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Today we welcome a special guest Professor Winfried Hensinger, the head of the Quantum Technologies research group at the University of Sussex. In this episode Aleks and Marcin ask Winfred what is quantum computing and how is this different to traditional computing? What different types of quantum computing technologies are available? And what problems can quantum computing solve?

Johan Vos joined us to talk about his new book 'Quantum Computing for Developers' which is available to read right now as part of the Manning Early Access Program (MEAP). Listen near the end of the show to learn how you can get a free copy or check the show notes for details. We talked with Johan about the core principles of Quantum Computing, the hardware and software involved, the differences between quantum computing and classical computing, a little bit of physics, and what can we developers do today to prepare for the perhaps-not-so-distant future of Quantum Computing.

Johan Vos joined us to talk about his new book 'Quantum Computing for Developers' which is available to read right now as part of the Manning Early Access Program (MEAP). Listen near the end of the show to learn how you can get a free copy or check the show notes for details. We talked with Johan about the core principles of Quantum Computing, the hardware and software involved, the differences between quantum computing and classical computing, a little bit of physics, and what can we developers do today to prepare for the perhaps-not-so-distant future of Quantum Computing.

The world of technology is on the brink of a revolutionary transformation , poised to redefine the limits of what’s possible in computing and information processing. At the forefront of this transformation is quantum computing, a field that has the potential to reshape industries, solve complex problems, and drive innovation to unprecedented heights. From quantum algorithms and cryptography to quantum communication and beyond, the impact of quantum computing is set to be most significant in several key areas.

Instantaneous quantum computing is a sub-universal quantum complexity class, whose circuits have proven to be hard to simulate classically in the Discrete-Variable (DV) realm. We extend this proof to the Continuous-Variable (CV) domain by using squeezed states and homodyne detection, and by exploring the properties of post-selected circuits. In order to treat post-selection in CVs we consider finitely-resolved homodyne detectors, corresponding to a realistic scheme based on discrete probability distributions of the measurement outcomes. The unavoidable errors stemming from the use of finitely squeezed states are suppressed through a qubit-into-oscillator GKP encoding of quantum information, which was previously shown to enable fault-tolerant CV quantum computation. Finally, we show that, in order to render post-selected computational classes in CVs meaningful, a logarithmic scaling of the squeezing parameter with the circuit size is necessary, translating into a polynomial scaling of the input energy.

In this thesis we examine a variety of techniques for reducing the resources required for fault-tolerant quantum computation. First, we show how to simplify universal encoded computation by using only transversal gates and standard error correction procedures, circumventing existing no-go theorems. We then show how to simplify ancilla preparation, reducing the cost of error correction by more than a factor of four. Using this optimized ancilla preparation, we develop improved techniques for proving rigorous lower bounds on the noise threshold. Additional overhead can be incurred because quantum algorithms must be translated into sequences of gates that are actually available in the quantum computer. In particular, arbitrary single-qubit rotations must be decomposed into a discrete set of fault-tolerant gates. We find that by using a special class of non-deterministic circuits, the cost of decomposition can be reduced by as much as a factor of four over state-of-the-art techniques, which typically use deterministic circuits. Finally, we examine global optimization of fault-tolerant quantum circuits under physical connectivity constraints. We adapt techniques from VLSI in order to minimize time and space usage for computations in the surface code, and we develop a software prototype to demonstrate the potential savings.

We develop a scheme for time-frequency encoded continuous-variable cluster-state quantum computing using quantum memories. In particular, we propose a method to produce, manipulate and measure 2D cluster states in a single spatial mode by exploiting the intrinsic time-frequency selectivity of Raman quantum memories. Time-frequency encoding enables the scheme to be extremely compact, requiring a number of memories that is a linear function of only the number of different frequencies in which the computational state is encoded, independent of its temporal duration. We therefore show that quantum memories can be a powerful component for scalable photonic quantum information processing architectures.

Quantum information science and technology is a rapidly growing interdisciplinary field drawing researchers from science and engineering fields. Traditional instruction in quantum mechanics is insufficient to prepare students for research in quantum computing because there is a lack of emphasis in the current curriculum on quantum formalism and dynamics. We are investigating the difficulties students have with quantum mechanics and are developing and evaluating quantum interactive learning tutorials (QuILTs) to reduce the difficulties. Our investigation includes interviews with individual students and the development and administration of free-response and multiple-choice tests. We discuss the implications of our research and development project on helping students learn quantum mechanics relevant for quantum computing.

