Saurya Das, Randy Kobes, Gabor Kunstatter
We show that by a suitable choice of a time dependent Hamiltonian, Deutsch's algorithm can be implemented by an adiabatic quantum computer. We extend our analysis to the Deutsch-Jozsa problem and estimate the required running time for both global and local adiabatic evolutions.
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Deutsch-Jozsa algorithm has been implemented via a quantum adiabatic evolution by S. Das et al. [Phys. Rev. A 65, 062310 (2002)]. This adiabatic algorithm gives rise to a quadratic speed up over classical algorithms. We show that a modified version of the adiabatic evolution in that paper can improve the performance to constant time.
In this work Controlled phase shift gates are implemented on a qaudrupolar system, by using non-adiabatic geometric phases. A general procedure is given, for implementing controlled phase shift gates in an 'N' level system. The utility of such controlled phase shift gates, is demonstrated here by implementing 3-qubit Deutsch-Jozsa algorithm on a 7/2 quadrupolar nucleus oriented in a liquid crystal matrix.
The goal of this paper is to study the effect of entanglement on the running time of a quantum computation. Adiabatic quantum computation is suited to this kind of study, since it allows us to explicitly calculate the time evolution of the entanglement throughout the calculation. On the other hand however, the adiabatic formalism makes it impossible to study the roles of entanglement and fidelity separately, which means that results have to be interpreted carefully. We study two algorithms: the search algorithm and the Deutsch-Jozsa algorithm. We find some evidence that entanglement can be con…
Quantum adiabatic algorithm is a method of solving computational problems by evolving the ground state of a slowly varying Hamiltonian. The technique uses evolution of the ground state of a slowly varying Hamiltonian to reach the required output state. In some cases, such as the adiabatic versions of Grover's search algorithm and Deutsch-Jozsa algorithm, applying the global adiabatic evolution yields a complexity similar to their classical algorithms. However, using the local adiabatic evolution, the algorithms given by J. Roland and N. J. Cerf for Grover's search [ Phys. Rev. A. {\bf 65} 0423…
A redundancy in the existing Deutsch-Jozsa quantum algorithm is removed and a refined algorithm, which reduces the size of the register and simplifies the function evaluation, is proposed. The refined version allows a simpler analysis of the use of entanglement between the qubits in the algorithm and provides criteria for deciding when the Deutsch-Jozsa algorithm constitutes a meaningful test of quantum computation.
A detailed description of the development of a three qubit NMR realization of the Deutsch-Jozsa algorithm [Collins et.al., Phys. Rev. A 62, 022304 (2000)] is provided. The theoretical and experimental techniques used for the reduction of the algorithm's evolution steps into a sequence of NMR pulses are discussed at length. This includes the description of general pulse sequence compilation techniques, various schemes for indirectly coupled gate realizations, experimental pulse parameterization techniques and bookkeeping methods for pulse phases.
We propose an optical implementation of the Deutsch-Jozsa Algorithm using classical light in a binary decision-tree scheme. Our approach uses a ring cavity and linear optical devices in order to efficiently quarry the oracle functional values. In addition, we take advantage of the intrinsic Fourier transforming properties of a lens to read out whether the function given by the oracle is balanced or constant.
Quantum correlations have been pointed out as the most likely source of the speed-up in quantum computation. Here we analyzed the presence of quantum correlations in the implementation of Deutsch-Jozsa algorithm running in the DQC1 and DQCp models of quantum computing. For some balanced functions, the qubits in DQC1 model are quantum correlated just in the intermediate steps of the algorithm for a given decomposition into one and two qubits gates. In the DQCp model the final state is strongly quantum correlated for some balanced functions, so that the pairwise entanglement between blocks scale…
Quantum parallelism is the main feature of quantum computation. In 1985 D. Deutsch showed that a single quantum computation may be sufficient to state whether a two-valued function of a two-valued variable is constant or not. Though the generalized problem with unconstrained domain and range size admits no deterministic quantum solution, a fully probabilistic quantum algorithm is presented in which quantum parallelism is harnessed to achieve a quicker exploration of the domain with respect to the classical ``sampling'' strategy.
