Numerical Analysis of Boosting Scheme for Scalable NMR Quantum Computation
Akira SaiToh, Masahiro Kitagawa
备注：
14 pages, 18 figures, RevTeX4, v2,v3: typos corrected, v4: minor changes in PROGRAM 1, conforming it to the actual programs used in the simulation, v5: correction of a typographical error in the inequality sign in PROGRAM 1, v6: this version contains a new section on classical correlations, v7: correction of a wrong use of terminology, v8: Appendix A has been added, v9: published in PRA
Among initialization schemes for ensemble quantum computation beginning at thermal equilibrium, the scheme proposed by Schulman and Vazirani [L. J. Schulman and U. V. 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.
We report the implementation of the central building block of the Schulman-Vazirani procedure for fully polarizing a subset of two-level quantum systems which are initially only partially polarized. This procedure consists of a sequence of unitary operations and incurs only a quasi-linear overhead in the number of quantum systems and operations required. The key building block involves three quantum systems and was implemented on a homonuclear three-spin system using room temperature liquid state nuclear magnetic resonance (NMR) techniques. This work was inspired by the state initialization ch…
Nuclear magnetic resonance offers an appealing prospect for implementation of quantum computers, because of the long coherence times associated with nuclear spins, and extensive laboratory experience in manipulating the spins with radio frequency pulses. Existing proposals, however, suffer from a signal-to-noise ratio that decays exponentially in the number of qubits in the quantum computer. This places a severe limit on the size of the computations that can be performed by such a computer; estimates of that limit are well within the range in which a conventional computer taking exponentially …
We present experimental results on the measurement of fidelity decay under contrasting system dynamics using a nuclear magnetic resonance quantum information processor. The measurements were performed by implementing a scalable circuit in the model of deterministic quantum computation with only one quantum bit. The results show measurable differences between regular and complex behaviour and for complex dynamics are faithful to the expected theoretical decay rate. Moreover, we illustrate how the experimental method can be seen as an efficient way for either extracting coarse-grained informatio…
We present here algorithmic cooling (via polarization-heat-bath)- a powerful method for obtaining a large number of highly polarized spins in liquid nuclear-spin systems at finite temperature. Given that spin-half states represent (quantum) bits, algorithmic cooling cleans dirty bits beyond the Shannon's bound on data compression, by employing a set of rapidly thermal-relaxing bits. Such auxiliary bits could be implemented using spins that rapidly get into thermal equilibrium with the environment, e.g., electron spins. Cooling spins to a very low temperature without cooling the environment cou…
An algorithm based on quantum phase estimation, which discriminates quantum states nondestructively within a set of arbitrary orthogonal states, is described and experimentally verified by a NMR quantum information processor. The procedure is scalable and can be applied to any set of orthogonal states. Scalability is demonstrated through Matlab simulation.
Nuclear Magnetic Resonance (NMR) has provided a valuable experimental testbed for quantum information processing (QIP). Here, we briefly review the use of nuclear spins as qubits, and discuss the current status of NMR-QIP. Advances in the techniques available for control are described along with the various implementations of quantum algorithms and quantum simulations that have been performed using NMR. The recent application of NMR control techniques to other quantum computing systems are reviewed before concluding with a description of the efforts currently underway to transition to solid st…
One-way quantum computing is an important and novel approach to quantum computation. By exploiting the existing particle-particle interactions, we report the first experimental realization of the complete process of deterministic one-way quantum Deutsch-Josza algorithm in NMR, including graph state preparation, single-qubit measurements and feed-forward corrections. The findings in our experiment may shed light on the future scalable one-way quantum computation.
We propose a scalable method on the basis of nth-order coupling operators to construct f-dependent phase transformations in the n-qubit modified Deutsch-Jozsa (D-J) quantum algorithm. The novel n-qubit entangling transformations are easily implemented via J-couplings between neighboring spins. The seven-qubit modified D-J quantum algorithm and seventh-order coupling transformations are then experimentally demonstrated with liquid state nuclear magnetic resonance (NMR) techniques. The method may offer the possibility of creating generally entangled states of n qubits and simulating n-body inter…
We have developed a concrete quantum simulation scheme and experimentally simulated a pairing model on an NMR quantum computer. The design of our experiment includes choosing an appropriate initial state in order to make our scheme scalable in near future, and the accomplishment of our experiment makes use of twice Fourier transforms so that our method is applicable to other physical models. Our results show that the experimental simulation can give the spectrum of the simulated Hamiltonian. Consequently, the potential power of a quantum computer on the simulation of complex physical systems i…
A proposal for a scalable, solid-state implementation of a quantum computer is presented. Qubits are fluorine nuclear spins in a solid crystal of fluorapatite [Ca_5 F(PO_4)_3] with resonant frequencies separated by a large field gradient. Quantum logic is accomplished using nuclear-nuclear dipolar couplings with decoupling and selective recoupling RF pulse sequences. Magnetic resonance force microscopy is used for readout. As many as 300 qubits can be implemented in the laboratory extremes of T=10 mK and B_0=20 T with the existing sensitivity of force microscopy.