Richard Feynman first proposed the idea of quantum computers thirty years ago. Since then, efforts have been undertaken to realize large-scale, fault-tolerant quantum computers that can factor large numbers much more quickly than classical computers, which would have significant implications for computer security. While there is no universally agreed upon technology for experimentally realizing quantum computers, many researchers look to ion traps as a promising technology. This thesis focuses on ion traps, how they fulfill the Divincenzo criteria, what obstacles must be overcome, and recent achievements in this field. We examine the physical principles of a linear Paul trap, including the confining potential and its quantum dynamics. In addition, we built a mechanical analogue of an ion trap for pedagogical purposes, and we provide an analysis of its trapping potential and compare it to a real ion trap, the Paul trap. Furthermore, we provide guidance for building a course module on ion trap based quantum computing; our guidance is based on course materials from several institutions.

Speaker: Umesh Vazirani Date: August, 2002

Unconventional superconductors exhibit an order parameter symmetry lower than the symmetry of the underlying crystal lattice. Recent phase sensitive experiments on YBCO single crystals have established the d-wave nature of the cuprate materials, thus identifying unambiguously the first unconventional superconductor. The sign change in the order parameter can be exploited to construct a new type of s-wave - d-wave - s-wave Josephson junction exhibiting a degenerate ground state and a double-periodic current-phase characteristic. Here we discuss how to make use of these special junction characteristics in the construction of a quantum computer. Combining such junctions together with a usual s-wave link into a SQUID loop we obtain what we call a `quiet' qubit --- a solid state implementation of a quantum bit which remains optimally isolated from its environment.

Holonomic Quantum Computation (HQC) is an all-geometrical approach to quantum information processing. In the HQC strategy information is encoded in degenerate eigen-spaces of a parametric family of Hamiltonians. The computational network of unitary quantum gates is realized by driving adiabatically the Hamiltonian parameters along loops in a control manifold. By properly designing such loops the non-trivial curvature of the underlying bundle geometry gives rise to unitary transformations i.e., holonomies that implement the desired unitary transformations. Conditions necessary for universal QC are stated in terms of the curvature associated to the non-abelian gauge potential (connection) over the control manifold. In view of their geometrical nature the holonomic gates are robust against several kind of perturbations and imperfections. This fact along with the adiabatic fashion in which gates are performed makes in principle HQC an appealing way towards universal fault-tolerant QC.

GE Global Research has enhanced a previously developed general-purpose quantum computer simulator, improving its efficiency and increasing its functionality. Matrix multiplication operations in the simulator were optimized by taking advantage of the particular structure of the matrices, significantly reducing the number of operations and memory overhead. The remaining operations were then distributed over a cluster, allowing feasible compute times for large quantum systems. The simulator was augmented to evaluate a step-by-step comparison of a quantum algorithm's ideal execution to its real-world performance, including errors. To facilitate the study of error propagation in a quantum system, the simulator s graphical user interface was enhanced to visualize the differences at each step in the algorithm s execution. To verify the simulator s accuracy, three ion trap-based experiments were simulated. The simulator output closely matches experimentalist s results, indicating that the simulator can accurately model such devices. Finally, alternative hardware platforms were researched to further improve the simulator performance. An FPGA-based accelerator was designed and simulated, resulting in substantial performance improvements over the original simulator. Together, this research produced a highly efficient quantum computer simulator capable of accurately modeling arbitrary algorithms on any hardware device.

This project supplies support for an additional graduate student, Mr. David Schuster, on experimental investigations on quantum coherence, entanglement, and quantum computation in solid-state, electronic realization of quantum bits based on superconducting single-electron devices, namely the single Cooper-pair box. Mr. Schuster has developed a process for fabrication of Al/AlOx/Al tunnel qubits with integrated transmission line resonators, and used these devices for cavity-QED manipulations and readout of qubits. This work has led to the first strong coupling of a solid-state qubit to a single photon, the first high-fidelity non-demolition readout of superconducting qubits, and the first high-visibility quantum control of superconducting qubits.