In 1985, David Deutsch challenged the Church-Turing thesis by stating that his quantum model of computation "could, in principle, be built and would have many remarkable properties not reproducible by any Turing machine". While this is thought to be true in general, there is usually no way of knowing that the corresponding classical algorithms are the best possible solutions. Here we provide an efficient classical simulation of the Deutsch-Jozsa algorithm, which was one of the first examples of quantum computational speed-up. Our conclusion is that the Deutsch-Jozsa quantum algorithm owes its …
The well-known Deutsch Algorithm (DA) and Deutsch-Jozsha Algorithm (DJA) both are used as an evidence to the power of quantum computers over classical computation mediums. In these theoretical experiments, it has been shown that a quantum computer can find the answer with certainty within a few steps although classical electronic systems must evaluate more iterations than quantum computer. In this paper, it is shown that a classical computation system formed by using ordinary electronic parts may perform the same task with equal performance than quantum computers. DA and DJA quantum circuits a…
We propose a physical scheme for implementing the Deutsch-Jozsa algorithm using atomic ensembles and optical devices. The scheme has inherent fault tolerance to the realistic noise and efficient scaling with the number of ensembles for some entangled states within the reach of current technology. It would be an important step toward more complex quantum computation via atomic ensembles.
We propose a variational principle to compute a quantum adiabatic brachistochrone (QAB) for open systems. Using the notion of "adiabatic speed" based on the energy gaps, we derive a Lagrangian associated to the functional measuring the time spent to achieve adiabatic behavior, which in turn allows us to perform the optimization. The QAB is illustrated for non-unitary dynamics of STIRAP process, the Deutsch-Jozsa quantum computing algorithm and of a transmon qutrit. A numerical protocol is devised, which allows to compute the QAB for arbitrary quantum systems for which exact simulations can be …
Recently, [{arXiv:0810.3134}] is accepted and published. We show that the Bell inequalities lead to a new type of linear-optical Deutsch algorithms. We have considered a use of entangled photon pairs to determine simultaneously and probabilistically two unknown functions. The usual Deutsch algorithm determines one unknown function and exhibits a two to one speed up in a certain computation on a quantum computer rather than on a classical computer. We found that the violation of Bell locality in the Hilbert space formalism of quantum theory predicts that the proposed {\it probabilistic} Deutsch…
Deutsch's algorithm for two qubits (one control qubit plus one auxiliary qubit) is extended to two $d$-dimensional quantum systems or qudits for the case in which $d$ is equal to $2^n$, $n=1,2,...$ . This allows one to classify a certain oracle function by just one query, instead of the $2^{n-1}+1$ queries required by classical means. The given algorithm for two qudits also solves efficiently the Bernstein-Vazirani problem. Entanglement does not occur at any step of the computation.
We analyse the design and optimisation of quantum logic circuits suitable for the experimental demonstration of a three-qubit quantum computation prototype based on optically-controlled, solid-state quantum logic gates. In these gates, the interaction between two qubits carried by the electron-spin of donors is mediated by the optical excitation of a control particle placed in their proximity. First, we use a geometrical approach for analysing the entangling characteristics of these quantum gates. Then, using a genetic programming algorithm, we develop circuits for the refined Deutsch-Jozsa al…
We report the first experimental demonstration of an all-optical one-way implementation of Deutsch's quantum algorithm on a four-qubit cluster state. All the possible configurations of a balanced or constant function acting on a two-qubit register are realized within the measurement-based model for quantum computation. The experimental results are in excellent agreement with the theoretical model, therefore demonstrating the successful performance of the algorithm.
We demonstrate experimentally the usefulness of selective pulses in NMR to perform quantum computation. Three different techniques based on selective pulse excitations have been proposed to prepare a spin system in a pseudo-pure state. We describe the design of novel ``portmanteau'' gates using the selective manipulation of level populations. A selective pulse implementation of the Deutsch-Jozsa algorithm for a two-qubit and a three-qubit quantum computer is demonstrated.
A hybrid model of the Deutsch-Jozsa algorithm is presented, inspired by the proposals of hybrid computation by S. Lloyd and P. van Loock et. al. The model is based on two observations made about both the discrete and continuous algorithms already available. First, the Fourier transform is a single-step operation in a continuous-variable (CV) setting. Additionally, any implementation of the oracle is nontrivial in both schemes. The steps of the computation are very similar to those in the CV algorithm, with the main difference being the way in which the qunats, or quantum units of analogic info…
We describe the first experimental realization of the Deutsch-Jozsa quantum algorithm to evaluate the properties of a 2-bit boolean function in the framework of one-way quantum computation. For this purpose a novel two-photon six-qubit cluster state was engineered. Its peculiar topological structure is the basis of the original measurement pattern allowing the algorithm realization. The good agreement of the experimental results with the theoretical predictions, obtained at $\sim$1kHz success rate, demonstrate the correct implementation of the algorithm.
