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 possibilities to overcome this, for practical purposes, fundamental limitation of quantum computers.
We study effects of the physical realization of quantum computers on their logical operation. Through simulation of physical models of quantum computer hardware, we analyse the difficulties that are encountered in programming physical implementations of quantum computers. We discuss the origin of the instabilities of quantum algorithms and explore physical mechanisms to enlarge the region(s) of stable operation.
The task of programming a quantum computer is just as strange as quantum mechanics itself. But it now looks like a simple 3D puzzle may be the future tool of quantum software engineers.
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 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.
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.
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.
Arrays of weakly-coupled quantum systems can be made to compute by subjecting them to a sequence of electromagnetic pulses of well-defined frequency and length. Such pulsed arrays are true quantum computers: bits can be placed in superpositions of 0 and 1, logical operations take place coherently, and dissipation is required only for error correction. Programming such computers is accomplished by selecting the proper sequence of pulses.
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 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.
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.
In this paper we discuss analogue computers based on quantum optical systems accelerating dynamic programming for some computational problems. These computers, at least in principle, can be realized by actually existing devices. We estimate an acceleration in resolving of some NP-hard problems that can be obtained in such a way versus deterministic computers
Problems in realization of silicon-based solid-state NMR quantum computer with ensemble addressing to qubits are considered. It is presented the extension of Kane's scheme to ensemble approach version with strip gates. For the initialization of nuclear quantum states it is proposed to use the solid-state effect in ENDOR technique whereby the nuclear spins can be practically fully polarized or, that is the same, indirect cooled to the spin temperature less than ~ 1 mK. It is suggested the possible planar silicon topology of such ensemble quantum computer and shown that the measurement with stan…
We execute the quantum eraser, the Elitzur-Vaidman bomb, and the Hardy's paradox experiment using high-level programming language on a generic, gate-based superconducting quantum processor made publicly available by IBM. The quantum circuits for these experiments use a mixture of one-qubit and multi-qubit gates and require high entanglement gate accuracy. The results aligned with theoretical predictions of quantum mechanics to high confidence on circuits using up to 3 qubits. The power of quantum computers and high-level language as a platform for experimenting and studying quantum phenomena i…
We realize Landau-Streater (LS) and Werner-Holevo (WH) quantum channels for qutrits on the IBM quantum computers. These channels correspond to interaction between the qutrit and its environment that result in the globally unitarily covariant qutrit transformation violating multiplicativity of the maximal $p$-norm. Our realization of LS and WH channels is based on embedding qutrit states into states of two qubits and using single-qubit and two-qubit CNOT gates to implement the specific interaction. We employ the standard quantum gates hence the developed algorithm suits any quantum computer. We…
We report the realization, using nuclear magnetic resonance techniques, of the first quantum computer that reliably executes an algorithm in the presence of strong decoherence. The computer is based on a quantum error avoidance code that protects against a class of multiple-qubit errors. The code stores two decoherence-free logical qubits in four noisy physical qubits. The computer successfully executes Grover's search algorithm in the presence of arbitrarily strong engineered decoherence. A control computer with no decoherence protection consistently fails under the same conditions.
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 report the first demonstration of a quantum game on an all-optical one-way quantum computer. Following a recent theoretical proposal we implement a quantum version of Prisoner's Dilemma, where the quantum circuit is realized by a 4-qubit box-cluster configuration and the player's local strategies by measurements performed on the physical qubits of the cluster. This demonstration underlines the strength and versatility of the one-way model and we expect that this will trigger further interest in designing quantum protocols and algorithms to be tested in state-of-the-art cluster resources.