This review provides a gentle introduction to one-way quantum computing in distributed architectures. One-way quantum computation shows significant promise as a computational model for distributed systems, particularly those architectures which rely on probabilistic entangling operations. We review the theoretical underpinnings of one-way quantum computation and discuss the practical issues related to exploiting the one-way model in distributed architectures.

This review provides a gentle introduction to one-way quantum computing in distributed architectures. One-way quantum computation shows significant promise as a computational model for distributed systems, particularly those architectures which rely on probabilistic entangling operations. We review the theoretical underpinnings of one-way quantum computation and discuss the practical issues related to exploiting the one-way model in distributed architectures.

We first consider the basic requirements for a quantum computer, arguing for the attractiveness of nuclear spins as information-bearing entities, and light for the coupling which allows quantum gates. We then survey the strengths of and immediate prospects for quantum information processing in ion traps. We discuss decoherence and gate rates in ion traps, comparing methods based on the vibrational motion with a method based on exchange of photons in cavity QED. We then sketch the main features of a quantum computer designed to allow an algorithm needing 10^6 Toffoli gates on 100 logical qubits. We find that around 200 ion traps linked by optical fibres and high-finesse cavities could perform such an algorithm in a week to a month, using components at or near current levels of technology.

It is generally believed that entanglement is essential for quantum computing. We present here a few simple examples in which quantum computing without entanglement is better than anything classically achievable, in terms of the reliability of the outcome after a xed number of oracle calls. Using a separable (that is, unentangled) n-qubit state, we show that the Deutsch-Jozsa problem and the Simon problem can be solved more reliably by a quantum computer than by the best possible classical algorithm, even probabilistic. We conclude that: (a) entanglement is not essential for quantum computing; and (b) some advantage of quantum algorithms over classical algorithms persists even when the quantum state contains an arbitrarily small amount of information|that is, even when the state is arbitrarily close to being totally mixed.

Quantum computing is expected to revolutionize cybersecurity. Traditional computers have calculated and processed data using binary bits from the beginning. Because they can only handle one set of inputs and one computation, current computers are constrained. Qubits, which fuel quantum computers, are volatile. The development of a large quantum computer is likely to cause cryptosystems to fail. Since quantum computers can solve the encryption method, the current cryptosystem will soon be outdated. The main problem of the quantum age will be coming up with cryptographic protocols that meet the needs of security, usability, and adaptability without letting down the users’ trust in the system. Quantum computers bring about significant leaps forward in terms of computing capability. They will make it possible to address previously intractable issues. In this paper, we will explain what quantum computing is and look at how it might be used in cybersecurity. Quantum computing could make cybersecurity less safe, so we talk about cybersecurity threats to learn more about them. We also introduce several quantum attacks and their countermeasures. Finally, we provide quantum approaches to cybersecurity concerns

Quantum computing is expected to revolutionize cybersecurity. Traditional computers have calculated and processed data using binary bits from the beginning. Because they can only handle one set of inputs and one computation, current computers are constrained. Qubits, which fuel quantum computers, are volatile. The development of a large quantum computer is likely to cause cryptosystems to fail. Since quantum computers can solve the encryption method, the current cryptosystem will soon be outdated. The main problem of the quantum age will be coming up with cryptographic protocols that meet the needs of security, usability, and adaptability without letting down the users’ trust in the system. Quantum computers bring about significant leaps forward in terms of computing capability. They will make it possible to address previously intractable issues. In this paper, we will explain what quantum computing is and look at how it might be used in cybersecurity. Quantum computing could make cybersecurity less safe, so we talk about cybersecurity threats to learn more about them. We also introduce several quantum attacks and their countermeasures. Finally, we provide quantum approaches to cybersecurity concerns

A scalable trapped-ion-based quantum-computing architecture requires the capability to optically address individual ions at several wavelengths. We demonstrate a dual-layered silicon nitride photonic platform for integration into planar ion traps designed for trapped-ion control in a 400 to 1100 nm wavelength range.

This work focuses on developing and applying the necessary methodology for the understanding and application of semiconductor quantum dots for quantum computing. Several major milestones were achieved during the present program including the demonstration of optically induced and detected quantum entanglement of two qubits, Rabi oscillation (one bit rotation) in single q-bit, and demonstration of the two-bit system. Future work is focusing on demonstrating a scalable system as well as working to developing lived coherent states based on optically driven spin systems.

