Isaac L. Chuang, Lieven M. K. Vandersypen, Xinlan Zhou, Debbie W. Leung, Seth Lloyd
Nuclear magnetic resonance techniques are used to realize a quantum algorithm experimentally. The algorithm allows a simple NMR quantum computer to determine global properties of an unknown function requiring fewer function ``calls'' than is possible using a classical computer.
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The possibility of realization of quantum gates by means of the non-adiabatic geometric phase is considered. It is shown that the non-adiabatic phase can be used for quantum gates realization as well as the adiabatic one.
The purpose of this paper is to study the realization theory of quantum linear systems. It is shown that for a general quantum linear system its controllability and observability are equivalent and they can be checked by means of a simple matrix rank condition. Based on controllability and observability a specific realization is proposed for general quantum linear systems in which an uncontrollable and unobservable subspace is identified. When restricted to the passive case, it is found that a realization is minimal if and only if it is Hurwitz stable. Computational methods are proposed to fin…
Stochastic realization of the wave function in quantum mechanics, with the inclusion of soliton representation of extended particles, is discussed. The concept of Stochastic Qubits is used for quantum computing modeling.
We study effects of the physical realization of quantum computers on their logical operation. Through simulation of physical models of quantum computer hardware, we analyze the difficulties that are encountered in programming physical realizations of quantum computers. Examples of logically identical implementations of the controlled-NOT operation and Grover's database search algorithm are used to demonstrate that the results of a quantum computation are unstable with respect to the physical realization of the quantum computer. We discuss the origin of these instabilities and discuss possibili…
This paper has been withdrawn by the author due to some problems.
We demonstrate the implementation of quantum cheque, proposed by Roy Moulick and Panigrahi [Quantum Inf. Process (2016) 15: 2475], using the five-qubit IBM quantum computer. Appropriate single qubit, CNOT and Fredkin gates have been implemented for the realization of the quantum cheque transaction in a quantum networked banking system. Quantum state tomography reveals the accuracy of the implementation with comparable results from the theoretical and experimental density matrices.
A quantum cryptosystem is proposed using single-photon states with different frequency spectra as information carriers. A possible experimental implementation of the cryptosystem is discussed.
We relate gate fidelities of experimentally realized quantum operations to the broadcasting property of their ideal operations, and show that the more parties a given quantum operation can broadcast to, the higher gate fidelities of its experimental realization are in general. This is shown by establishing the correspondence between two operational quantities, quantum state shareability and quantum broadcasting. This suggests that, to assess an experimental realization using gate fidelities, the worst case of realization such as noisy operations should be taken into account and then compared t…
Design of a large-scale quantum computer has paramount importance for science and technologies. We investigate a scheme for realization of quantum algorithms using noncomposite quantum systems, i.e., systems without subsystems. In this framework, $n$ artificially allocated "subsystems" play a role of qubits in $n$-qubits quantum algorithms. With focus on two-qubit quantum algorithms, we demonstrate a realization of the universal set of gates using a $d=5$ single qudit state. Manipulation for an ancillary level in the systems allows effective implementation of operators from ${\rm U}(4)$ group …
We realize the probabilistic cloning and identifying linear independent quantum states of multi-particles system, given prior probability, with universal quantum logic gates using the method of unitary representation. Our result is universal for separate state and entanglement. We also provide the realization in the condition given $M$ initial copies for each state.
We present the first experimental demonstration of the ''optimal'' and ''universal'' quantum entangling process involving qubits encoded in the polarization of single photons. The structure of the ''quantum entangling machine'' consists of the quantum injected optical parametric amplifier by which the contextual realization of the 1->2 universal quantum cloning and of the universal NOT (U-NOT) gate has also been achieved.
In quantum information theory, entropic inequalities act as the necessary and sufficient conditions to noncontextuality. Here, we first experimentally demonstrate the violation of the entropic noncontextual inequality in a four-level quantum system, by using the five-qubit IBM quantum computer. The experimental result disproves the existence of a local realist model.
Boson realizations map operators and states of groups to transformations and states of bosonic systems. We devise a graph-theoretic algorithm to construct the boson realizations of the canonical SU$(n)$ basis states, which reduce the canonical subgroup chain, for arbitrary $n$. The boson realizations are employed to construct $\mathcal{D}$-functions, which are the matrix elements of arbitrary irreducible representations, of SU$(n)$ in the canonical basis. We demonstrate that our $\mathcal{D}$-function algorithm offers significant advantage over the two competing procedures, namely factorizatio…
We propose a scheme to realize $1\to 2$ universal quantum cloning machine (UQCM) with superconducting quantum interference device (SQUID) qubits, embeded in a high-Q cavity. CNOT operations are derived to present our scheme, and the two-photon Raman resonance processes are used to increase the operation rate. Compared with previous works, our scheme has advantages in the experimental realization and further utilization.