The adiabatic approximation exhibits wide applicability in quantum mechanics, providing a simple approach for nontransitional dynamics in quantum systems governed by slowly varying time-dependent Hamiltonians. However, the standard adiabatic theorem is specifically derived for closed quantum systems. In a realistic open system scenario, the inevitable system-reservoir interaction must be taken into account, which strongly impacts the generalization of the adiabatic behavior. In this paper, we introduce sufficient conditions for the adiabatic approximation in open quantum systems. These conditi…
An NMR realization of a two-qubit quantum gate which processes quantum information indirectly via couplings to a spectator qubit is presented in the context of the Deutsch-Jozsa algorithm. This enables a successful comprehensive NMR implementation of the Deutsch-Jozsa algorithm for functions with three argument bits and demonstrates a technique essential for multi-qubit quantum computation.
The present work points out that the Deutsch-Jozsa algorithm was the first formal description of a quantum decider. In particular, it is studied here the class of languages whose indicator functions allow the Deutsch-Jozsa algorithm to output a monochromatic result, beyond the trivial case z = 0 for constant indicator functions. To illustrate examples of randomly balanced languages and some monochromatic cases, it was performed classical computational simulations of the Deutsch-Jozsa quantum algorithm for the specific cases of 4 and 6 qubits, respectively. The general case of the Deutsch-Jozsa…
We propose a protocol to construct the 35 $f$-controlled phase gates of a three-qubit refined Deutsch-Jozsa (DJ) algorithm, by using single-qubit $σ_z$ gates, two-qubit controlled phase gates, and two-target-qubit controlled phase gates. Using this protocol, we discuss how to implement the three-qubit refined DJ algorithm with superconducting transmon qutrits resonantly coupled to a single cavity. Our numerical calculation shows that implementation of this quantum algorithm is feasible within the present circuit QED technique. The experimental realization of this algorithm would be an importan…
In the rapidly growing area of quantum information, the Deutsch algorithm is ubiquitous and, in most cases, the first one to be introduced to any student of this relatively new field of research. The reason for this historical relevance stems from the fact that, although extremely simple, the algorithm conveys all the main features of more complex quantum computations. In spite of its simplicity, the uncountable experimental realizations of the algorithm in a broad variety of physical systems are in general quite involved. The aim of this work is two-fold: to introduce the basic concepts of qu…
A long-standing aim of quantum information research is to understand what gives quantum computers their advantage. This requires separating problems that need genuinely quantum resources from those for which classical resources are enough. Two examples of quantum speed-up are the Deutsch-Jozsa and Simon's problem, both efficiently solvable on a quantum Turing machine, and both believed to lack efficient classical solutions. Here we present a framework that can simulate both quantum algorithms efficiently, solving the Deutsch-Jozsa problem with probability 1 using only one oracle query, and Sim…
The wide set of control parameters and reduced size scale make semiconductor quantum dots attractive candidates to implement solid-state quantum computation. Considering an asymmetric double quantum dot coupled by tunneling, we combine the action of a laser field and the spontaneous emission of the excitonic state to protect an arbitrary superposition state of the indirect exciton and ground state. As a by-product we show how to use the protected state to solve the Deutsch problem.