We propose to use NMR as a testbed to develop general methods for solving computational problems on EQC's, to study the fundamental physics and computer science of these machines, and to learn how to make optimal use of the trade-offs that their unique capabilities permit us to make. Specifically, we intend to explore the critical issue of decoherence in a real quantum information processor, including its nature, its simulation, and methods of controlling it. The lessons thereby learned are expected to be broadly applicable throughout the field of quantum information processing, and particularly to proposed implementations based on solid-state NMR. Liquid-state NMR is thus an invaluable if not indispensable step in the field's efforts to bootstrap its way towards scalable quantum information processing. The results obtained during the two years covered by this report (July 1, 2001 - June 30, 2003) fall into four principal classes: 1) Development of methods for obtaining precise coherent control over nuclear spin systems with a well-characterized Hamiltonian and relaxation superoperator, and for quantifying the precision of such control. 2) Validation of these methods by implementing simple quantum algorithms, communications protocols, and other quantum phenomena that make essential use of entangling unitary operations and/or measurements. 3) Simulation of quantum systems using the unitary and nonunitary control operations that are available in liquid-state NMR spectroscopy. 4) Reviews, commentary and educational articles. We stress that although these studies utilized liquid-state NMR spectroscopy as a testbed for the development and validation of our techniques and simulations, the results will be directly applicable to a wide range of physical systems now being studied for quantum information processing purposes, once sufficient favorable ratios of gate operation to decoherence times have been obtained.

The prospects of quantum computing have driven efforts to realize fully functional quantum processing units (QPUs). Recent success in developing proof-of-principle QPUs has prompted the question of how to integrate these emerging processors into modern high-performance computing (HPC) systems. We examine how QPUs can be integrated into current and future HPC system architectures by accounting for functional and physical design requirements. We identify two integration pathways that are differentiated by infrastructure constraints on the QPU and the use cases expected for the HPC system. This includes a tight integration that assumes infrastructure bottlenecks can be overcome as well as a loose integration that assumes they cannot. We find that the performance of both approaches is likely to depend on the quantum interconnect that serves to entangle multiple QPUs. We also identify several challenges in assessing QPU performance for HPC, and we consider new metrics that capture the interplay between system architecture and the quantum parallelism underlying computational performance.

A two-party quantum communication process with classical inputs and outcomes can be simulated by replacing the quantum channel with a classical one. The minimal amount of classical communication required to reproduce the statistics of the quantum process is called its communication complexity. In the case of many instances simulated in parallel, the minimal communication cost per instance is called the asymptotic communication complexity. Previously, we reduced the computation of the asymptotic communication complexity to a convex minimization problem. In most cases, the objective function does not have an explicit analytic form, as the function is defined as the maximum over an infinite set of convex functions. Therefore, the overall problem takes the form of a minimax problem and cannot directly be solved by standard optimization methods. In this paper, we introduce a simple algorithm to compute the asymptotic communication complexity. For some special cases with an analytic objective function one can employ available convex-optimization libraries. In the tested cases our method turned out to be notably faster. Finally, using our method we obtain 1.238 bits as a lower bound on the asymptotic communication complexity of a noiseless quantum channel with the capacity of 1 qubit. This improves the previous bound of 1.208 bits.

This is a discussion of quantum computing at the Boulder Future Salon in April of 2006. For our discussion of quantum computing, we chose the book "Programming The Universe" by Seth Lloyd. So this is actually a book discussion, basically it is me (Wayne), Amanda, Annie, Larry, and John discussing "Programming The Universe" in particular and the future of quantum computing in general. We touch on a wide variety of topics, such as what would you use a quantum computer for, as opposed to a classical computer, would you just do quantum chemistry, or could you use a quantum computer for everything that you use a classical computer for, how would you program a quantum computer, does the brain do quantum computing (relationship between consciousness and quantum computing?), how does decoherence work in a quantum computer, can you simulate the universe on a quantum computer, how does the expansion of the universe drive computation, what is the nature of entropy, photons as heat engines, the anthropic principle, black holes, can decoherence be managed in biomolecules at normal temperatures, and so on. If you find this discussion enjoyable and you live in the Denver/Boulder region, you should come to the Boulder Future Salon in person. Check out our upcoming schedule of topics and meetings at http://boulderfuture.org . You can even sign up on our Yahoo! Group at http://groups.yahoo.com/group/boulderfuture and you will get emails announcing every upcoming meeting and topic.