Searching for marked items from an unsorted database is an important scientific problem and a benchmark for computing devices as well. Using a 7-qubit liquid NMR quantum computer, we have demonstrated successfully an hybrid quantum fetching algorithm that finds marked items using only a single query. The essential idea is the operation of quantum computers in parallel. We gave the detailed pulse sequence for coherent control of the 7 qubits. The pulse sequence demonstrated here is not only useful for ensemble quantum computation, but also can be regarded as a general purpose control-gate which…
We have studied a system composed by two endohedral fullerene molecules. We have found that this system can be used as good candidate for the realization of Quantum Gates Each of these molecules encapsules an atom carrying a spin,therefore they interact through the spin dipole interaction. We show that a phase gate can be realized if we apply on each encased spin static and time dependent magnetic field. We have evaluated the operational time of a $π$-phase gate, which is of the order of ns. We made a comparison between the theoretical estimation of the gate time and the experimental decoheren…
This study examines the simulation of quantum algorithms on a classical computer. The program code implemented on a classical computer will be a straight connection between the mathematical formulation of quantum mechanics and computational methods. The computational language will include formulations such as quantum state, superposition and quantum operator.
A scheme for distributed quantum measurement that allows nondestructive or indirect Bell measurement was proposed by Gupta et al., (Int. J. Quant. Infor. \textbf{5} (2007) 627) and subsequently realized experimentally using an NMR-based three-qubit quantum computer by Samal et al., (J. Phys. B, \textbf{43} (2010) 095508). In the present work, a similar experiment is performed using the five-qubit super-conductivity-based quantum computer, which has been recently placed in cloud by IBM Corporation. The experiment confirmed that the Bell state can be constructed and measured in a nondestructive …
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.
While not yet in commercial existence, quantum computers have the ability to solve certain classes of problems that are not efficiently solvable on existing Turing Machine based (classical) computers. For quantum computers to be of use, methods of programming them must exist. Proposals exist for programming quantum computers, but all of the existing ones suffer from flaws that make them impractical in commercial software development environments. Cove is a framework for programming quantum computers that extends existing classical languages to allow for quantum computation, thus providing a qu…
Quantum computing is a new emerging computer technology. Current quantum computing devices are at a development stage where they are gradually becoming suitable for small real-world applications. This lecture is devoted to the practical aspects of programming such quantum computing devices. The first part of these lecture notes focuses on programming gate-based quantum computers, and the second part shows how to program quantum annealers.
With the rapid development of quantum hardware technologies, benchmarking the performance of quantum computers has become attractive. In this paper, we propose a new aspect of benchmarking quantum computers by evaluating the limitation of hardware utilization using a multi-programming mechanism -- a technique that simultaneously executes multiple circuits in a quantum machine. This is the first attempt to compare the evaluation of multi-programming on trapped-ion and superconducting devices. Based on the experimental results, performing multi-programming on a trapped-ion device demonstrates be…
The number of qubits in current quantum computers is a major restriction on their wider application. To address this issue, Ying conceived of using two or more small-capacity quantum computers to produce a larger-capacity quantum computing system by quantum parallel programming ([M. S. Ying, Morgan-Kaufmann, 2016]). In doing so, the main obstacle is separating the quantum gates in the whole circuit to produce a tensor product of the local gates. In this study, we theoretically analyse the (sufficient and necessary) separability conditions of multipartite quantum gates in finite or infinite dim…
We present a new quantum programming language called "Quala" that enables true full-stack programming of quantum hardware. Quala allows seamless integration of abstraction layers such as the digital circuit layer and the analog control pulse waveform layer. Additionally, the language supports user-issued low-level hardware instructions like FPGA actions. Mid-circuit measurements and branching decision logic support real-time, adaptive programs. This flexibility allows users to write code for everything from quantum error correction to analog quantum simulation. The combination of a user-facing…
It is well known that Grover's algorithm asymptotically transforms an equal superposition state into an eigenstate (of a given basis). Here, we demonstrate a verification algorithm based on weak measurement which can achieve the same purpose even if the qubit is not in an equal superposition state. The proposed algorithm highlights the distinguishability between any arbitrary single qubit superposition state and an eigenstate. We apply this algorithm to propose the scheme of a Quantum Locker, a protocol in which any legitimate party can verify his/her authenticity by using a newly developed qu…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental properties of complex systems. This formal language allows the expression of quantumized algorithms, which are extensions of randomized algorithms in that probabilities can be negative, and events can cancel out. An illustration of the power of quantumized algorithms is the ability to efficiently solve the satisfiability problem, something that many believe is beyon…
We propose a runtime architecture that can be used in the development of a quantum programming language and its programming environment. The proposed runtime architecture enables dynamic interaction between classical and quantum data following the restriction that a quantum computer is available in the cloud as a batch computer, with no interaction with the classical computer during its execution. It is done by leaving the quantum code generation for the runtime and introducing the concept of futures for quantum measurements. When implemented in a quantum programming language, those strategies…
It is well-known that decoherence is a crucial barrier in realizing various quantum information processing tasks; on the other hand, it plays a pivotal role in explaining how a quantum system's fragile state leads to the robust classical state. Zurek [Nat. Phys. 5, 181-188 (2009)] has developed the theory which successfully describes the emergence of classical objectivity of quantum system via decoherence, introduced by the environment. Here, we consider two systems for a model universe, in which the first system shows a random quantum state, and the other represents the environment. We take 2…
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.