We prove that a generic three-qubit quantum logic gate can be implemented using at most 98 one-qubit rotations about the $y$- and $z$-axes and 40 CNOT gates, beating an earlier bound of 64 CNOT gates.
We establish a general principle for the tomographic approach to quantum state reconstruction, till now based on a simple rotation transformation in the phase space, which allows us to consider other types of transformations. Then, we will present different realizations of the principle in specific examples.
We propose and discuss a specific scheme allowing to realize a Quantum Cryptography qutrit protocol. This protocol exploits the polarization properties of single frequency and single spatial mode biphotons.
We report an experimental realization of entanglement concentration using two polarization-entangled photon pairs produced by pulsed parametric down-conversion. In the meantime, our setup also provides a proof-in-principle demonstration of a quantum repeater. The quality of our procedure is verified by observing a violation of Bell's inequality by more than 5 standard deviations. The high experimental accuracy achieved in the experiment implies that the requirement of tolerable error rate in multi-stage realization of quantum repeaters can be fulfilled, hence providing a practical toolbox for …
We report experimental implementation of discrete Fourier transformation(DFT) on a nuclear magnetic resonance(NMR) quantum computer. Experimental results agree with theoretical results. Using the pulse sequences we introduced, DFT can be realized on any L-bit quantum number in principle.
We present a computational circuit which realizes contextually the Tele-UNOT gate and the universal optimal quantum cloning machine (UOQCM). We report the experimental realization of the probabilistic UOQCM with polarization encoded qubits. This is achieved by combining on a symmetric beam-splitter the input qubit with an ancilla in a fully mixed state.
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.
A simultaneous realization of the Universal Optimal Quantum Cloning Machine (UOQCM) and of the Universal-NOT gate by a quantum injected optical parametric amplification (QIOPA), is reported. The two processes, forbidden in their exact form for fundamental quantum limitations, are found universal and optimal, and the measured fidelity F<1 is found close to the limit values evaluated by quantum theory. This work may enlighten the yet little explored interconnections of fundamental axiomatic properties within the deep structure of quantum mechanics.
The realization of transfer functions of Linear Quantum Stochastic Systems (LQSSs) is an issue of fundamental importance for the practical applications of such systems, especially as coherent controllers for other quantum systems. In this paper, we review two realization methods proposed by the authors in [1], [2], [3], [4]. The first one uses a cascade of a static linear quantum-optical network and single-mode optical cavities, while the second uses a feedback network of such cavities, along with static linear quantum-optical networks that pre- and post-process the cavity network inputs and o…
We study possible realizations of generalized quantum measurements on measurement-assisted programmable quantum processors. We focus our attention on the realization of von Neumann measurements and informationally complete POVMs. It is known that two unitary transformations implementable by the same programmable processor require mutually {\it orthogonal} states. It turns out that the situation with von Neumann measurements is different. Specifically, in order to realize two such measurements one does not have to use orthogonal program states. On the other hand, the number of the implementable…
We report the realization of an entangled quantum superposition of M=12 photons by a high gain, quantum-injected optical parametric amplification. The system is found so highly resilient against decoherence to exhibit directly accessible mesoscopic interference effects at normal temperature. By modern tomographic methods the non-separability and the quantum superposition are demonstrated for the overall mesoscopic output state of the dynamic ''closed system''. The device realizes the condition conceived by Erwin Schroedinger with his 1935 paradigmatic ''Cat'' apologue, a fundamental landmark i…
We discuss an efficient physical realization of topological quantum walks on a finite lattice. The $N$-point lattice is realized with $\log_2 N$ qubits, and the quantum circuit utilizes a number of quantum gates which is polynomial in the number of qubits. In a certain scaling limit, we show that a large number of steps is implemented with a number of quantum gates which is independent of the number of steps. We ran the quantum algorithm on the IBM-Q five-qubit quantum computer, thus experimentally demonstrating topological features, such as boundary bound states, on a lattice with $N=4$ point…
Among the many proposals for the realization of a quantum computer, holonomic quantum computation (HQC) is distinguished from the rest in that it is geometrical in nature and thus expected to be robust against decoherence. Here we analyze the realization of various quantum gates by solving the inverse problem: Given a unitary matrix, we develop a formalism by which we find loops in the parameter space generating this matrix as a holonomy. We demonstrate for the first time that such a one-qubit gate as the Hadamard gate and such two-qubit gates as the CNOT gate, the SWAP gate and the discrete F…
By a significant modification of the standard protocol of quantum state Teleportation two processes ''forbidden'' by quantum mechanics in their exact form, the Universal NOT gate and the Universal Optimal Quantum Cloning Machine, have been implemented contextually and optimally by a fully linear method. In particular, the first experimental demonstration of the Tele-UNOT Gate, a novel quantum information protocol has been reported (cfr. quant-ph/0304070). A complete experimental realization of the protocol is presented here.