Linear optical quantum computing (LOQC) seems attractively simple: information is borne entirely by light and processed by components such as beam splitters, phase shifters and detectors. However this very simplicity leads to limitations, such as the lack of deterministic entangling operations, which are compensated for by using substantial hardware overheads. Here we quantify the resource costs for full scale LOQC by proposing a specific protocol based on the surface code. With the caveat that our protocol can be further optimised, we report that the required number of physical components is at least five orders of magnitude greater than in comparable matter-based systems. Moreover the resource requirements grow higher if the per-component photon loss rate is worse than one in a thousand, or the per-component noise rate is worse than $10^{-5}$. We identify the performance of switches in the network as the single most influential factor influencing resource scaling.

Recently, several claims have been made that certain fundamental problems of distributed computing, including Leader Election and Distributed Consensus, begin to admit feasible and efficient solutions when the model of distributed computation is extended so as to apply quantum processing. This has been achieved in one of two distinct ways: (1) by initializing the system in a quantum entangled state, and/or (2) by applying quantum communication channels. In this paper, we explain why some of these prior claims are misleading, in the sense that they rely on changes to the model unrelated to quantum processing. On the positive side, we consider the aforementioned quantum extensions when applied to Linial's well-established LOCAL model of distributed computing. For both types of extensions, we put forward valid proof-of-concept examples of distributed problems whose round complexity is in fact reduced through genuinely quantum effects, in contexts which do not depend on the anonymity of nodes. Finally, we show that even the quantum variants of the LOCAL model have non-trivial limitations, captured by a very simple (purely probabilistic) notion which we call "physical locality" (PLOCAL). While this is strictly weaker than the "computational locality" of the classical LOCAL model, it nevertheless implies that for many distributed combinatorial optimization problems, such as Maximal Independent Set, the best currently known lower time bounds cannot be broken by applying quantum processing, in any conceivable way.

The time-dependent matrix-product-state (TDMPS) simulation method has been used for numerically simulating quantum computing for a decade. We introduce our C++ library ZKCM_QC developed for multiprecision TDMPS simulations of quantum circuits. Besides its practical usability, the library is useful for evaluation of the method itself. With the library, we can capture two types of numerical errors in the TDMPS simulations: one due to rounding errors caused by the shortage in mantissa portions of floating-point numbers; the other due to truncations of nonnegligible Schmidt coefficients and their corresponding Schmidt vectors. We numerically analyze these errors in TDMPS simulations of quantum computing.

Quantum computer possesses quantum parallelism and offers great computing power over classical computer \cite{er1,er2}. As is well-know, a moving quantum object passing through a double-slit exhibits particle wave duality. A quantum computer is static and lacks this duality property. The recently proposed duality computer has exploited this particle wave duality property, and it may offer additional computing power \cite{r1}. Simply put it, a duality computer is a moving quantum computer passing through a double-slit. A duality computer offers the capability to perform separate operations on the sub-waves coming out of the different slits, in the so-called duality parallelism. Here we show that an $n$-dubit duality computer can be modeled by an $(n+1)$-qubit quantum computer. In a duality mode, computing operations are not necessarily unitary. A $n$-qubit quantum computer can be used as an $n$-bit reversible classical computer and is energy efficient. Our result further enables a $(n+1)$-qubit quantum computer to run classical algorithms in a $O(2^n)$-bit classical computer. The duality mode provides a natural link between classical computing and quantum computing. Here we also propose a recycling computing mode in which a quantum computer will continue to compute until the result is obtained. These two modes provide new tool for algorithm design. A search algorithm for the unsorted database search problem is designed.

A backup of the "Quantum Computing Problems" wiki (database name: quantumproblemswiki ) on Miraheze , self-generated by Miraheze itself every month to honor our backups commitment.

