Ensemble Quantum Computation Research Articles

Experimental realization of post-selected weak measurements on an NMR quantum processor

The ability to post-select the outcomes of an experiment is a useful theoretical concept and experimental tool. In the context of weak measurements, post-selection can lead to surprising results such as complex weak values outside the range of eigenvalues. Usually post-selection is realized by a projective measurement, which is hard to implement in ensemble systems such as NMR. We demonstrate the first experiment of a weak measurement with post-selection on an NMR quantum information processor. Our setup is used for measuring complex weak values and weak values outside the range of eigenvalues. The scheme for overcoming the problem of post-selection in an ensemble quantum computer is general and can be applied to any circuit-based implementation. This experiment paves the way for studying and exploiting post-selection and weak measurements in systems where projective measurements are hard to realize experimentally.

Bounds on the quantity of entanglement in parallel quantum computing of a single ensemble quantum computer

Speeding up of the processing of quantum algorithms has been focused on from the point of view of an ensemble quantum computer (EQC) working in a parallel mode. As a consequence of such efforts, additional speed up has been achieved for processing both Shor’s and Grover’s algorithms. On the other hand, in the literature there is scarce concern about the quantity of entanglement contained in EQC approaches, for this reason in the present work we study such a quantity. As a first result, an upper bound on the quantity of entanglement contained in EQC is imposed. As a main result we prove that equally weighted states are not appropriate for EQC working in parallel mode. In order that our results are not exclusively purely theoretical, we exemplify the situation by discussing the entanglement on an ensemble of n1 = 3 diamond quantum computers.

Modelling Parallel Quantum Computing Using Transactional Memory

We propose a model for parallel quantum computing in a single ensemble quantum computer using Haskell's software transaction memory. The parallel ensemble quantum computer possesses, besides quantum parallelism, a kind of classical single-instruction-multiple-data parallelism. It explores additional speedup by making quantum computers working in parallel, as in classical computation. The whole state is prepared in such a way a subset of qubits is in a mixed state representing the communicating quantum computers while the other qubits in pure state are the proper argument registers of each quantum computer. Essentially, this particular way of structuring the state of the parallel quantum computer fits with what is well know as multithreading programming. Software transactional memory is a promising new approach to programming shared-memory parallel programs. The functional programming language Haskell elegantly implements this abstraction for concurrent communication.

Testing Evolution Equation for Entanglement of Two-Qubit Systems in Noisy Channels on Ensemble Quantum Computers

We report the experimental demonstration of decoherence dynamics of entanglement for the four Bell states in two-qubit nuclear-spin systems on ensemble quantum computers. Using artificial error operators to simulate noisy channels, we experimentally investigate the effect of noises on the four Bell states, and furthermore observe the time evolution of entanglement for the four Bell states in different noisy channels by calculating concurrences. Our experimental results show that the concurrences of the different Bell states under the same artificial error operations have the same values within the experimental error, and are independent of the different Bell states. These experimental results verify the theoretical evolution equation developed by Konrad et al.[Nature Phys. 4 (2008) 99] for two-qubit entanglement.

Preservation of quantum states via a super-Zeno effect on ensemble quantum computers

Following a recent proposal by Dhar et al (2006 Phys. Rev. Lett. 96 100405), we demonstrate experimentally the preservation of quantum states in a two-qubit system based on a super-Zeno effect using liquid-state nuclear magnetic resonance techniques. Using inverting radiofrequency pulses and delicately selecting time intervals between two pulses, we suppress the effect of decoherence of quantum states. We observe that preservation of the quantum state |11⟩ with the super-Zeno effect is three times more efficient than the ordinary one with the standard Zeno effect.

Algorithms on ensemble quantum computers.