Nuclear magnetic resonance (NMR) provides an experimental setting to explore physical implementations of quantum information processing (QIP). Here we introduce the basic background for understanding applications of NMR to QIP and explain their current successes, limitations and potential. NMR spectroscopy is well known for its wealth of diverse coherent manipulations of spin dynamics. Ideas and instrumentation from liquid state NMR spectroscopy have been used to experiment with QIP. This approach has carried the field to a complexity of about 10 qubits, a small number for quantum computation …
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…
In this paper, we report an experimental realization of quantum switch using nuclear spins and magnetic resonant pulses. The nuclear spins of H and C in carbon-13 labelled chloroform are used to carry the information, then nuclear magnetic resonance pulses are applied to perform either bypass or cross function to achieve the switching. Compared with a traditional space or time domain switch, this switching architecture is much more scalable, therefore a high throughput switching device can be built simply by increasing the number of I/O ports. In addition, it can be used not only as a device t…
Algorithmic Cooling is a method that uses novel data compression techniques and simplecquantum computing devices to improve NMR spectroscopy, and to offer scalable NMR quantum computers. The algorithm recursively employs two steps. A reversible entropy compression of the computation quantum-bits (qubits) of the system and an irreversible heat transfer from the system to the environment through a set of reset qubits that reach thermal relaxation rapidly. Is it possible to experimentally demonstrate algorithmic cooling using existing technology? To allow experimental algorithmic cooling, the the…
Application of multiple rounds of Quantum Error Correction (QEC) is an essential milestone towards the construction of scalable quantum information processing devices. However, experimental realizations of it are still in their infancy. The requirements for multiple round QEC are high control fidelity and the ability to extract entropy from ancilla qubits. Nuclear Magnetic Resonance (NMR) based quantum devices have demonstrated high control fidelity with up to 12 qubits. On the other hand, the major challenge in the NMR QEC experiment is to efficiently supply ancilla qubits in highly pure stat…
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 …
An efficient technique to generate ensembles of spins that are highly polarized by external magnetic fields is the Holy Grail in Nuclear Magnetic Resonance (NMR) spectroscopy. Since spin-half nuclei have steady-state polarization biases that increase inversely with temperature, spins exhibiting high polarization biases are considered cool, even when their environment is warm. Existing spin-cooling techniques are highly limited in their efficiency and usefulness. Algorithmic cooling is a promising new spin-cooling approach that employs data compression methods in open systems. It reduces the en…
Photonic measurement-based quantum computation (MBQC) is a promising route towards fault-tolerant universal quantum computing. A central challenge in this effort is the huge overhead in the resources required for the construction of large photonic clusters using probabilistic linear-optics gates. Although strong single-photon nonlinearity ideally enables deterministic construction of such clusters, it is challenging to realise in a scalable way. Here we explore the prospects of using moderate nonlinearity (with conditional phase shifts smaller than $π$) to boost photonic quantum computing and …
Linear chains of spins acting as quantum wires are a promising approach to achieve scalable quantum information processors. Nuclear spins in apatite crystals provide an ideal test-bed for the experimental study of quantum information transport, as they closely emulate a one-dimensional spin chain. Nuclear Magnetic Resonance techniques can be used to drive the spin chain dynamics and probe the accompanying transport mechanisms. Here we demonstrate initialization and readout capabilities in these spin chains, even in the absence of single-spin addressability. These control schemes enable prepari…
We propose a new design for a quantum information processor where qubits are encoded into Hyperfine states of ions held in a linear array of individually tailored microtraps and sitting in a spatially varying magnetic field. The magnetic field gradient introduces spatially dependent qubit transition frequencies and a type of spin-spin interaction between qubits. Single and multi-qubit manipulation is achieved via resonant microwave pulses as in liquid-NMR quantum computation while the qubit readout and reset is achieved through trapped-ion fluorescence shelving techniques. By adjusting the mic…
We have taken significant steps towards the realization of a practical quantum computer: using nuclear spins and magnetic resonance techniques at room temperature, we provided proof of principle of quantum computing in a series of experiments which culminated in the implementation of the simplest instance of Shor's quantum algorithm for prime factorization (15=3x5), using a seven-spin molecule. This algorithm achieves an exponential advantage over the best known classical factoring algorithms and its implementation represents a milestone in the experimental exploration of quantum computation. …
A significant hurdle towards realization of practical and scalable quantum computing is to protect the quantum states from inherent noises during the computation. In physical implementation of quantum circuits, a long-distance interaction between two qubits is undesirable since, it can be interpreted as a noise. Therefore, multiple quantum technologies and quantum error correcting codes strongly require the interacting qubits to be arranged in a nearest neighbor (NN) fashion. The current literature on converting a given quantum circuit to an NN-arranged one mainly considered chained qubit topo…
Searching large databases is an important problem with broad applications. The Grover search algorithm provides a powerful method for quantum computers to perform searches with a quadratic speedup in the number of required database queries over classical computers. It is an optimal search algorithm for a quantum computer, and has further applications as a subroutine for other quantum algorithms. Searches with two qubits have been demonstrated on a variety of platforms and proposed for others, but larger search spaces have only been demonstrated on a non-scalable NMR system. Here, we report res…