Quantum bits have technological imperfections. Additionally, the capacity of a component that can be implemented feasibly is limited. Therefore, distributed quantum computation is required to scale up quantum computers. This dissertation presents a new quantum computer architecture which takes into account imperfections, aimed to realize distributed computation by connecting quantum computers each of which consists of multiple quantum CPUs and memories. Quantum CPUs employ a quantum error correcting code which has faster logical gates and quantum memories employ a code which is superior in space resource requirements. This dissertation focuses on quantum error correcting codes, giving a practical, concrete method for tolerating static losses such as faulty devices for the surface code. Numerical simulation with practical assumptions showed that a yield of functional qubits of 90% is marginally capable of building large-scale systems, by culling the poorer 50% of lattices during post-fabrication testing. Yield 80% is not usable even when culling 90% of generated lattices. For internal connections in a quantum computer and for connections between quantum computers, this dissertation gives a fault-tolerant method that bridges heterogeneous quantum error correcting codes. Numerical simulation showed that the scheme, which discards any quantum state in which any error is detected, always achieves an adequate logical error rate regardless of physical error rates in exchange for increased resource consumption. This dissertation gives a new extension of the surface code suitable for memories. This code is shown to require fewer physical qubits to encode a logical qubit than conventional codes. This code achieves the reduction of 50% physical qubits per a logical qubit. Collectively, the elements to propose the distributed quantum computer architecture are brought together.

We show a method for implementing universal quantum computing using of a singlet and triplets of nanowire double quantum dots coupled to a one-dimensional transmission line resonator. This method is attractive for both quantum computing and quantum control with inhibition of spontaneous emission, enhanced spin qubit lifetime, strong coupling and quantum nondemolition measurements of spin qubits. We analyze the performance and stability of all required operations and emphasize that all techniques are feasible with current experimental technology.

State selective field ionization detection techniques in physics require a specific progression through a complicated atomic state space to optimize state selectivity and overall efficiency. For large principle quantum number n, the theoretical models become computationally intractable and any results are often rendered irrelevant by small deviations from ideal experimental conditions, for example external electromagnetic fields. Several different proposals for quantum information processing rely heavily upon the quality of these detectors. In this paper, we show a proof of principle that it is possible to optimize experimental field profiles in situ by running a genetic algorithm to control aspects of the experiment itself. A simple experiment produced novel results that are consistent with analyses of existing results.

We develop a scalable architecture for quantum computation using controllable electrons of double-dot molecules coupled to a microwave stripline resonator on a chip, which satisfies all Divincenzo criteria. We analyze the performance and stability of all required operations and emphasize that all techniques are feasible with current experimental technologies.

Dedicated research into the design and construction of a large scale Quantum Information Processing (QIP) system is a complicated task. The design of an experimentally feasible quantum processor must draw upon results in multiple fields; from experimental efforts in system control and fabrication through to far more abstract areas such as quantum algorithms and error correction. Recently, the adaptation of topological coding models to physical systems in optics has illustrated a possible long term pathway to truly large scale QIP. As the topological model has well defined protocols for Quantum Error Correction (QEC) built in as part of its construction, a more grounded analysis of the {\em classical} processing requirements is possible. In this paper we analyze the requirements for a classical processing system, designed specifically for the topological cluster state model. We demonstrate that via extensive parallelization, the construction of a classical "front-end" system capable of processing error correction data for a large topological computer is possible today.

Ever since entanglement was identified as a computational and cryptographic resource, effort has been made to find an efficient way to tell whether a given density matrix represents an unentangled, or separable, state. Essentially, this is the quantum separability problem. Chapters 1 to 3 motivate a new interior-point algorithm which, given the expected values of a subset of an orthogonal basis of observables of an otherwise unknown quantum state, searches for an entanglement witness in the span of the subset of observables. When all the expected values are known, the algorithm solves the separability problem. In Chapter 4, I give the motivation for the algorithm and show how it can be used in a particular physical scenario to detect entanglement (or decide separability) of an unknown quantum state using as few quantum resources as possible. I then explain the intuitive idea behind the algorithm and relate it to the standard algorithms of its kind. I end the chapter with a comparison of the complexities of the algorithms surveyed in Chapter 3. Finally, in Chapter 5, I present the details of the algorithm and discuss its performance relative to standard methods.

In the absence of any efficient classical schemes for verifying a universal quantum computer, the importance of limiting the required quantum resources for this task has been highlighted recently. Currently, most of efficient quantum verification protocols are based on cryptographic techniques where an almost classical verifier executes her desired encrypted quantum computation remotely on an untrusted quantum prover. In this work we present a new protocol for quantum verification by incorporating existing techniques in a non-standard composition to reduce the required quantum communications between the verifier and the prover.

