NMR Quantum Computer Research Articles

Minimum-Time Selective Control of Homonuclear Spins

In NMR (Nuclear Magnetic Resonance) quantum computation, the selective control of multiple homonuclear spins is usually slow because their resonance frequencies are very close to each other. To quickly implement controls against decoherence effects, this paper presents an efficient numerical algorithm fordesigning minimum-time local transformations in two homonuclear spins. We obtain an accurate minimum-time estimation via geometric analysis on the two-timescale decomposition of the dynamics. Such estimation narrows down the range of search for the minimum-time control with a gradient-type optimization algorithm. Numerical simulations show that this method can remarkably reduce the search efforts, especially when the frequency difference is very small and the control field is high. Its effectiveness is further demonstrated by NMR experiments with two homunuclear carbon spins in a trichloroethylene (C2H1Cl3) sample system.

Engineering of an all-heteronuclear 5-qubit NMR quantum computer.

The realization of an all-heteronuclear 5-qubit nuclear magnetic resonance quantum computer is reported, from the design and synthesis of a suitable molecule through the engineering of a prototype 6-channel probe head. Full control over the quantum computer is shown by a benchmark experiment.

Time-optimized quantum QFT gate in an Ising coupling system

Quantum Fourier transform (QFT) is a quantum analogue of the classical discrete Fourier transform. It is a fundamental quantum gate in quantum algorithms which has an exponential advantage over the classical computation and has been excessively studied. Normally, an n-qubit quantum Fourier transform could be resolved into the tensor product of n single-qubit operations, and each operation could be implemented by a Hadamard gate and a controlled phase gate. Then the complexity of an n-qubit QFT is of order O(n2). To reduce the complexity of quantum operations, optimal control (OC) method has recently been used successfully to find the minimum time for implementing a quantum operation. Up to now, two types of quantum optimal control methods have been presented, i.e. analytical and numerical methods. The analytical approach is to change the problem of efficient synthesis of unitary transformations into the geometrical one of finding the shortest paths. Numerical optimal control procedures are based on the gradient methods (GRAPE, Gradient Ascent Pulse Engineering) and Krotov methods. Notable application mainly focus on nuclear magnetic resonance fields, including imaging, liquid-state NMR, solid-state NMR, and NMR quantum computation. One obvious advantage of optimal control NMR quantum computation is that the OC unitary evolution transformation pulse sequences are normally shorter than the conventional corresponding ones. Here we use the optimal control method to find the minimum duration for implementing QFT quantum gate. A linear spin chain with nearest-neighbor Ising interaction is used to find the optimization. And the optimized pulse sequence is experimentally demonstrated on an NMR quantum information processor. By using optimal control method with numerical calculation, a three-qubit QFT in an indirect-linear-coupling chain system is optimized. The duration of the OC QFT is obviously shorter than that of conventional approaches. The OC pulse sequence has been experimentally implemented on a liquid-state NMR spectrometer. To verify the optimally controlled pulse sequence for the three-qubit QFT, different initial states are assumed. The accuracy of the OC pulse sequence could be demonstrated by the consistency of theoretical simulation spectra with the experimental results. The good consistency between the simulation and the experimental spectra demonstrates that the OC QFT is of high fidelity.

Experimental heat-bath cooling of spins

Algorithmic cooling (AC) is a method to purify quantum systems, such as ensembles of nuclear spins, or cold atoms in an optical lattice. When applied to spins, AC produces ensembles of highly polarized spins, which enhance the signal strength in nuclear magnetic resonance (NMR). According to this cooling approach, spin-half nuclei in a constant magnetic field are considered as bits, or more precisely quantum bits, in a known probability distribution. Algorithmic steps on these bits are then translated into specially designed NMR pulse sequences using common NMR quantum computation tools. The algorithmic cooling of spins is achieved by alternately combining reversible, entropy-preserving manipulations (borrowed from data compression algorithms) with selective reset, the transfer of entropy from selected spins to the environment. In theory, applying algorithmic cooling to sufficiently large spin systems may produce polarizations far beyond the limits due to conservation of Shannon entropy. Here, only selective reset steps are performed, hence we prefer to call this process “heat-bath” cooling, rather than algorithmic cooling. We experimentally implemented two consecutive steps of selective reset, thus transferring entropy from two selected spins to the environment. We performed such cooling experiments, with commercially available labeled molecules, on standard liquid-state NMR spectrometers. We report in particular on our original experiment, unpublished until now except on the arXiv (quant-ph/0511156) in 2005, which was, to the best of our knowledge, the world’s first experiment that yielded polarizations results that bypassed Shannon’s entropy-conservation bound, so that the entire spin-system was cooled.