The quantum dynamics of a driven single-band tight-binding model with different boundary conditions is considered. The relation between the Hamiltonian describing the single-band tight-binding dynamics and the Hamiltonian of a discrete-charge mesoscopic quantum circuit is elucidated. It is shown that the former Hamiltonian, with Dirichlet boundary conditions, can be considered as a realization of the deformed parafermionic polynomial algebras.
We generalize the quantum Prisoner's Dilemma to the case where the players share a non maximally entangled states. We show that the game exhibits an intriguing structure as a function of the amount of entanglement with two thresholds which separate a classical region, an intermediate region and a fully quantum region. Furthermore this quantum game is experimentally realized on our nuclear magnetic resonance quantum computer.
Due to its geometric nature, holonomic quantum computation is fault-tolerant against certain types of control errors. Although proposed more than a decade ago, the experimental realization of holonomic quantum computation is still an open challenge. In this Letter, we report the first experimental demonstration of nonadiabatic holonomic quantum computation in liquid NMR quantum information processors. Two non-commuting holonomic single-qubit gates, rotations about x-axis and about z-axis, and the two-qubit holonomic control-NOT gate are realized with high fidelity by evolving the work qubits a…
We report the realization of a nuclear magnetic resonance (NMR) quantum computer which combines the quantum Fourier transform (QFT) with exponentiated permutations, demonstrating a quantum algorithm for order-finding. This algorithm has the same structure as Shor's algorithm and its speed-up over classical algorithms scales exponentially. The implementation uses a particularly well-suited five quantum bit molecule and was made possible by a new state initialization procedure and several quantum control techniques.
Quantum walks are a promising framework for developing quantum algorithms and quantum simulations. They represent an important test case for the application of quantum computers. Here we present different forms of discrete-time quantum walks (DTQWs) and show their equivalence for physical realizations. Using an appropriate digital mapping of the position space on which a walker evolves to the multiqubit states of a quantum processor, we present different configurations of quantum circuits for the implementation of DTQWs in one-dimensional position space. We provide example circuits for a five-…
Practical Scheme for Realization of a Quantum Battery
本研究提出一种由非马尔可夫环境下结构化储库中原子-腔相互作用系统构成的量子电池实用方案，探究腔-储库耦合多参数对电池性能的影响，方案简单有望实际落地。
We report the experimental realization and characterization of one 60-mode copy, and of two 30-mode copies, of a dual-rail quantum-wire cluster state in the quantum optical frequency comb of a bimodally pumped optical parametric oscillator. This is the largest entangled system ever created whose subsystems are all available simultaneously. The entanglement proceeds from the coherent concatenation of a multitude of EPR pairs by a single beam splitter, a procedure which is also a building block for the realization of hypercubic-lattice cluster states for universal quantum computing.
Using virtual spin formalism it is shown that a quantum particle with eight energy levels can store three qubits. The formalism allows to realize a universal set of quantum gates. Feasible formalism implementation is suggested which uses nuclear spin-7/2 as a storage medium and radio frequency pulses as the gates. One pulse realization of all universal gates has been found, including three-qubit Toffoli gate.
The essence of the famed long-range entanglement as revealed in topologically ordered state is the paradoxical coexistence of short-range correlation and nonlocal information that cannot be removed through constant-depth local quantum circuits. Its realization in different quantum states is a focus research topic in both quantum computation and quantum matter. However, the proved realizations are subject to the paradigm of topological order (including its extensions), i.e. via a quantum code structure with macroscopic code distance. Here, we broaden the knowledge of long-range entangled states…
Nonlinear optical realization of non-integrable phases accompanying quantum phase transitions
本文提出利用具有四方对称性的各向异性低双折射光纤中的非线性光学效应，通过绝热调节非线性磁化率使斯托克斯矢量积累与量子相变具有相同规范结构的非可积 Hannay 角，并讨论了纳米晶体沉积的实验实现方案。
We present a scheme for realization of quantum mechanical weak values of observables using entangled photons produced in parametric down conversion. We consider the case when the signal and idler modes are respectively in a coherent state and vacuum. We use a low efficiency detector to detect the photons in the idler mode.This weak detection leads to a large displacement and fluctuations in the signal field's quantum state which can be studied by monitoring the photon number and quadrature distributions.
