Construction of a universal quantum computer

Theoretical Computer Science, 2008

Manin, Feynman, and Deutsch have viewed quantum computing as a kind of universal physical simulation procedure. Much of the writing about quantum logic circuits and quantum Turing machines has shown how these machines can simulate an arbitrary unitary transformation on a finite number of qubits. The problem of universality has been addressed most famously in a paper by Deutsch, and later by Bernstein and Vazirani as well as Kitaev and Solovay. The quantum logic circuit model, developed by Feynman and Deutsch, has been more prominent in the research literature than Deutsch's quantum Turing machines. Quantum Turing machines form a class closely related to deterministic and probabilistic Turing machines and one might hope to find a universal machine in this class. A universal machine is the basis of a notion of programmability. The extent to which universality has in fact been established by the pioneers in the field is examined and this key notion in theoretical computer science is scrutinised in quantum computing by distinguishing various connotations and concomitant results and problems.

2019

The primordial model of quantum computation was introduced over thirty years ago and the first quantum algorithms have appeared for over twenty years. Yet the exact architectures for quantum computer seem foreign to an undergraduate student major in computer science or engineering, even though the mass media has helped popularize the terminologies in the past decade. Despite being a cutting-edge technology from both the theoretical and the experimental perspectives, quantum computation is indeed imminent and it would be helpful to give the undergraduate students at least a skeleton understanding of what a quantum computer stands for. Since instruction-set architectures originated from classical computing models are familiar, we propose analogously a set of quantum instructions, which can be composed to implement renowned quantum algorithms. Albeit the similarity one can draw between classical and quantum computer architectures, current quantum instructions are fundamentally incommensurable from their classical counterparts because they lack the innate capability to implement logical deductions and recursions. We discuss this trait in length and illustrate why it is held responsible that current quantum computers not be considered general computers.

Reports on Progress in Physics, 1998

The subject of quantum computing brings together ideas from classical information theory, computer science, and quantum physics. This review aims to summarise not just quantum computing, but the whole subject of quantum information theory. Information can be identified as the most general thing which must propagate from a cause to an effect. It therefore has a fundamentally important role in the science of physics. However, the mathematical treatment of information, especially information processing, is quite recent, dating from the mid-twentieth century. This has meant that the full significance of information as a basic concept in physics is only now being discovered. This is especially true in quantum mechanics. The theory of quantum information and computing puts this significance on a firm footing, and has lead to some profound and exciting new insights into the natural world. Among these are the use of quantum states to permit the secure transmission of classical information (quantum cryptography), the use of quantum entanglement to permit reliable transmission of quantum states (teleportation), the possibility of preserving quantum coherence in the presence of irreversible noise processes (quantum error correction), and the use of controlled quantum evolution for efficient computation (quantum computation). The common theme of all these insights is the use of quantum entanglement as a computational resource.

Citeseer

Probing the Structure of Quantum Mechanics - Nonlinearity, Nonlocality, Computation and Axiomatics, 2002

Using the 'between quantum and classical' models that have been constructed explicitly within the hidden measurement approach of quantum mechanics we investigate the possibility to construct a 'between quantum and classical' computer. In this view, the pure quantum computer and the classical Turing machine can be seen as two special cases of our general computer. We have shown in earlier research that the intermediate 'between quantum and classical' systems cannot be described within standard quantum theory. We argue that the general categoral approach of state property systems might provide a unified framework for the study of these 'between quantum and classical' models, and hence also for the study of classical and quantum computers as special cases.

