Here's everything you need to know about the coming quantum revolution. Quantum computing takes advantage of the strange ability of subatomic particles to exist in more than one state at any time. Due to the way the tiniest of particles behave, operations can be done much more quickly and use less energy than classical computers. In classical computing, a bit is a single piece of information that can exist in two states — 1 or 0. Quantum computing uses quantum bits, or 'qubits' instead.

These are quantum systems with two states. However, unlike a usual bit, they can store much more information than just 1 or 0, because they can exist in any superposition of these values.

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A qubit can be thought of like an imaginary sphere. Whereas a classical bit can be in two states — at either of the two poles of the sphere — a qubit can be any point on the sphere. This means a computer using these bits can store a huge amount more information using less energy than a classical computer. Until recently, it seemed like Google was leading the pack when it came to creating a quantum computer that could surpass the abilities of conventional computers.

In a Nature article published in March , the search giant set out ambitious plans to commercialise quantum technology in the next five years.

## Quantum Computation - Scholarpedia

Even that, however, was far from stable, as the system could only hold its quantum microstate for 90 microseconds, a record, but far from the times needed to make quantum computing practically viable. Where IBM has gone further than Google, however, is making quantum computers commercially available. Since , it has offered researchers the chance to run experiments on a five-qubit quantum computer via the cloud and at the end of started making its qubit system available online too.

But quantum computing is by no means a two-horse race. Californian startup Rigetti is focusing on the stability of its own systems rather than just the number of qubits and it could be the first to build a quantum computer that people can actually use. Intel, too, has skin in the game. It is almost certain that one of the reasons for this scarcity of quantum algorithms is related to the lack of our understanding of what makes a quantum computer quantum see also Preskill and Shor Quantum computers, unfortunately, do not seem to allow such simple characterization.

The non-commutativity in quantum computing lies much deeper, and it is still unclear how to cash it into useful currency. Quantum computing skeptics Levin happily capitalize on this puzzle: If no one knows why quantum computers are superior to classical ones, how can we be sure that they are , indeed, superior?

One well-known answer to the question, popularized by Deutsch , takes its motivation from the circumstance that in some quantum circuit model algorithms, there are steps in which it appears as though functions are evaluated for each of their possible input values simultaneously. Something like the following transformation, for instance, is typical note that normalization factors have been omitted :.

The idea that we should take this at face value—that quantum computers actually do compute a function for many different input values simultaneously—is what Duwell calls the Quantum Parallelism Thesis QPT. For Deutsch, who accepts it as true, the only reasonable explanation for the QPT is that the many worlds interpretation MWI of quantum mechanics is also true. For Deutsch, a quantum computer in superposition, like any other quantum system, exists in some sense in many classical universes simultaneously.

These provide the physical arena within which the computer effects its parallel computations.

This conclusion is also endorsed by Hewitt-Horsman and by Wallace For Steane , in contrast, quantum computers are not well described in terms of many worlds or even quantum parallelism. Among other things, Steane argues that the motivation for the QPT is at least partly due to misleading aspects of the standard quantum formalism, for some classical systems can be similarly described so as to suggest parallelism. Further, the Gottesman-Knill theorem Nielsen and Chuang, shows that many algorithms, which suggest parallelism when written in standard notation, can be re-expressed in an alternative notation so as to lend themselves straightforwardly to an efficient classical simulation.

Additionally, comparing the information actually produced by quantum and classical algorithms state collapse entails that only one evaluation instance in 1 is ever accessible, while a classical computer must actually produce every instance suggests that quantum algorithms perform not more but fewer, cleverer, computations than classical algorithms see, also, 4. Phase relations, however, are global properties of a state. Thus a quantum computation, Duwell argues, does not consist solely of local parallel computations. Defending the MWI, Hewitt-Horsman argues contra Steane that to state that quantum computers do not actually generate each of the evaluation instances represented in 1 is false according to the view: on the MWI such information could be extracted in principle given sufficiently advanced technology.

Further, Hewitt-Horsman emphasizes that the MWI is not motivated simply by a suggestive mathematical representation. Wallace argues similarly.

The latter employs decoherence as a criterion for distinguishing macroscopic worlds from one another. Quantum circuit model algorithms, however, utilize coherent superpositions. To distinguish computational worlds, therefore, one must weaken the decoherence criterion, but Cuffaro argues that this move is ad hoc. Further, Cuffaro argues that the MWQC is for all practical purposes incompatible with measurement based computation , for even granting a weakened world identification criterion, there is no natural way in this model to identify worlds that are stable and independent in the way required.