Shor's algorithm can find prime factors of a large number more efficiently than any known classical algorithm. Understanding the properties that gives the speedup is essential for a general and scalable construction. Here we present a realization of Shor's algorithm, that does not need any of the simplifications presently needed in current experiments and also gives smaller systematic errors than any former experimental implementation. Our realization is based on classical pass-transistor logic, runs at room temperature, and uses the same amount of resources as a scalable quantum computer. In …
A general multi-step N->M probabilistic optimal universal cloning protocol is presented together with the experimental realization of the (1 -> 3) and (2 -> 3) machines. Since the present method exploits the bosonic nature of the photons, it can be applied to any particle obeying to the Bose statistics. On a technological perspective, the present protocol is expected to find applications as a novel, multi-qubit symmetrizator device to be used in modern quantum information networks.
Atomic Interferometer has two quantum unitary gates that must be realized for quantum sensing purposes from atomic gravimeter and atomic interferometer gyroscope. An optimal cost function which define the distance between two unitary operator is defines and based on it a pulse based stochastic gradient descent algorithm is derived for implementation of atomic mirror and atomic beam-splitter gates. By using numerical optimal control for those gate realization, we achieved to gate fidelity of 0.995 and 0.998 for mirror and beam-splitter gates, respectively. For this research, a two-level atomic …
We implement a quantum walk in phase space with a new mechanism based on the superconducting resonator-assisted double quantum dots. By analyzing the hybrid system, we obtain the necessary factors of realization of a quantum walk in phase space: the walker, coin, coin flipping and conditional phase shift. In order to implement the coin flipping operator, we add a driving field to the resonator. The interaction between the quantum dots and resonator field is used to implement conditional phase shift. Furthermore, we show with different driving fields the quantum walk in phase space exhibits a b…
According to the theoretical results, the quantum searching algorithm can be generalized by replacing the Walsh-Hadamard(W-H) transform by almost any quantum mechanical operation. We have implemented the generalized algorithm using nuclear magnetic resonance techniques with a solution of chloroform molecules. Experimental results show the good agreement between theory and experiment.
In this paper, the degenerate ground states of Z2 topological order on a plane with holes (the so-called surface codes) are used as the protected code subspace to build a topological quantum computer by tuning their quantum tunneling effect. Using a designer Hamiltonian - the Kitaev toric-code model as an example, we study quantum tunneling effects of the surface codes and obtain its effective theory. Finally, we show how to do topological quantum computation including the initialization, the unitary transformation and the measurement.
Quantum mechanics forbids deterministic discrimination among non-orthogonal states. Nonetheless, the capability to distinguish nonorthogonal states unambiguously is an important primitive in quantum information processing. In this work, we experimentally implement generalized measurements in an optical system and demonstrate the first optimal unambiguous discrimination between three nonorthogonal states, with a success rate of 55%, to be compared with the 25% maximum achievable using projective measurements. Furthermore we present the first realization of unambiguous discrimination between a p…
Any residual coupling of a quantum computer to the environment results in computational errors. Encoding quantum information in a so-called decoherence-free subspace provides means to avoid these errors. Despite tremendous progress in employing this technique to extend memory storage times by orders of magnitude, computation within such subspaces has been scarce. Here, we demonstrate the realization of a universal set of quantum gates acting on decoherence-free ion qubits. We combine these gates to realize the first controlled-NOT gate within a decoherence-free, scalable quantum computer.
In this article, we review the basic concepts of quantum radars as such types of the devices while highlighting differences with their classical analogs. We discuss how several concepts from traditional radars technology, e.g., target detection sensitivity, noise resilience and ranging accuracy can be translated to quantum radars. We examine such new far-field sensing protocols as quantum illumination (QI), and engineering opportunities enabled by its different realizations. We consider possibilities of achieving super-sensitivity and super-resolution using quantum correlations, and discuss po…
We report an experimental realization of one-way quantum computing on a two-photon four-qubit cluster state. This is accomplished by developing a two-photon cluster state source entangled both in polarization and spatial modes. With this special source, we implemented a highly efficient Grover's search algorithm and high-fidelity two qubits quantum gates. Our experiment demonstrates that such cluster states could serve as an ideal source and a building block for rapid and precise optical quantum computation.