Today's computers work on bits that exist as either 0 or 1. Quantum computers aren't limited to two states; they encode information as quantum bits, or qubits, which can exist in superposition. Qubits represent atoms, ions, photons or electrons and their respective control devices that are working together to act as computer memory and a processor. Because a quantum computer can contain these multiple states simultaneously, it has the potential to be millions of times more powerful than today's most powerful supercomputers. A processor that can use registers of qubits will be able to perform calculations using all the possible values of the input registers simultaneously. This superposition causes a phenomenon called quantum parallelism, and is the motivating force behind the research being carried out in quantum computing. www.giapjournals.com/ijsrtm/ 628 computer could efficiently solve this problem using Shor's algorithm to find its factors. This ability would allow a quantum computer to decrypt many of the cryptographic systems in use today. In particular, most of the popular public key ciphers are based on the difficulty of factoring integers. These are used to protect secure Web pages, encrypted email, and many other types of data. Breaking these would have significant ramifications for electronic privacy and security. An example of this is a password cracker that attempts to guess the password for an encrypted file (assuming that the password has a maximum possible length).

Electronic Notes in Theoretical Computer Science, 2006

It is reasonable to assume that quantum computations take place under the control of the classical world. For modelling this standard situation, we introduce a Classically-controlled Quantum Turing Machine (CQTM) which is a Turing machine with a quantum tape for acting on quantum data, and a classical transition function for a formalized classical control. In a CQTM, unitary transformations and quantum measurements are allowed. We show that any classical Turing machine is simulated by a CQTM without loss of efficiency. Furthermore, we show that any k-tape CQTM is simulated by a 2-tape CQTM with a quadratic loss of efficiency. In order to compare CQTMs to existing existing models of quantum computation, we prove that any uniform family of quantum circuits (A. C. Yao 1993) is efficiently approximated by a CQTM. Moreover we prove that any semi-uniform family of quantum circuits (H. Nishimura and M. Ozawa 2002), and any measurement calculus pattern (V. Danos, E. Kashefi, P. Panangaden 2004) are efficiently simulated by a CQTM. Finally, we introduce a Measurement-based Quantum Turing Machine (MQTM) which is a restriction of CQTMs where only projective measurements are allowed. We prove that any CQTM is efficiently simulated by a MQTM. In order to appreciate the similarity between programming classical Turing machines and programming CQTMs, some examples of CQTMs are given.

Microelectronics (MIEL), 2012 28th …, 2012

Quantum computing is a process that incorporates interacting physical systems that represent quantum bits and quantum gates. We present the quantum bit (qubit), the quantum register and the quantum gates. The qubit is described as a vector in a two-dimensional Hilbert space and the quantum register, which comprises a number of qubits, as a vector in a multidimensional Hilbert space. Quantum gates are Hilbert space operators that rotate the qubit or the quantum register vectors. Quantum computations are modeled and described using a quantum circuit model. We also present a quantum computer simulator based on the circuit model of quantum computation. In this model quantum computations and quantum algorithms are represented by circuits, which comprise quantum gates and quantum registers. The well-known Deutsch's algorithm is described and the corresponding quantum circuit is presented. Possible applications of quantum computers are be presented and discussed.

2001

We revisit the question of universality in quantum computing and propose a new paradigm. Instead of forcing a physical system to enact a predetermined set of universal gates (e.g., singlequbit operations and CNOT), we focus on the intrinsic ability of a system to act as a universal quantum computer using only its naturally available interactions. A key element of this approach is the realization that the fungible nature of quantum information allows for universal manipulations using quantum information encoded in a subspace of the full system Hilbert space, as an alternative to using physical qubits directly. Starting with the interactions intrinsic to the physical system, we show how to determine the possible universality resulting from these interactions over an encoded subspace. We outline a general Lie-algebraic framework that can be used to find the encoding for universality, and give examples relevant to solid-state quantum computing.

Progress in Quantum Electronics, 1998

Quantum computers require quantum logic, something fundamentally different to classical Boolean logic. This difference leads to a greater efficiency of quantum computation over its classical counter-part. In this review we explain the basic principles of quantum computation, including the construction of basic gates, and networks. We illustrate the power of quantum algorithms using the simple problem of Deutsch, and explain, again in very simple terms, the well known algorithm of Shor for factorisation of large numbers into primes. We then describe physical implementations of quantum computers, focusing on one in particular, the linear ion-trap realization. We explain that the main obstacle to building an actual quantum computer is the problem of decoherence, which we show may be circumvented using the methods of quantum error correction.