We discuss the implementation of arbitrary precision composite pulses developed using the methods of Brown et al. [Phys. Rev. A 70 (2004) 052318]. We give explicit results for pulse sequences designed to tackle both the simple case of pulse length errors and for the more complex case of off-resonance errors. The results are developed in the context of NMR quantum computation, but could be applied more widely.

While solid-state devices offer naturally reliable hardware for modern classical computers, thus far quantum information processors resemble vacuum tube computers in being neither reliable nor scalable. Strongly correlated many body states stabilized in topologically ordered matter offer the possibility of naturally fault tolerant computing, but are both challenging to engineer and coherently control and cannot be easily adapted to different physical platforms. We propose an architecture which achieves some of the robustness properties of topological models but with a drastically simpler construction. Quantum information is stored in the symmetry-protected degenerate ground states of spin-1 chains, while quantum gates are performed by adiabatic non-Abelian holonomies using only single-site fields and nearest-neighbor couplings. Gate operations respect the symmetry, and so inherit some protection from noise and disorder from the symmetry-protected ground states.

We present a complete scheme for quantum information processing using the unique features of alkaline earth atoms. We show how two completely independent lattices can be formed for the $^1$S$_0$ and $^3$P$_0$ states, with one used as a storage lattice for qubits encoded on the nuclear spin, and the other as a transport lattice to move qubits and perform gate operations. We discuss how the $^3$P$_2$ level can be used for addressing of individual qubits, and how collisional losses from metastable states can be used to perform gates via a lossy blockade mechanism.

We review the progress and main challenges in implementing large-scale quantum computing by optical control of electron spins in quantum dots (QDs). Relevant systems include self-assembled QDs of III-V or II-VI compound semiconductors (such as InGaAs and CdSe), monolayer fluctuation QDs in compound semiconductor quantum wells, and impurity centers in solids such as P-donors in silicon and nitrogen-vacancy centers in diamond. The decoherence of the electron spin qubits is discussed and various schemes for countering the decoherence problem are reviewed. We put forward designs of local nodes consisting of a few qubits which can be individually addressed and controlled. Remotely separated local nodes are connected by photonic structures (microcavities and waveguides) to form a large-scale distributed quantum system or a quantum network. The operation of the quantum network consists of optical control of a single electron spin, coupling of two spins in a local nodes, optically controlled quantum interfacing between stationary spin qubits in QDs and flying photon qubits in waveguides, rapid initialization of spin qubits, and qubit-specific single-shot non-demolition quantum measurement. The rapid qubit initialization may be realized by selectively enhancing certain entropy dumping channels via phonon or photon baths. The single-shot quantum measurement may be in-situ implemented through the integrated photonic network. The relevance of quantum non-demolition measurement to large-scale quantum computation is discussed. To illustrate the feasibility and demand, the resources are estimated for the benchmark problem of factorizing 15 with Shor's algorithm.

Fault tolerant quantum computing methods which work with efficient quantum error correcting codes are discussed. Several new techniques are introduced to restrict accumulation of errors before or during the recovery. Classes of eligible quantum codes are obtained, and good candidates exhibited. This permits a new analysis of the permissible error rates and minimum overheads for robust quantum computing. It is found that, under the standard noise model of ubiquitous stochastic, uncorrelated errors, a quantum computer need be only an order of magnitude larger than the logical machine contained within it in order to be reliable. For example, a scale-up by a factor of 22, with gate error rate of order $10^{-5}$, is sufficient to permit large quantum algorithms such as factorization of thousand-digit numbers.

This work is about diagrammatic languages, how they can be represented, and what they in turn can be used to represent. More specifically, it focuses on representations and applications of string diagrams. String diagrams are used to represent a collection of processes, depicted as "boxes" with multiple (typed) inputs and outputs, depicted as "wires". If we allow plugging input and output wires together, we can intuitively represent complex compositions of processes, formalised as morphisms in a monoidal category. [...] The first major contribution of this dissertation is the introduction of a discretised version of a string diagram called a string graph. String graphs form a partial adhesive category, so they can be manipulated using double-pushout graph rewriting. Furthermore, we show how string graphs modulo a rewrite system can be used to construct free symmetric traced and compact closed categories on a monoidal signature. The second contribution is in the application of graphical languages to quantum information theory. We use a mixture of diagrammatic and algebraic techniques to prove a new classification result for strongly complementary observables. [...] We also introduce a graphical language for multipartite entanglement and illustrate a simple graphical axiom that distinguishes the two maximally-entangled tripartite qubit states: GHZ and W. [...] The third contribution is a description of two software tools developed in part by the author to implement much of the theoretical content described here. The first tool is Quantomatic, a desktop application for building string graphs and graphical theories, as well as performing automated graph rewriting visually. The second is QuantoCoSy, which performs fully automated, model-driven theory creation using a procedure called conjecture synthesis.