Probably the simplest and most frequently used way to illustrate the power of quantum computing is to solve the so-called {\it Deutsch's problem}. Consider a Boolean function $f: \{0,1\} \to \{0,1\}$ and suppose that we have a (classical) black box to compute it. The problem asks whether $f$ is constant (that is, $f(0) = f(1)$) or balanced ($f(0) \not= f(1)$). Classically, to solve the problem seems to require the computation of $f(0)$ and $ f(1)$, and then the comparison of results. Is it possible to solve the problem with {\em only one} query on $f$? In a famous paper published in 1985, Deut…
Suppressing undesired nonunitary effects is a major challenge in quantum computation and quantum control. In this work, by considering the adiabatic dynamics in presence of a surrounding environment, we theoretically and experimentally analyze the robustness of adiabaticity in open quantum systems. More specifically, by considering a decohering scenario, we exploit the validity conditions of the adiabatic approximation as well as its sensitiveness to the resonance situation, which typically harm adiabaticity in closed systems. As an illustration, we implement an oscillating Landau-Zener Hamilt…
It has been more than 20 years since Deutsch and Hayden proved the locality of quantum theory, using the Heisenberg picture of quantum computational networks. Of course, locality holds even in the face of entanglement and Bell's theorem. Today, most researchers in quantum foundations are still convinced not only that a local description of quantum systems has not yet been provided, but that it cannot exist. The main goal of this paper is to address this misconception by re-explaining the descriptor formalism in a hopefully accessible and self-contained way. It is a step-by-step guide to how an…
We offer an improved method for using a nuclear-magnetic-resonance quantum computer (NMRQC) to solve the Deutsch-Jozsa problem. Two known obstacles to the application of the NMRQC are exponential diminishment of density-matrix elements with the number of bits, threatening weak signal levels, and the high cost of preparing a suitable starting state. A third obstacle is a heretofore unnoticed restriction on measurement operators available for use by an NMRQC. Variations on the function classes of the Deutsch-Jozsa problem are introduced, both to extend the range of problems advantageous for quan…
We introduce an approach for quantum computing in continuous time based on the Lewis-Riesenfeld dynamic invariants. This approach allows, under certain conditions, for the design of quantum algorithms running on a nonadiabatic regime. We show that the relaxation of adiabaticity can be achieved by processing information in the eigenlevels of a time dependent observable, namely, the dynamic invariant operator. Moreover, we derive the conditions for which the computation can be implemented by time independent as well as by adiabatically varying Hamiltonians. We illustrate our results by providing…
Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled logic gates by controlled dynamics of qubits. In controlled dynamics, one qubit undergoes coherent evolution and acquires appropriate phase, depending on the state of other qubits. If the evolution is geometric, then the phase acquired depend only on the geometry of the path executed, and is robust against certain types of errors. This phenomenon leads to an inh…
The use of superposition of states in quantum computation, known as quantum parallelism, has significant advantage in terms of speed over the classical computation. It can be understood from the early invented quantum algorithms such as Deutsch's algorithm, Deutsch-Jozsa algorithm and its variation as Bernstein-Vazirani algorithm, Simon algorithm, Shor's algorithms etc. Quantum parallelism also significantly speeds up the database search algorithm, which is important in computer science because it comes as a subroutine in many important algorithms. Quantum database search of Grover achieves th…
Nuclear magnetic resonance (NMR) has been widely used as a demonstrative medium for showcasing the ability for quantum computations to outperform classical ones. A large number of such experiments performed have been implementations of the Deutsch-Jozsa algorithm. It is known, however, that in some cases the Deutsch-Jozsa problem can be solved classically using as many queries to the black-box as in the quantum solution. In this paper we describe experiments in which we take the contrasting approach of using NMR as a classical computing medium, treating the nuclear spin vectors classically and…
We present an original model of paraconsistent Turing machines (PTMs), a generalization of the classical Turing machines model of computation using a paraconsistent logic. Next, we briefl y describe the standard models of quantum computation: quantum Turing machines and quantum circuits, and revise quantum algorithms to solve the so-called Deutsch's problem and Deutsch-Jozsa problem. Then, we show the potentialities of the PTMs model of computation simulating the presented quantum algorithms via paraconsistent algorithms. This way, we show that PTMs can resolve some problems in exponentially l…
We develop a classical model of computation (the S model) which captures some important features of quantum computation, and which allows to design fast algorithms for solving specific problems. In particular, we show that Deutsch's problem can be trated within the S model of computation in the same way as within quantum computation; also Grover's search problem of an unsorted database finds a surprisingly fast solution. The correct understanding of these results put into a new perspective the relationship between quantum and classical computation.