SPIN MODEL OF FULL SUMMATOR ON PERES GATES

Four-spin model of single-digit summator for solid state nuclear magnetic resonance (NMR) quantum computer is proposed. Correctness of summator’s operation is analyzed in dependence of system parameters. It is found that the summator on Peres gates works correctly in time of four π-pulses on pure numerical and superposition states. Optimal values for exchange in teractions and maximum distance between q- bits necessary for correct summator’s operation are obtained from the analysis of fidelity function.

Efficient entanglement operator for a multi-qubit system

In liquid-state nuclear magnetic resonance quantum computation, a selective entanglement operator between qubits 2 and 3 of a three-qubit molecule is conventionally realized by applying a pair of short π-pulses to qubit 1. This method, called refocusing, is well suited to heteronuclear molecules. When the molecule is homonuclear, however, the π-pulses applied to qubit 1 often induce unwanted z-rotations on qubits 2 and 3, even if the z-components of qubits 2 and 3 are left unchanged. This phenomenon is known as the transient Bloch-Siegert effect, and compensation thereof is required for precise gate operation. We propose an alternative refocusing method, in which a weak square pulse is applied to qubit 1. This technique has the advantage of curbing the Bloch-Siegert effect, making it suitable for both hetero- and homonuclear molecules.

Electronic structures and magnetic properties of Sc4O2@C80(CF3)n (n = 2 and 4)

The electronic structures and magnetic properties of endohedral metallofullerenes based on an encapsulated scandium oxide cluster of Sc4O2 within a C80 fullerene cage with the trifluoromethyl group CF3 were studied for nuclear magnetic resonance (NMR) quantum computers for the control of nuclear spin gates. The effects of the trifluoromethyl group with the fullerene cage on electronic structures and magnetic properties were investigated by quantum calculation using the density function theory. The addition of the substituent group CF3 on Sc4O2@C80(CF3)4 caused asymmetrical electronic structures and magnetic parameters with a widely separated chemical shift of 13C, 45Sc, and 17O-NMR. The isotropic A-tensor in the hyperfine coupling constant of ScII atoms in the Sc4O2@C80(CF3)2 cation radical originated from the electron density distribution localized on the s-orbital in Sc atoms. The spin–lattice relaxation time of 45Sc in the Sc4O2@C80(CF3)2 cation was calculated to be 72 µs, which can be applied to the use of nuclear spins as quantum bits in NMR quantum computers.

Implementation of a simple operator-quantum-error-correction scheme

It is often assumed that the ancilla qubits required for encoding a qubit in quantum error correction (QEC) have to be in pure states, $|00...0>$ for example. In this letter, we seek an encoding scheme, in which the ancillae may be in a uniformly mixed state. We demonstrate our scheme experimentally by making use of a three-qubit NMR quantum computer. Moreover, the encoded state has an interesting nature in terms of Quantum Discord, or purely quantum correlations between the data-qubit and ancillae.

Influence of chemical substitution in ScxY3−xN@C80(CF3)n endohedral fullerenes on magnetic properties

Electronic structures and magnetic properties on nitride mixed metal cluster within fullerene cage of ScxY3−xN@C80(CF3)n at n=0, 2 and 8 were studied for controlling spin gate in the nuclear magnetic resonance quantum computer. Addition of trifluoromethyl groups on the fullerene carbon cage encapsulated with nitride mixed metal cluster provided influence of optical properties at excited state and magnetic parameters of chemical shift in 45Sc, 89Y, 14N, 19F and 13C-NMR. The chemical shift was originated in magnetic interaction of nuclear quadruple interaction based on asymmetry of electron field graduation and asymmetrical parameters with a bias value of electrostatic potential and electron density distribution of spd-hybrid orbital by inductive effect.

