes), superposition (through qubit spins, such as in quantum annealing), and entanglement (through Bell pairs and otherwise). These quantum signatures are unique and identifiable. This is not surprising, given that quantum statistics means studying how wave functions behave in a quantum mechanical system, in a statistical format (i.e. distribution-based). The key point is that only a quantum system could have produced such output, and thus it can be used as a source of provable randomness.

      As an indication of the unique signifiers of quantum phenomena, one relevant interpretation of quantum statistics is Porter–Thomas distribution. These are distributions in which the probabilities themselves are exponentially distributed random variables. The quantum statistics are known and have been developed elsewhere in physics to model quantum many-body systems. The practical application is that quantum statistical distributions can be set up to generate either predictable patterns or randomness. In particular, many applications require a guaranteed source of randomness. True randomness instills trust in believing that events have been fairly determined. Some of the immediate applications for randomness are cryptography (setting the parameters for a system that cannot be back-doored or otherwise breached), and blockchains more generally, both in cryptography and in facilitating the creation of next-generation consensus algorithms (PBFT) based on entropy. Other uses for randomness include running lotteries (picking numbers fairly) and auditing election results (selecting precincts to review at random).

      At present, most randomness is not guaranteed to be random, and a potential trend would be the widespread use of quantum computers to generate guaranteed randomness for use in various security applications.

4.2Interference

      In physics, wave interference is a phenomenon in which two waves in a system have either a reinforcing or canceling effect upon one another. There can be positive coherence if the two waves are in the same phase, reinforcing each other in a stronger way, as in the ocean when multiple big waves come into shore at once. Alternatively, there can be negative coherence if waves are in phases that counterpose or cancel each other out, such as when there is noise from the environment.

      Interference is used in building quantum circuits and calculating with vectors in quantum computing. A quantum circuit harnesses the qubit wave action with matrix multiplications (linear algebra). Each time a vector (corresponding to qubit position) is multiplied by a matrix (the computational movement through the quantum gate system), the matrix combines numbers in the vector, and the combination either reinforces the numbers or cancels them out. In this real physical sense, coherent wave behavior is calculated as a vector passing through quantum gates. This is an important factor that is competing against the fact that coherent wave behavior is the environmental noise of the system. The coherent action of the waves is fragile, and can be easily destroyed if the system has too much noise or other interference.

      This is a challenge in quantum computing because irrespective of the qubit-generation method (superconducting circuits, trapped ions, topological matter, etc.), there is always going to be noise in the system, and if the noise overwhelms the coherent wave activity, the quantum computer is not going to work. Hence, quantum error correction becomes important for mitigating the noise.

4.2.1 Interference and amplitude

      The wave behavior of qubits and interference is seen in modeling coherent wave action through quantum gates (protecting against noise in quantum circuit design), and also in another property of the quantum mechanical domain, amplitude. Whereas probabilities are assigned to the different possible states of the world in classical systems, amplitudes are the analog in quantum systems. Amplitudes are more complicated than probabilities, in that they can interfere destructively and cancel each other out, be complex numbers, and not sum to one. A quantum computer is a device that maintains a state that is a superposition of every configuration of qubits measured in amplitude. For practical computation, the amplitudes are converted into probabilities (probability is the squared absolute value of its amplitude). A key challenge is figuring out how to obtain a quantum speed advantage by exploiting amplitudes. This is not as straightforward as using the superposition property of qubits to model a greater number of possibilities, since simply measuring random configurations will not coalesce into problem-solving answers. Hence, quantum statistical models are implicated to exploit amplitudes such that certain patterns of interference are produced.

      To produce the kinds of interference patterns that might be directed into problem answers, one strategy is engaging the properties of wave coherence. In a quantum circuit, each of the amplitudes of the possible output states is the sum of exponentially many possible contributions. These contributions are complex numbers pointing in every direction in the complex plane, and the final amplitude is whatever residue is left over after the complex numbers have mostly collapsed and canceled each other out in the ending state. The idea is to incorporate this model of amplitudes into a quantum-solvable process.

      An analogy in the everyday world can be made with light. A beam from a laser pointer could be shone through a field of ground-up glass to see where the light ends up on a screen at the end of the field. This produces a speckling pattern, in that as the beam goes through the field, there are darker points where there is destructive interference, and lighter points where there is constructive interference. Running many samples firmly establishes the pattern of where the individual photon lands. The consistency of the speckle pattern can then be analyzed to see if the photon preferentially lands on the lighter points of the constructive interference or the darker points of the destructive interference.

      There are two possible ways the amplitude interference patterns can be used, to produce a reliably repeatable pattern or to produce a random pattern. The first idea is to generate a predictable pattern, which implies that this particular interference system can be used to encode a real-world problem, such that a useful answer can be interpreted. Conceptually, this is more or less how quantum annealing operates, although qubit spins, not interference, is the mechanism. The same principle is at work in encoding a real-world problem into a quantum-solvable process where the quantum system runs and provides an answer. The other possibility is that a predictable pattern is not the outcome, that the result is random, which is helpful in another way. Gaussian output is an indication of randomness, of a well-formed statistically sound mechanism for generating randomness. Overall, the implication of quantum statistics is that quantum randomness can be produced, even in NISQ devices.

4.3Noisy Intermediate-Scale Quantum Devices

      The long-term goal of quantum computing is to realize universal quantum computation on fault-tolerant quantum information processors. In the shorter term, the objective is to solve problems with NISQ devices, which are quantum processors that are not error-corrected. Quantum computing is developing in different steps based on available technical functionality. The first phase of quantum computing (2001–2012) consisted of several demonstrations of 1–2 qubits and up to 10-qubit systems using a variety of hardware approaches. The second phase of quantum computing is currently underway (2012–2019) and includes general-purpose 30–70 qubit systems with gate model superconducting circuits, and special-purpose 2048-qubit systems with quantum annealing machine superconducting circuits. The landmark discovery in 2012 of high-temperature superconductors helped to propel the development of general-purpose gate model logic in superconducting circuits, in which operations can be controlled. Superconducting circuits, whether based in standard gate models or quantum annealing machines, are the only hardware approaches that are commercially available as of June 2019.

      Existing quantum computers are NISQ devices, meaning imperfect, modestly sized quantum computing machines (Preskill, 2018). NISQ devices are an important advance over the few-qubit systems that largely served as a proof of concept. The challenge with NISQ devices is finding relevant problems that can be solved with only 50–100 qubits without error correction. In the longer-term, quantum computers are foreseen to have the most significant advantage over classical СКАЧАТЬ