Quantum computers are hypothetical devices, based on quantum physics, that would enable us to perform certain computations hundreds of orders of magnitude faster than digital computers. This feature is coined as "quantum supremacy" and one aspect or another of such quantum computational supremacy might be brought about in experiments in the near future: by implementing quantum error-correction, systems of non-interacting bosons, exotic new phases of matter called anyons, quantum annealing, or in various other ways. A main concern regarding the feasibility of quantum computers is that quantum systems are inherently noisy: we cannot accurately control them, and we cannot accurately describe them. We will describe an optimistic hypothesis of quantum noise that would allow quantum computing and a pessimistic hypothesis that wouldn't. The quantum computer puzzle is deciding between these two hypotheses. Here is a brief summary of the author's pessimistic point of view as explained in the paper: understanding quantum computers in the presence of noise requires consideration of behavior at different scales. In the small scale, standard models of noise from the mid-90s are suitable, and quantum evolutions and states described by them manifest a very low-level computational power. This small-scale behavior has far-reaching consequences for the behavior of noisy quantum systems at larger scales. On the one hand, it does not allow reaching the starting points for quantum fault tolerance and quantum supremacy, making them both impossible at all scales. On the other hand, it leads to novel implicit ways for modeling noise at larger scales and to various predictions on the behavior of noisy quantum systems.
Quantum computers are hypothetical devices, based on quantum physics, that would enable us to perform certain computations hundreds of orders of magnitude faster than digital computers. This feature is coined as "quantum supremacy" and one aspect or another of such quantum computational supremacy might be brought about in experiments in the near future: by implementing quantum error-correction, systems of non-interacting bosons, exotic new phases of matter called anyons, quantum annealing, or in various other ways. A main concern regarding the feasibility of quantum computers is that quantum systems are inherently noisy: we cannot accurately control them, and we cannot accurately describe them. We will describe an optimistic hypothesis of quantum noise that would allow quantum computing and a pessimistic hypothesis that wouldn't. The quantum computer puzzle is deciding between these two hypotheses. Here is a brief summary of the author's pessimistic point of view as explained in the paper: understanding quantum computers in the presence of noise requires consideration of behavior at different scales. In the small scale, standard models of noise from the mid-90s are suitable, and quantum evolutions and states described by them manifest a very low-level computational power. This small-scale behavior has far-reaching consequences for the behavior of noisy quantum systems at larger scales. On the one hand, it does not allow reaching the starting points for quantum fault tolerance and quantum supremacy, making them both impossible at all scales. On the other hand, it leads to novel implicit ways for modeling noise at larger scales and to various predictions on the behavior of noisy quantum systems.
Quantum computation is not an imminent achievement . We will not wake up tomorrow and find quantum computers on our desks. At the time of this writing, IBM has just unveiled the Condor – a chip containing 1,121 superconducting qubits. This number will likely increase (perhaps spectacularly) in the near future. However, the qubits have a relatively large error rate and, in the absence of a breakthrough advance that significantly lowers this rate, one would need hundreds of physical qubits to realize an error-corrected logical qubit. Predicting how long it will take to achieve the controlled manipulation of thousands of (logical) qubits (i.e., a number of qubits consistent with the “useful” implementation of known quantum algorithms) is probably not a rational undertaking, at least for a scientist. The most pessimistic experts regard the lively research activity in quantum computation as a waste of time and resources. But the pervading mood in this field is one of cautious optimism, particularly considering the possibility of achieving useful tasks (e.g., simulating quantum systems) with a sufficiently large number of “imperfect” qubits. Expediency may be responsible for some of this optimism; a good feeling about the prospects for quantum computation certainly helps when it comes to publishing papers and getting funded. Ultimately, however, the responsibility for the wise distribution of resources rests with the funding agencies; scientists, on the other hand, are called to explore every aspect of real and possible worlds that looks fascinating and worthy of their curiosity. From this perspective, quantum computation (defined broadly) offers plenty of opportunities for producing “good science.” The problems brought to the fore by the development of this field range from basic questions regarding the foundations of quantum mechanics and unsolved problems in computational complexity, to the investigation of new phases of matter (e.g., topological quantum phases), the quest for “complete” control over quantum systems, and the critical need for significant advances in materials science and device fabrication (e.g., engineering nanoscale heterostructures with atomic precision). Progress in these areas will naturally open new possibilities for interesting applications. Precisely identifying these applications is premature, but building a (general purpose) quantum computer will not necessarily be among the first of them.