A scheme for secure multiparty quantum summation was proposed by Run-hau Shi et al.,(SCIENTIFIC REPORTS, 6:19655, DOI:10.1038/srep19655). IBM Corporation has released a superconductivity based 5-qubit quantum computer named "Quantum Experience" and placed it on "cloud". In this paper we take advantage of the online availability of this real quantum processor(ibmqx2) and carry out the above protocol that has never been experimentally demonstrated earlier. Here, we set up experiments for secure quantum summation of one-qubit secret states . Besides, we propose a protocol for square and cubic sum…
Quantum process tomography is a procedure by which the unknown dynamical evolution of an open quantum system can be fully experimentally characterized. We demonstrate explicitly how this procedure can be implemented with a nuclear magnetic resonance quantum computer. This allows us to measure the fidelity of a controlled-not logic gate and to experimentally investigate the error model for our computer. Based on the latter analysis, we test an important assumption underlying nearly all models of quantum error correction, the independence of errors on different qubits.
Topological quantum computing has recently proven itself to be a powerful computational model when constructing viable architectures for large scale computation. The topological model is constructed from the foundation of a error correction code, required to correct for inevitable hardware faults that will exist for a large scale quantum device. It is also a measurement based model of quantum computation, meaning that the quantum hardware is responsible only for the construction of a large, computationally universal quantum state. This quantum state is then strategically consumed, allowing for…
To overcome the difficulty of realizing large-scale quantum Fourier transform (QFT) within existing technology, this paper presents a resource-saving method, namely t-bit semiclassical QFT over (Z_(2^n)), which could realize large-scale QFT using arbitrary-scale quantum register. Using our method, the scale of quantum register can be determined flexibility according to the scale of quantum system, enabling the quantum resource and speed of realizing QFT to be optimal. By developing a feasible method to realize the control quantum gate R_k, we experimentally demonstrate the 2-bit semiclassical …
Quantum computers are able to outperform classical algorithms. This was long recognized by the visionary Richard Feynman who pointed out in the 1980s that quantum mechanical problems were better solved with quantum machines. It was only in 1994 that Peter Shor came up with an algorithm that is able to calculate the prime factors of a large number vastly more efficiently than known possible with a classical computer. This paradigmatic algorithm stimulated the flourishing research in quantum information processing and the quest for an actual implementation of a quantum computer. Over the last fi…
Major obstacles remain to the implementation of macroscopic quantum computing: hardware problems of noise, decoherence, and scaling; software problems of error correction; and, most important, algorithm construction. Finding truly quantum algorithms is quite difficult, and many of these genuine quantum algorithms, like Shor's prime factoring or phase estimation, require extremely long circuit depth for any practical application, which necessitates error correction. In contrast, we show that machine learning can be used as a systematic method to construct algorithms, that is, to non-algorithmic…
The first realization of solid state quantum computer was demonstrated recently by using artificial atoms -- transmons in superconducting resonator. Here, we propose a novel architecture of flexible and scalable quantum computer based on a waveguide circuit coupling many quantum nodes of controlled atomic ensembles. For the first time, we found the optimal practically attainable parameters of the atoms and circuit for 100{%} efficiency of quantum memory for multi qubit photon fields and confirmed experimentally the predicted perfect storage. Then we revealed self modes for reversible transfer …