A general approach for transitionless quantum driving in open quantum systems is introduced. Under the assumption of adiabatic evolution for time-local master equations, we derive the generalized transitionless Lindbladian required to implement a shortcut to adiabaticity in an open system scenario. The general counter-diabatic Lindbladian obtained accounts for a phase freedom, which translates into a set of free parameters throughout the dynamics. We then discuss how our generalized approach allows us to recover the transitionless Lindbladian introduced by G. Vacanti et al. [New J. Phys. 16, 0…
Universal quantum gates and quantum error correction~(QEC) lie in the heart of quantum information science. Large-scale quantum computing depends on a universal set of quantum gates, in which some gates may be easily carried out, while others are hard with a certain physical system. There is a unique three-qubit quantum gate called the Deutsch gate~[$\mathbb{D}(θ)$], from which alone a circuit can be constructed so that any feasible quantum computing is attainable. As far as we know, however, $\mathbb{D}(θ)$ has not been demonstrated. Here we design an easily realizable $\mathbb{D}(θ)$ by usin…
We consider Deutsch's computational model of a quantum system evolving in a spacetime containing closed timelike curves. Although it is known that this model predicts non-linear and non-unitary evolutions of the system, we demonstrate that it also gives rise to evolutions which are a discontinuous function of the input state. These discontinuities persist for the most natural modifications of Deutsch's approach.
In this article we present an ongoing effort to formalise quantum algorithms and results in quantum information theory using the proof assistant Isabelle/HOL. Formal methods being critical for the safety and security of algorithms and protocols, we foresee their widespread use for quantum computing in the future. We have developed a large library for quantum computing in Isabelle based on a matrix representation for quantum circuits, successfully formalising the no-cloning theorem, quantum teleportation, Deutsch's algorithm, the Deutsch-Jozsa algorithm and the quantum Prisoner's Dilemma. We di…
We propose a genetic-algorithm-based method to find the unitary transformations for any desired quantum computation. We formulate a simple genetic algorithm by introducing the "genetic parameter vector" of the unitary transformations to be found. In the genetic algorithm process, all components of the genetic parameter vectors are supposed to evolve to the solution parameters of the unitary transformations. We apply our method to find the optimal unitary transformations and to generalize the corresponding quantum algorithms for a realistic problem, the one-bit oracle decision problem, or the o…
The phenomenon of quantum entanglement is fundamental to the implementation of quantum computation, and requires at least two qubits for its demonstration. However, both Deutsch algorithm and Grover's search algorithm for two bits do not use entanglement. We develop a Deutsch-like problem, where we consider all possible binary functions for two bit inputs and distinguish their even or odd nature. The quantum algorithm to solve this problem requires entanglement at the level of two qubits. The final solution suggests that an NMR implementation of the problem would lead to interesting results.
We show that a set of gates that consists of all one-bit quantum gates (U(2)) and the two-bit exclusive-or gate (that maps Boolean values $(x,y)$ to $(x,x \oplus y)$) is universal in the sense that all unitary operations on arbitrarily many bits $n$ (U($2^n$)) can be expressed as compositions of these gates. We investigate the number of the above gates required to implement other gates, such as generalized Deutsch-Toffoli gates, that apply a specific U(2) transformation to one input bit if and only if the logical AND of all remaining input bits is satisfied. These gates play a central role in …
We consider a family of unstructured problems, for which we propose a method for constructing analog, continuous-time quantum algorithms that are more efficient than their classical counterparts. In this family of problems, which we refer to as `scrambled output' problems, one has to find a minimum-cost configuration of a given integer-valued n-bit function whose output values have been scrambled in some arbitrary way. Special cases within this set of problems are Grover's search problem of finding a marked item in an unstructured database, certain random energy models, and the functions of th…
We prove the existence of a class of two--input, two--output gates any one of which is universal for quantum computation. This is done by explicitly constructing the three--bit gate introduced by Deutsch [Proc.~R.~Soc.~London.~A {\bf 425}, 73 (1989)] as a network consisting of replicas of a single two--bit gate.
We describe a method to axiomatize computations in deterministic Turing machines. When applied to computations in non-deterministic Turing machines, this method may produce contradictory (and therefore trivial) theories, considering classical logic as the underlying logic. By substituting in such theories the underlying logic by a paraconsistent logic we define a new computation model, the paraconsistent Turing machine. This model allows a partial simulation of superposed states of quantum computing. Such a feature allows the definition of paraconsistent algorithms which solve (with some restr…
We show that by a suitable choice of time-dependent Hamiltonian, the search for a marked item in an unstructured database can be achieved in unit time, using Adiabatic Quantum Computation. This is a considerable improvement over the O(sqrt(N)) time required in previous algorithms. The trade-off is that in the intermediate stages of the computation process, the ground state energy of the computer increases to a maximum of O(sqrt(N)), before returning to zero at the end of the process.