One of the main drivers for growing the field of quantum computation has been the prospect of creating a quantum computer capable of carrying out Shor's algorithm for huge numbers.Nonetheless, it is critical to recognise that quantum computers will probably only significantly speed up a small subset of issues if one wants to acquire a more comprehensive perspective on them.Building a system that can accommodate a lot of qubits while preserving stability and coherence is one of the biggest problems in quantum computing.Due to their extreme sensitivity to noise and mistakes, quantum systems are particularly susceptible to computing errors.Building a usable quantum computer requires error mitigation and correction, but the techniques for doing this are still in the early phases of research.In quantum computing, all processes and schemes must be reversible in accordance with the law of unitary development.The circuit model is taken into account in the NISQ framework, but there is also the one-way or measurement-based quantum computation approach, which is not reversible but is demonstrated to be comparable to the circuit model.Noisy suggests that the computing capacity of such quantum computers is constrained because of sufficiently high error and decoherence rates.While they are likely too huge to be replicated by traditional computers using brute force, Intermediate-Scale suggests that they are still too small to be mistake corrected, which also adds to the preceding argument about how noisy they are.P stands for the usage of perfect qubits with perfect quantum gates and no decoherence.The capability to control and protect our qubits in a quantum computer to the degree necessary to run such algorithms is commonly described as fault-tolerant quantum computation.This review paper examines the numerous quantum computing strategies, such as Noisy Intermediate Scale Computing (NISQ) , Perfect Intermediate Scale Computing (PISQ), and Fault Tolerant Intermediate Scale Computing (FTISQ), as well as potential future lines of inquiry.
We give a computational complexity argument against the feasibility of quantum computers. We identify a very low complexity class of probability distributions described by noisy intermediate-scale quantum computers, and explain why it will allow neither good-quality quantum error-correction nor a demonstration of "quantum supremacy." Some general principles governing the behavior of noisy quantum systems are derived. Our work supports the "physical Church thesis" studied by Pitowsky (1990) and follows his vision of using abstract ideas about computation to study the performance of actual physical computers.
In the current Noisy Intermediate-Scale Quantum era, noise is widely regarded as the primary obstacle to achieving fault-tolerant quantum computation. However, certain stages of the quantum computing pipeline can, in fact, benefit from this noise. In this work, we exploit the Eigenstate Thermalization Hypothesis to show that noise generically accelerates a fundamental task in quantum computing -- the preparation of Gibbs states. We demonstrate this behavior using classical and quantum simulations with Haar-random and phase-flip noise, respectively, on a spin-1/2 chain with a local Hamiltonian. Our non-integrable model sees ~3.5x faster thermalization in the presence of noise, while our integrable model, which would not otherwise thermalize, reaches a thermal state due to noise. Since certifying a local Gibbs state is relatively easy on a quantum computer, our approach provides a new practical solution to a key problem in quantum computing. More broadly, these results establish a new paradigm in which noise can be harnessed on quantum computers, enabling practical advantages before the years of fault-tolerance.
Over the last three decades computers have become exceptionally compact and faster. Now that we have reached the fifth generation of computers which include concepts of artificial intelligence, what’s next? There is a lot of fuss about quantum computers being a strong contender for the next generation of computing. Recently we heard stories about small scale quantum computers being built by technology giants like IBM and Google and also an instance of quantum supremacy.
One of the key features of quantum computing is its core concept, leveraging the principles of quantum mechanics, which we have avoided with our classic computers. Quantum computers are the first ones to deviate from the basic concept of bits. To understand this difference in the fundamental concepts, we start with basic building blocks in conventional computers, bits and draw contrasts with those in quantum computers. Further explore how rudimentary operations are performed in both machines by comparing addition operations of 2 and 3 bits. Followed by a brief detail on current research on quantum computers and claims on their supremacy over current machines. Then we elaborate on the world of new possibilities and unsolvable problems quantum computers have the ability to tackle.
This paper aims at giving a gist of quantum computing to beginners, starting with fundamentals to current research by identifying stark contrasts with conventional machines. It also explores the need of new computation powers and why we have reached almost the tail end of processing power of classical computers.