In ensemble (or bulk) quantum computation, all computations are performed on an ensemble of computers rather than on a single computer. Measurements of qubits in an individual computer cannot be performed; instead, only expectation values (over the complete ensemble of computers) can be measured. As a result of this limitation on the model of computation, many algorithms cannot be processed directly on such computers, and must be modified, as the common strategy of delaying the measurements usually does not resolve this ensemble-measurement problem. Here we present several new strategies for resolving this problem. Based on these strategies we provide new versions of some of the most important quantum algorithms, versions that are suitable for implementing on ensemble quantum computers, e.g., on liquid NMR quantum computers. These algorithms are Shor’s factorization algorithm, Grover’s search algorithm (with several marked items), and an algorithm for quantum fault-tolerant computation. The first two algorithms are simply modified using a randomizing and a sorting strategies. For the last algorithm, we develop a classical-quantum hybrid strategy for removing measurements. We use it to present a novel quantum fault-tolerant scheme. More explicitly, we present schemes for fault-tolerant measurement-free implementation of Toffoli and sigma_{z}^{1/4}, as these operations cannot be implemented “bitwise”, and their standard fault-tolerant implementations require measurement.

Quantum Parallelism as a Tool for Ensemble Spin Dynamics Calculations

Efficient simulations of quantum evolutions of spin-1/2 systems are relevant for ensemble quantum computation as well as in typical NMR experiments. We propose an efficient method to calculate the dynamics of an observable provided that the initial excitation is "local." It resorts to a single entangled pure initial state built as a superposition, with random phases, of the pure elements that compose the mixture. This ensures self-averaging of any observable, drastically reducing the calculation time. The procedure is tested for two representative systems: a spin star (cluster with random long range interactions) and a spin ladder.

Simulation of general three-body interactions in a nuclear magnetic resonance ensemble quantum computer

Three-body interaction plays an important role in many-body physics, and quantum computer is efficient in simulating many-body interactions. We have experimentally demonstrated the general three-body interactions in a three-qubit nuclear magnetic resonance ensemble quantum computer. Using a nuclear magnetic resonance computer we implemented general forms of three-body interactions including σ 1 x σ 2 z σ 3 x and σ 1 x σ 2 z σ 3 y The results show good agreement between theory and experiment. We have also given a concise and practical formula for a general n-body interaction in terms of one-and two-body interactions.

Experimental Realization of Arbitrary Accuracy Iterative Phase Estimation Algorithms on Ensemble Quantum Computers

We report the first experimental demonstration of a nuclear magnetic resonance (NMR) realization of iterative phase estimation algorithms. Using feedback and iterations, we experimentally obtain the phase with 6 bits of precision on a two-qubit NMR quantum computer. Furthermore, we experimentally demonstrate the effect of gate noise on the iterative phase estimation algorithm. Our experimental results show that errors of measurements of the phase depend strongly on the precision of coupling gates. This experiment can be used as a benchmark for multi-qubit realizations of quantum information processing and precision measurements.

Publisher's Note: Efficient algorithm for multiqudit twirling for ensemble quantum computation [Phys. Rev. A75, 042311 (2007)

Publisher's Note: Efficient algorithm for multiqudit twirling for ensemble quantum computation [Phys. Rev. A<b>75</b>, 042311 (2007)

Cooling toolbox for atoms in optical lattices

We propose and analyse several schemes for cooling bosonic and fermionic atoms in an optical lattice potential close to the ground state of the no-tunnelling regime. Some of the protocols rely on the concept of algorithmic cooling, which combines occupation number filtering with ideas from ensemble quantum computation. We also design algorithms that create an ensemble of defect-free quantum registers. We study the efficiency of our protocols for realistic temperatures and in the presence of a harmonic confinement. We also propose an incoherent physical implementation of filtering which can be operated in a continuous way.

Ensemble quantum computation and algorithmic cooling in optical lattices

AbstractWe show how to perform universal quantum computation with atoms confined in optical lattices which works both in the presence of defects and without individual addressing. We further present a scheme for cooling atoms close to the ground state of the Mott‐insulator regime. This method is based on a similar set of operations as for ensemble quantum computation and aims at cooling to temperatures which are low enough for the experimental realization of quantum simulation in present setups.