Magnetic properties of endohedral metallofullerenes based on asymmetric nitride yttrium cluster within azafullerenes

Magnetic properties of endohedral metallofullerene based on asymmetric triyttrium cluster of Y3N within azafullerene cage of C79N were studied to control spin-flop of nuclear magnetic resonance quantum computer. Difference of nuclear magnetic resonance peaks were exerted by symmetry of structure, electron density distribution and magnetic interaction. In the present calculation, magnetic properties of Y3N@C80, (Y3N@C80)−1, Y3N@C80 (CF3)2, Y3N@C79N and (C79N)+1 were compared for spin controlling in nuclear magnetic resonance quantum computers. The chemical shift of Y3N@C79N appeared the highest magnetic field side. Difference of electron density and magnetic parameters are cause of this result. The chemical shift of Y3N@C80 (CF3)2 had the widest peak in all of samples. Substituent groups of (CF3)2 caused the wide peaks by breaking symmetry of the an fullerene cages. The effect of difference of fullerene cage was shown in NMR chemical shift.

Electronic structure and magnetic properties of endohedral metallofullerenes based on mixed metal cluster within fullerene cage with trifluoromethyl groups

Endohedral metallofullerenes based on encapsulated nitride scandium cluster within C80 fullerene cage with trifluoromethyl group of CF3 were characterized as a candidate model for controlling nuclear spin gate in NMR quantum computers. Effects of yttrium in nitride scandium cluster of Sc3N within the fullerene cage with trifluoromethyl group on electronic structures and magnetic properties were investigated. Electronic structure and chemical shifts in 45Sc, 89Y, 19F, 13C and 14N atoms were calculated by quantum calculation using density functional theory. Addition of yttrium in nitride scandium cluster of Sc3N within the fullerene cage provided a different position of chemical shift in 45Sc, 89Y, 19F, 13C and 14N atoms. This result was originated in magnetic interaction with spin-local interaction, dipole-dipole interaction and nuclear quadrupole interaction based on nuclear quadrupole moment and asymmetry of electron field gradient with a bias value of charge and spin density distribution of spd-hybrid orbital by inductive effect.

Quantum Simulation of 2p-π Electronic Hamiltonian in Molecular Ethylene by Using an NMR Quantum Computer

Classical simulation of a quantum system is a hard problem. It’s known that these problems can be solved efficiently by using quantum computers. This study demonstrates the simulation of the molecular Hamiltonian of 2p-π electrons of ethylene in order to calculate the ground state energy. The ground state energy is estimated by an iterative phase estimation algorithm. The ground state is prepared by the adiabatic state preparation and the implementation of the procedure is carried out by numerical simulation of two-qubit NMR quantum simulator. The readout scheme of the simulator is performed by extracting binary bits via NMR interferometer.

Preparing Pseudo-Pure States in a Quadrupolar Spin System Using Optimal Control

Pseudo-pure state (PPS) preparation is crucial in nuclear magnetic resonance quantum computation. There have been some methods in spin-1/2 systems and a few attempts in quadrupolar spin systems. As optimal control via gradient ascent pulses engineering (GRAPE) has been widely used in quantum information science, we apply this technique to PPS preparation in quadrupolar spin systems. This approach shows an effective and fast quantum control method for both the state preparation and the realization of quantum gates in quadrupolar systems.

Concatenated Composite Pulses Compensating Simultaneous Systematic Errors

In NMR experiments and quantum computation, many pulse (quantum gate) sequences called the composite pulses, were developed to suppress one of two dominant errors; a pulse length error and an off-resonance error. We describe, in this paper, a general prescription to design a single-qubit concatenated composite pulse (CCCP) that is robust against two types of errors simultaneously. To this end, we introduce a new property, which is satisfied by some composite pulses and is sufficient to obtain a CCCP. Then we introduce a general method to design CCCPs with shorter execution time and less number of pulses.