It was Richard Feynman who first proposed, in 1982, the far-reaching concept of \na ”quantum computer”—a device more powerful than classical computers. The idea \nof a quantum computer is to employ the fascinating and often counterintuitive \nlaws of quantum mechanics to process information. It is far from obvious that \nthe proposed concept of a quantum computer is more powerful than its classical \ncounterpart, it was only in 1994 when Peter Shor theoretically demonstrated the \nexistence of a quantum algorithm for factorizing integers into prime factors \nthat runs in polynomial time unlike its classical counterpart which works in \nsub-exponential time. The factorization of integers into prime factors is the \nbasis of asymmetric cryptography. These early theoretical results lunched an \nimmense interest of the scientific community. Already during ’90s, the first \nproposals for the physical implementation of quantum computation emerged. Ever \nsince, many experimental groups around the world pursued different physical \nimplementations of quantum bits (qubits). The first decade of the new century \nsaw a steady improvement in the control and decoherence time (the time over \nwhich the information carried by the qubit is lost) for various qubits by many \norders of magnitude. The natural next step in this context is to answer the \nquestion of how to scale the system up to include many qubits and thus build a \nquantum computer? One of the main parts of this thesis addresses exactly this \nquestion, namely the question of architecture and scalability of future quantum \ncomputer. \n \nAmong various different physical realizations of qubits, the idea of using \nelectron spins trapped in electrostatic semiconductor quantum dots as the \nbuilding blocks of a quantum computer (the so-called spin qubits), put forward \nby Daniel Loss and David DiVincenzo in 1997, triggered tremendous interest in \nscientific community. Nevertheless, the implementation of the original \nLoss-DiVincenzo proposal posed a considerable technical challenge. It used \nquantum tunneling between qubits to enable their communication with each other, \nand thus required that the qubits to be placed very close to each other. This \nrequirement not only leaves little \nspace for the placement of the vast amount of gates and wirings needed to define \nthe electrostatic quantum dots, but also makes it challenging to control the \nlocal magnetic field needed for single-qubit operations. For these reasons, no \nsystem with more than a couple of spin qubits has been \nsuccessfully implemented thus far. In the first part of this thesis, we leap \nover this long-standing problem with an entirely different strategy of using \nmetallic floating gates or ferromagnets to couple together qubits that are \nseparated over a long distance. Our scheme works for any type of \nspin qubits, including the qubits based on nitrogen-vacancy center (NV-center) \nin diamond and technologically very important silicon qubits. \n \nThe main topic of this thesis is related to quantum computer. Still, quite \nunexpectedly, some of the ideas we employed in order to tackle the problem of \nquantum computer scalability can be utilized in a completely different field of \nresearch, namely, in the field of magnetic field sensing. Qubit are not only a \nnecessary ingredient of quantum computer but they also provide a way to measure \nvery accurately magnetic fields. The magnetometer build upon the qubit based on \nNV-center, so-called NV-magnetometer, emerged in recent years as most sensitive \nmagnetic moment sensor. These magnetometers are able to detect about hundred \nnuclear spins within a minute of acquisition time. In the second part of this \nthesis, we propose an entirely novel experimental realization of \nNV-magnetometers which increases present NV-center sensitivities by four orders \nof magnitude at room temperature. This unprecedented amplification of \nsensitivity will render magnetometers capable of detecting individual nuclear \nspins. This amplification is achieved by introducing a ferromagnetic particle \nbetween the nuclear spin that needs to be detected and the NV-magnetometer. Our \nsetup, in contrast to existing schemes, is particularly advantageous because, \ndue to the large amplification of sensitivity, the nuclear spin need not lie \nwithin a few nanometers of the surface but rather can be detectable at a \ndistance of 30 nm. With these novelties, our scheme provides chemically \nsensitive spin detection under ambient conditions allowing nanoscale resolution \nof nuclear magnetic moments in biological systems—the holy grail of nuclear \nmagneticresonance. \n \nIn the last part of the thesis we focus our attention to a new direction in \nquantum computer implementation that deals with topological quantum computer \nintroduced by Alexei Kitaev in 1997; in this approach the idea is to use \nquasiparticles with ”fractional” statistics and to perform the single- and \ntwo-qubit gates by merely exchanging these quasiparticles. Additionally, \ninformation in this system is stored non-locally thus it mitigates the problem \nof decoherence caused by local noise from the environment. Majorana fermions are \none of the most well known examples of such excitations. We analyze transport \nsignatures of different topological states in one-dimensional systems, like \nMajorana fermions and fractionally charged states. We envision an Aharonov-Bohm \nsetup wherein conductance measurement provides a clear signature of presence of \nfractionally charged fermionic states, since oscillations with double period \nemerge in this case. Additionally, we propose a very simple setup that enables \nexistence of degenerate mid-gap states, so-called Tamm-Shockley states that are \ncharacterized by fractional charge and discuss possible ways of detecting these \nstates experimentally. \n