A new model of quantum computing has recently been proposed which, in analogy with a classical lambda-calculus, exploits quantum processes which operate on other quantum processes. One such quantum meta-operator takes N unitary transformations as input, coherently permutes their ordering, and outputs a new composite operator which can be applied to a quantum state. Here we propose an optical device which implements this type of coherent operator permutation. This device requires only one physical implementation of each operator to be permuted.

One-way quantum computation proceeds by sequentially measuring individual spins (qubits) in an entangled many-spin resource state. It remains a challenge, however, to efficiently produce such resource states. Is it possible to reduce the task of generating these states to simply cooling a quantum many-body system to its ground state? Cluster states, the canonical resource for one-way quantum computing, do not naturally occur as ground states of physical systems. This led to a significant effort to identify alternative resource states that appear as ground states in spin lattices. An appealing candidate is a valence-bond-solid state described by Affleck, Kennedy, Lieb, and Tasaki (AKLT). It is the unique, gapped ground state for a two-body Hamiltonian on a spin-1 chain, and can be used as a resource for one-way quantum computing. Here, we experimentally generate a photonic AKLT state and use it to implement single-qubit quantum logic gates.

We discuss a model for quantum computing with initially mixed states. Although such a computer is known to be less powerful than a quantum computer operating with pure (entangled) states, it may efficiently solve some problems for which no efficient classical algorithms are known. We suggest a new implementation of quantum computation with initially mixed states in which an algorithm realization is achieved by means of optimal basis independent transformations of qubits.

In the measurement-based quantum computing, there is a natural "causal cone" among qubits of the resource state, since the measurement angle on a qubit has to depend on previous measurement results in order to correct the effect of byproduct operators. If we respect the no-signaling principle, byproduct operators cannot be avoided. In this paper, we study the possibility of acausal measurement-based quantum computing by using the process matrix framework [O. Oreshkov, F. Costa, and C. Brukner, Nature Communications {\bf3}, 1092 (2012)]. We construct a resource process matrix for acausal measurement-based quantum computing. The resource process matrix is an analog of the resource state of the causal measurement-based quantum computing. We find that the resource process matrix is (up to a normalization factor and trivial ancilla qubits) equivalent to the decorated graph state created from the graph state of the corresponding causal measurement-based quantum computing.

In the measurement-based quantum computing, there is a natural "causal cone" among qubits of the resource state, since the measurement angle on a qubit has to depend on previous measurement results in order to correct the effect of byproduct operators. If we respect the no-signaling principle, byproduct operators cannot be avoided. In this paper, we study the possibility of acausal measurement-based quantum computing by using the process matrix framework [O. Oreshkov, F. Costa, and C. Brukner, Nature Communications {\bf3}, 1092 (2012)]. We construct a resource process matrix for acausal measurement-based quantum computing. The resource process matrix is an analog of the resource state of the causal measurement-based quantum computing. We find that the resource process matrix is (up to a normalization factor and trivial ancilla qubits) equivalent to the decorated graph state created from the graph state of the corresponding causal measurement-based quantum computing.

The network paradigm for quantum computing involves interconnecting many modules to form a scalable machine. Typically it is assumed that the links between modules are prone to noise while operations within modules have significantly higher fidelity. To optimise fault tolerance in such architectures we introduce a hierarchical generalisation of the surface code: a small `patch' of the code exists within each module, and constitutes a single effective qubit of the logic-level surface code. Errors primarily occur in a two-dimensional subspace, i.e. patch perimeters extruded over time, and the resulting noise threshold for inter-module links can exceed ~ 10% even in the absence of purification. Increasing the number of qubits within each module decreases the number of qubits necessary for encoding a logical qubit. But this advantage is relatively modest, and broadly speaking a `fine grained' network of small modules containing only ~ 8 qubits is competitive in total qubit count versus a `course' network with modules containing many hundreds of qubits.