Quantum and classical parallelism in parity algorithms for ensemble quantum computers

The determination of the parity of a string of $N$ binary digits is a well-known problem in classical as well as quantum information processing, which can be formulated as an oracle problem. It has been established that quantum algorithms require at least $N∕2$ oracle calls. We present an algorithm that reaches this lower bound and is also optimal in terms of additional gate operations required. We discuss its application to pure and mixed states. Since it can be applied directly to thermal states, it does not suffer from signal loss associated with pseudo-pure-state preparation. For ensemble quantum computers, the number of oracle calls can be further reduced by a factor ${2}^{k}$, with $k∊{1,2,\dots{},{\mathrm{log}}_{2}(N∕2)}$, provided the signal-to-noise ratio is sufficiently high. This additional speed-up is linked to (classical) parallelism of the ensemble quantum computer. Experimental realizations are demonstrated on a liquid-state NMR quantum computer.

Numerical analysis of boosting scheme for scalable NMR quantum computation

Among initialization schemes for ensemble quantum computation beginning at thermal equilibrium, the scheme proposed by Schulman and Vazirani [in Proceedings of the 31st ACM Symposium on Theory of Computing (STOC'99) (ACM Press, New York, 1999), pp. 322--329] is known for the simple quantum circuit to redistribute the biases (polarizations) of qubits and small time complexity. However, our numerical simulation shows that the number of qubits initialized by the scheme is rather smaller than expected from the von Neumann entropy because of an increase in the sum of the binary entropies of individual qubits, which indicates a growth in the total classical correlation. This result---namely, that there is such a significant growth in the total binary entropy---disagrees with that of their analysis.

Ensemble Quantum Computation with Atoms in Periodic Potentials

We show how to perform universal quantum computation with atoms confined in optical lattices which works both in the presence of defects and without individual addressing. The method is based on using the defects in the lattice, wherever they are, both to "mark" different copies on which ensemble quantum computation is carried out and to define pointer atoms which perform the quantum gates. We also show how to overcome the problem of scalability in this system.

Realization of the new summing algorithm on an NMR ensemble quantum computer

A summing algorithm is to evaluate and sum up a set of function samples. The paper [J. Phys. A. 35, L597(2001)] presented a new summing algorithm using ensemble computing which results in an exponential speedup. Here, we experimentally implemented the new algorithm on a four-qubit liquid state nuclear magnetic resonance ensemble system.

Parallel quantum computing in a single ensemble quantum computer

We propose a parallel quantum computing mode for ensemble quantum computer. In this mode, some qubits are in pure states while other qubits are in mixed states. It enables a single ensemble quantum computer to perform ``single-instruction-multidata'' type of parallel computation. Parallel quantum computing can provide additional speedup in Grover's algorithm and Shor's algorithm. In addition, it also makes a fuller use of qubit resources in an ensemble quantum computer. As a result, some qubits discarded in the preparation of an effective pure state in the Schulman-Varizani and the Cleve-DiVincenzo algorithms can be reutilized.

Experimental realization of a fetching algorithm in a 7-qubit NMR spin Liouville space computer

Using a 7-qubit spin Liouville space computer, we have demonstrated successfully a fetching algorithm that finds marked items using only a single query. The essential idea is the operation of quantum computers in classical parallel. We gave the detailed pulse sequence for coherent control of the 7 qubits. A generalization of the pulse sequences for arbitrary qubit number is also provided.

Laser phase modulation approaches towards ensemble quantum computing.

Selective control of decoherence is demonstrated for a multilevel system by generalizing the instantaneous phase of any chirped pulse as individual terms of a Taylor series expansion. In the case of a simple two-level system, all odd terms in the series lead to population inversion, while the even terms lead to self-induced transparency. These results also hold for multiphoton transitions that do not have any lower-order photon resonance or any intermediate virtual state dynamics within the laser pulse width. Such results form the basis of a robustly implementable CNOT gate.

A simulator for ensemble quantum computing

A quantum computer simulator based on the principles of ensemble quantum computing using nuclear magnetic resonance (NMR) is presented. The first version of ensemble quantum computer simulator (enQC-lator) is based on density matrix description of the NMR and models the implementation of quantum computation in a NMR spectrometer. The simulator is designed to perform general purpose quantum computing and will be useful to evaluate quantum-computing codes prior to their actual implementation and to design new ones. The performance of the simulator is demonstrated in several logical operations and algorithms.