Consider a solution of a decision problem, say satisfiability , with a quantum algorithm based on the circuit model. What we are given here as input is a proposition in the propositional calculus and we have to decide whether it has a satisfying truth assignment. The quantum adiabatic algorithm may give us similar results, contingent upon the existence of an energy gap that decreases polynomially with the input.

This question also raises important issues about how to measure the complexity of a given quantum algorithm. The answer differs, of course, according to the particular model at hand. In the adiabatic model, for example, one needs only to estimate the energy gap behavior and its relation to the input size encoded in the number of degrees of freedom of the Hamiltonian of the system. In the measurement-based model, one counts the number of measurements needed to reveal the solution that is hidden in the input cluster state since the preparation of the cluster state is a polynomial process, it does not add to the complexity of the computation.

But in the circuit model things are not as straightforward. After all, the whole of the quantum-circuit-based computation can be be simply represented as a single unitary transformation from the input state to the output state. This feature of the quantum circuit model supports the conjecture that the power of quantum computers, if any, lies not in quantum dynamics i. But this Hilbert subspace is thus a subspace spanned by a polynomial number of vectors and is thus at most a polynomial subspace of the total Hilbert space.

A classical simulation of the quantum evolution on a Hilbert space with polynomial number of dimensions that is, a Hilbert space spanned by a number of basis vectors which is polynomial in the number of qubits involved in the computation , however, can be carried out in a polynomial number of classical computations.

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## Fundamentals Of Quantum Computing

Were quantum dynamics the sole ingredient responsible to the efficiency of quantum computing, the latter could be mimicked in a polynomial number of steps with a classical computer see, e. This is not to say that quantum computation is no more powerful than classical computation. All these steps count as computational steps as far as the efficiency of the algorithm is concerned.

See also Bub a.

## What are quantum computers and how do they work? WIRED explains

The trick is to perform these local one- or two-qubit transformations in polynomial time, and it is likely that it is here where the physical power of quantum computing may be found. The quantum information revolution has prompted several physicists and philosophers to claim that new insights can be gained from the rising new science into conceptual problems in the foundations of quantum mechanics Fuchs , Bub Yet while one of the most famous foundational problems in quantum mechanics, namely the quantum measurement problem , remains unsolved even within quantum information theory see Hagar and Hagar and Hemmo for a critique of the quantum information theoretic approach to the foundations of quantum mechanics and the role of the quantum measurement problem in this context , some quantum information theorists dismiss it as a philosophical quibble Fuchs The measurement problem itself, furthermore, is regarded as a misunderstanding of quantum theory.

But recent advances in the realization of a large scale quantum computer may eventually prove quantum information theorists wrong: Rather than supporting the dismissal of the quantum measurement problem, these advances may surprisingly lead to its empirical solution. The speculative idea is the following. These circumstances may be realized, moreover, if decoherence effects could be suppressed Bassi et al. Now one of the most difficult obstacles that await the construction of a large scale quantum computer is its robustness against decoherence effects Unruh Another philosophical implication of the realization of a large scale quantum computer regards the long-standing debate in the philosophy of mind on the autonomy of computational theories of the mind Fodor In the shift from strong to weak artificial intelligence, the advocates of this view tried to impose constraints on computer programs before they could qualify as theories of cognitive science Pylyshyn These constraints include, for example, the nature of physical realizations of symbols and the relations between abstract symbolic computations and the physical causal processes that execute them.

The search for the computational feature of these theories, i. In other words, the advocates of weak AI were looking for computational properties, or kinds, that would be machine independent , at least in the sense that they would not be associated with the physical constitution of the computer, nor with the specific machine model that was being used. These features were thought to be instrumental in debates within cognitive science, e. Note, however, that once the physical Church-Turing thesis is violated, some computational notions cease to be autonomous. Advances in quantum computing may thus militate against the functionalist view about the unphysical character of the types and properties that are used in computer science.

In fact, these types and categories may become physical as a result of this natural development in physics e. Consequently, efficient quantum algorithms may also serve as counterexamples to a-priori arguments against reductionism Pitowsky A Brief History of the Field 1. Basics 2. Quantum Algorithms 3. Philosophical Implications 4. Basics In this section we will review the basic paradigm for quantum algorithms, namely the quantum circuit model, which is composed of the basic quantum units of information qubits and the basic logical manipulations thereof quantum gates.

### What quantum computing would accomplish

Bibliography Aaronson, S. Jack Copeland, Carl J. Posy, Oron Shagrir eds.