The quantum circuit model is an abstraction that hides the underlying physical implementation of gates and measurements on a quantum computer. For precise control of real quantum hardware, the ability to execute pulse and readout-level instructions is required. To that end, we introduce Qiskit Pulse, a pulse-level programming paradigm implemented as a module within Qiskit-Terra \cite{Qiskit}. To demonstrate the capabilities of Qiskit Pulse, we calibrate both un-echoed and echoed variants of the cross-resonance entangling gate with a pair of qubits on an IBM Quantum system accessible through th…
The equivalence between the instructions used to define programs and the input data on which the instructions operate is a basic principle of classical computer architectures and programming. Replacing classical data with quantum states enables fundamentally new computational capabilities with scaling advantages for many applications, and numerous models have been proposed for realizing quantum computation. However, within each of these models, the quantum data are transformed by a set of gates that are compiled using solely classical information. Conventional quantum computing models thus bre…
The emphasis is made on the juxtaposition of (quantum~theorem) proving versus quantum (theorem~proving). The logical contents of verification of the statements concerning quantum systems is outlined. The Zittereingang (trembling input) principle is introduced to enhance the resolution of predicate satisfiability problem provided the processor is in a position to perform operations with continuous input. A realization of Zittereingang machine by a quantum system is suggested.
Designing and implementing algorithms for medium and large scale quantum computers is not easy. In previous work we have suggested, and developed, the idea of using machine learning techniques to train a quantum system such that the desired process is "learned," thus obviating the algorithm design difficulty. This works quite well for small systems. But the goal is macroscopic physical computation. Here, we implement our learned pairwise entanglement witness on Microsoft's Q#, one of the commercially available gate model quantum computer simulators; we perform statistical analysis to determine…
Recent developments in quantum hardware indicate that systems featuring more than 50 physical qubits are within reach. At this scale, classical simulation will no longer be feasible and there is a possibility that such quantum devices may outperform even classical supercomputers at certain tasks. With the rapid growth of qubit numbers and coherence times comes the increasingly difficult challenge of quantum program compilation. This entails the translation of a high-level description of a quantum algorithm to hardware-specific low-level operations which can be carried out by the quantum device…
We discuss the problem of finite-horizon dynamic programming (DP) on a quantum computer. We introduce a query model for studying quantum and classical algorithms for solving DP problems, and provide example oracle constructions for the travelling salesperson problem, the minimum set-cover problem, and the edit distance problem. We formulate open questions regarding quadratic quantum speedups for DP and discuss their implications. We then prove lower bounds for the query complexity of quantum algorithms and classical randomized algorithms for DP, and show that no greater-than-quadratic speedup …
Qubit mapping is essential to quantum computing's fidelity and quantum computers' resource utilization. Yet, the existing qubit mapping schemes meet some challenges (e.g., crosstalk, SWAP overheads, diverse device topologies, etc.), leading to qubit resource under-utilization, high error rate, and low fidelity in computing results. This paper presents QuCloud+, a new qubit mapping scheme capable of handling these challenges. QuCloud+ has several new designs. (1) QuCloud+ enables multi-programming quantum computing on quantum chips with 2D/3D topology. (2) It partitions physical qubits for conc…
We report an experimental demonstration of a one-way implementation of a quantum algorithm solving Simon's Problem - a black box period-finding problem which has an exponential gap between the classical and quantum runtime. Using an all-optical setup and modifying the bases of single-qubit measurements on a five-qubit cluster state, key representative functions of the logical two-qubit version's black box can be queried and solved. To the best of our knowledge, this work represents the first experimental realization of the quantum algorithm solving Simon's Problem. The experimental results are…