Holonomic quantum computation is the idea to use non-Abelian geometric phases to implement universal quantum gates that are robust to fluctuations in control parameters. Here, we propose a compact design for a holonomic quantum computer based on coupled three-level systems. The scheme does not require adiabatic evolution and can be implemented in arrays of atoms or ions trapped in tailored standing wave potentials.
We demonstrate a five-bit nuclear-magnetic-resonance quantum computer that distinguishes among various functions on four bits, making use of quantum parallelism. Its construction draws on the recognition of the sufficiency of linear coupling along a chain of nuclear spins, the synthesis of a suitably coupled molecule, and the use of a multi-channel spectrometer.
We report the first experimental realization of an ''optimal'' quantum device able to perform a Minimal Disturbance Measurement (MDM) on polarization encoded qubits saturating the theoretical boundary established between the classical knowledge acquired of any input state, i.e. the classical "guess", and the fidelity of the same state after disturbance due to measurement . The device has been physically realized by means of a linear optical qubit manipulation, post-selection measurement and a classical feed-forward process.
Quantum state transfer between different sites is a significant problem for quantum networks and quantum computers. By selecting quantum walks with two coins as the basic model and two coin spaces as the communication carriers, we successfully implement quantum state transfer on various graphs (EPL, \textbf{124} (2018) 60009) \cite{Shang_2019}. Here, we demonstrate the experimental implementation of this scheme using IBM quantum experience platform. In particular, we show the transfer of Bell state, GHZ state and W state on complete graph on the quantum device. Also, we observe that our protoc…
The connection between the quantum-vacuum geometric phases (which originates from the vacuum zero-point electromagnetic fluctuation) and the non-normal product procedure is considered in the present Letter. In order to investigate this physically interesting geometric phases at quantum-vacuum level, we suggest an experimentally feasible scheme to test it by means of a noncoplanarly curved fiber made of gyrotropic media. A remarkable feature of the present experimental realization is that one can easily extract the nonvanishing and nontrivial quantum-vacuum geometric phases of left- and/or righ…
The 1->3 quantum phase covariant cloning, which optimally clones qubits belonging to the equatorial plane of the Bloch sphere, achieves the fidelity Fcov(1->3)=0.833, larger than for the 1->3 universal cloning Funiv(1->3)=0.778. We show how the 1->3 phase covariant cloning can be implemented by a smart modification of the standard universal quantum machine by a projection of the output states over the symmetric subspace. A complete experimental realization of the protocol for polarization encoded qubits based on non-linear and linear methods will be discussed.
Optimal quantum machines can be implemented by linear projective operations. In the present work a general qubit symmetrization theory is presented by investigating the close links to the qubit purification process and to the programmable teleportation of any generic optimal anti-unitary map. In addition, the contextual realization of the N ->M cloning map and of the teleportation of the N->(M-N) universal NOT gate is analyzed by a novel and very general angular momentum theory. An extended set of experimental realizations by state symmetrization linear optical procedures is reported. These in…
The possibilities of recording, storage and reconstruction of short single photon wave packets in the photon echo technique are analyzed. The influence of the photon field and medium parameters on the quality and precision of the photon quantum state reconstruction is theoretically studied.
Dissipative realization of a quantum distance-based classifier using open quantum walks
本文展示了在开放量子行走计算模型中运行先前提出的量子距离分类器的可行性，并证明其预期运行时间在较慢的 regime 中仍保持有限。
We report the first experimental demonstration of a quantum controlled-NOT gate for different photons, which is classically feed-forwardable. In the experiment, we achieved this goal with the use only of linear optics, an entangled ancillary pair of photons and post-selection. The techniques developed in our experiment will be of significant importance for quantum information processing with linear optics.
We present a scheme to achieve maximally entangled states, controlled phase-shift gate, and SWAP gate for two superconducting-quantum-interference-device (SQUID) qubits, by placing SQUIDs in a microwave cavity. We also show how to transfer quantum information from one SQUID qubit to another. In this scheme, no transfer of quantum information between the SQUIDs and the cavity is required, the cavity field is only virtually excited and thus the requirement on the quality factor of the cavity is greatly relaxed.
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