Implementing quantum logic gates with gradient ascent pulse engineering: principles and practicalities

We briefly describe the use of gradient ascent pulse engineering (GRAPE) pulses to implement quantum logic gates in nuclear magnetic resonance quantum computers, and discuss a range of simple extensions to the core technique. We then consider a range of difficulties that can arise in practical implementations of GRAPE sequences, reflecting non-idealities in the experimental systems used.

Electronic structure and magnetic properties of 31P@C60-SWCNT as peapods

Design of the NMR quantum computer of 1D spin chains based on 31P@C60-SWCNT as peapods was studied. Electronic structure and magnetic properties of 31P@C60 encapsulating fullerenes within SWCNT as peapods was investigated by quantum chemical calculation. Characterization of chemical shifts of 13C, principle g-tensor and A-tensor of hyperfine structure for phosphorus atom with electronic spin S = 3/2 and nuclear spin I = 1/2 were studied. The excited energy and wavelength at 1512 nm and 728 nm confirmed assignment of the first and second states as van Hove transitions. Molecular design of carbon peapods is important to control quantum spin qubits, splitting by spin-local interaction and dipole-dipole interaction based on p-orbital spin density distribution under hybrization of molecular orbital at excited state and grand state.

Implementation of two‐qubit and three‐qubit quantum computers using liquid‐state nuclear magnetic resonance

AbstractThe field of quantum computing has grown rapidly in the last years. Most realizations of quantum computers were done on liquid‐state NMR quantum computers so far. We present in a didactic approach how to build small NMR quantum computers with two and three qubits. The two‐qubit quantum computer was implemented on α‐D‐methylglucose using 13C spins, whereas the three‐qubit quantum computer was implemented on 4‐bromo‐1,1,2‐trifluoro‐1‐butene using 19F spins. We describe in detail how to initialize these systems by generating pseudo‐pure states. For initialization, we used the spatial averaging method, which has the advantage that it can be easily understood by product operators. Furthermore, the implementation of quantum logic gate operations will be presented. © 2012 Wiley Periodicals, Inc. Concepts Magn Reson Part A 40: 25–37, 2012.

Experimental Demonstration of Probabilistic Quantum Cloning

The method of quantum cloning is divided into two main categories: approximate and probabilistic quantum cloning. The former method is used to approximate an unknown quantum state deterministically, and the latter can be used to faithfully copy the state probabilistically. Thus far, many approximate cloning machines have been experimentally demonstrated, but probabilistic cloning remains an experimental challenge, as it requires more complicated networks and a higher level of precision control. In this work, we design an efficient quantum network with a limited amount of resources and perform the first experimental demonstration of probabilistic quantum cloning in a NMR quantum computer. In our experiment, the optimal cloning efficiency proposed by Duan and Guo [Phys. Rev. Lett. 80, 4999 (1998)] is achieved.

CONSTRUCTION AND APPLICATION OF FOUR-QUBIT SWAP LOGIC GATE IN NMR QUANTUM COMPUTING

In NMR quantum computing, spin states of spin-1/2 nuclei are called qubits. Quantum logic gates are represented by unitary matrices. As a universal gate, controlled-NOT (CNOT) is a two-qubit gate. For the IS (I = 1/2 and S = 1/2) spin system, two-qubit CNOT gate is represented by a 4 × 4 matrix. SWAP logic gate, which exchanges two quantum states, is constructed by CNOT gates. In this study, first, four-qubit CNOT gates are constructed for the IS (I = 3/2, S = 3/2) spin system. Then, by using these CNOT gates, a four-qubit SWAP logic gate is found. As an application and verification, an obtained SWAP logic gate is applied to the matrix representation of product operators for the IS (I = 3/2, S = 3/2) spin system. SWAP logic gate can also be presented by an NMR pulse sequence. By using the product operator theory, the pulse sequence of the SWAP logic gate is applied to product operators of the IS (I = 3/2, S = 3/2) spin system. The expected exchange results are obtained for both the matrix representation and the pulse sequence of SWAP logic gate.

Experimental demonstration of deterministic one-way quantum computation on a NMR quantum computer

One-way quantum computing is an important and novel approach to quantum computation. By exploiting the existing particle-particle interactions, we report an 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.