ROM-based quantum computation (QC) is an alternative to oracle-based QC. It has the advantages of being less ``magical'', and being more suited to implementing space-efficient computation (i.e. computation using the minimum number of writable qubits). Here we consider a number of small (one and two-qubit) quantum algorithms illustrating different aspects of ROM-based QC. They are: (a) a one-qubit algorithm to solve the Deutsch problem; (b) a one-qubit binary multiplication algorithm; (c) a two-qubit controlled binary multiplication algorithm; and (d) a two-qubit ROM-based version of the Deutsc…
We present a novel use case for quantum computation: the sensitivity analysis for a risk model used at Deutsche Börse Group. Such an analysis is computationally too expensive to perform on classical computers. We show in detail how the risk model and its analysis can be implemented as a quantum circuit. We test small scale versions of the model in simulation and find that the expected quadratic speedup compared to the classical implementation used at Deutsche Börse Group can be realized. Full scale production usage would be possible with less than 200 error corrected qubits. Our quantum algori…
We examine the use of adiabatic quantum algorithms to solve structured, or nested, search problems. We construct suitable time dependent Hamiltonians and derive the computation times for a general class of nested searches involving n qubits. As expected, we find that as additional structure is included, the Hamiltonians become more local and the computation times decrease.
Impact of Temporally Correlated Dephasing Noise on the Fidelity of the 2-Qubit Deutsch-Jozsa Algorithm
本文通过Qiskit数值模拟研究Ornstein-Uhlenbeck时间相关退相位噪声对2量子比特Deutsch-Jozsa算法保真度的影响，发现保真度对相关时间呈非单调依赖，且标准马尔可夫模型仅在极短相关时间下有效，揭示了非马尔可夫建模对近量子设备算法性能评估的必要性。
Geometric phases have been used in NMR, to implement controlled phase shift gates for quantum information processing, only in weakly coupled systems in which the individual spins can be identified as qubits. In this work, we implement controlled phase shift gates in strongly coupled systems, by using non-adiabatic geometric phases, obtained by evolving the magnetization of fictitious spin-1/2 subspaces, over a closed loop on the Bloch sphere. The dynamical phase accumulated during the evolution of the subspaces, is refocused by a spin echo pulse sequence and by setting the delay of transition …
In these notes we present preliminary results on quantum-like algorithms where tensor product is replaced by geometric product. Such algorithms possess the essential properties typical of quantum computation (entanglement, parallelism) but employ additional algebraic structures typical of geometric algebra -- structures absent in standard quantum computation. As a test we reformulate in Geometric Algebra terms the Deutsch-Jozsa problem.
We show how to control and perform universal three-qubit quantum computation with trapped electron quantum states. The three qubits are the electron spin, and the first two quantum states of the cyclotron and axial harmonic oscillators. We explicitly show how the universal gates can be performed. As an example of a non-trivial quantum algorithm, we outline the implementation of the Deutsch-Jozsa algorithm in this system.
Phase space tableau simulation for quantum computation
本文提出一种基于相空间框架和扩展稳定子理论的新型表模拟方法，可高效经典模拟超出稳定子形式体系的量子电路，并在隐藏移位和Deutsch--Jozsa算法上验证了性能。
We discuss applications of shortcuts to adiabaticity (STA) to adiabatic quantum computation. After reviewing the fundamental properties and the present status of STA from the author's personal point of view, we apply the method to the adiabatic algorithm of the Grover's problem. We discuss two possible implementations of STA for the adiabatic quantum computations: the method of quantum adiabatic brachistochrone and the Lewis-Riesenfeld invariant-based inverse engineering.
We present a computational framework based on geometric structures. No quantum mechanics is involved, and yet the algorithms perform tasks analogous to quantum computation. Tensor products and entangled states are not needed -- they are replaced by sets of basic shapes. To test the formalism we solve in geometric terms the Deutsch-Jozsa problem, historically the first example that demonstrated the potential power of quantum computation. Each step of the algorithm has a clear geometric interpetation and allows for a cartoon representation.
It is shown that efficient and robust universal quantum computation is possible using the stimulated Raman adiabatic passage with a qubit chain as a pointer register.
We show a superpolynomial oracle separation between the power of adiabatic quantum computation with no sign problem and the power of classical computation.
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