Magnetic Resonance Quantum Information Processor Research Articles

Simulating the effect of weak measurements by a phase damping channel and determining different measures of bipartite correlations in nuclear magnetic resonance

Quantum discord is a measure based on local projective measurements which captures quantum correlations that may not be fully captured by entanglement. A change in the measurement process, achieved by replacing rank-one projectors with a weak positive operator-valued measure (POVM), allows one to define weak variants of quantum discord. In this work, we experimentally simulate the effect of a weak POVM on a nuclear magnetic resonance quantum information processor. The two-qubit system under investigation is part of a three-qubit system, where one of the qubits is used as an ancillary to implement the phase damping channel. The strength of the weak POVM is controlled by varying the strength of the phase damping channel. We experimentally observed two weak variants of quantum discord namely, super quantum discord and weak quantum discord, in two-qubit Werner and Bell-diagonal states. The resultant dynamics of the states is investigated as a function of the measurement strength.

Quantum algorithm for solving linear differential equations: Theory and experiment

We present and experimentally realize a quantum algorithm for efficiently solving the following problem: given an $N\times N$ matrix $\mathcal{M}$, an $N$-dimensional vector $\textbf{\emph{b}}$, and an initial vector $\textbf{\emph{x}}(0)$, obtain a target vector $\textbf{\emph{x}}(t)$ as a function of time $t$ according to the constraint $d\textbf{\emph{x}}(t)/dt=\mathcal{M}\textbf{\emph{x}}(t)+\textbf{\emph{b}}$. We show that our algorithm exhibits an exponential speedup over its classical counterpart in certain circumstances. In addition, we demonstrate our quantum algorithm for a $4\times4$ linear differential equation using a 4-qubit nuclear magnetic resonance quantum information processor. Our algorithm provides a key technique for solving many important problems which rely on the solutions to linear differential equations.

Preparation of pseudo-pure states for NMR quantum computing with one ancillary qubit

Quantum state preparation plays an equally important role as quantum operations and measurements in quantum information processing. The previous methods for initialization require either an exponential number of experiments, or cause signal reduction or place restrictions on molecular structures. In this study, we propose three types of quantum circuits for preparing the pseudo-purelinebreak states of ($n-1$) qubits in the $n$-coupled Hilbert space, which simply needs the assistance of one ancilla spin and two different experiments independent of $n$. Most importantly, our methods work well on homo-nuclear and hetero-nuclear molecules without the reduction of signals in the gradient field. As a proof-of-principle demonstration, we experimentally prepared the pseudo-pure states of heteronuclear 2-qubit and homonuclear 4-qubit molecules using a nuclear magnetic resonance quantum information processor.

Experimental detection of qubit-ququart pseudo-bound entanglement using three nuclear spins

In this work, we experimentally created and characterized a class of qubit-ququart PPT (positive under partial transpose) entangled states using three nuclear spins on an nuclear magnetic resonance (NMR) quantum information processor. Entanglement detection and characterization for systems with a Hilbert space dimension ≥2⊗3 is nontrivial since there are states in such systems which are both PPT as well as entangled. The experimental detection scheme that we devised for the detection of qubit-ququart PPT entanglement was based on the measurement of three Pauli operators with high precision, and is a key ingredient of the protocol in detecting entanglement. The family of PPT-entangled states considered in the current study are incoherent mixtures of five pure states. All the five states were prepared with high fidelities and the resulting PPT entangled states were prepared with mean fidelity ≥ 0.95. The entanglement thus detected was validated by carrying out full quantum state tomography (QST).

Experimentally identifying the entanglement class of pure tripartite states

We use concurrence as an entanglement measure and experimentally demonstrate the entanglement classification of arbitrary three-qubit pure states on a nuclear magnetic resonance (NMR) quantum information processor. Computing the concurrence experimentally under three different bipartitions, for an arbitrary three-qubit pure state, reveals the entanglement class of the state. The experiment involves measuring the expectation values of Pauli operators. This was achieved by mapping the desired expectation values onto the local $z$ magnetization of a single qubit. We tested the entanglement classification protocol on twenty seven different generic states and successfully detected their entanglement class. Full quantum state tomography was performed to construct experimental tomographs of each state and negativity was calculated from them, to validate the experimental results.

Experimental quantum Hamiltonian identification from measurement time traces

Identifying Hamiltonian of a quantum system is of vital importance for quantum information processing. In this article, we realized and benchmarked a quantum Hamiltonian identification algorithm recently proposed (Zhang and Sarovar, 2014). we realized the algorithm on a liquid nuclear magnetic resonance quantum information processor using two types of working media with different forms of Hamiltonian. Our experiment realized the quantum identification algorithm based on free induction decay signals. We also showed how to process data obtained in a practical experiment. We studied the influence of decoherence by numerical simulations. Our experiments and simulations demonstrate that the algorithm is effective and robust.

Experimental quantum simulation of Avian Compass in a nuclear magnetic resonance system

Avian magnetoreception is the capacity for avians to sense the direction of the Earth’s magnetic field. Discovered more than forty years ago, it has attracted intensive studies over the years. One promising model for describing this capacity in avians is the widely used reference-and-probe model where radical pairs within the eyes of bird combines to form singlet and triplet quantum states. The yield depends on the angle between the Earth’s magnetic field and the molecules’ axis, hence the relative value of yield of the singlet state or triplet state enables avians to sense the direction. Here we report the experimental demonstration of avian magnetoreception in a nuclear magnetic resonance quantum information processor. It is shown clearly from the experiment that the yield of the singlet state attains maximum when it is normal to the Earth’s magnetic field, and the experimental results agree with theory very well.

Realization of an entanglement-assisted quantum delayed-choice experiment

The puzzling properties of quantum mechanics, wave-particle duality, entanglement and superposition, were dissected experimentally at past decades. However, hidden-variable (HV) models, based on three classical assumptions of wave-particle objectivity, determinism and independence, strive to explain or even defeat them. The development of quantum technologies enabled us to test experimentally the predictions of quantum mechanics and HV theories. Here, we report an experimental demonstration of an entanglement-assisted quantum delayed-choice scheme using a liquid nuclear magnetic resonance quantum information processor. This scheme we realized is based on the recently proposed scheme [Nat. Comms. 5:4997(2014)], which gave different results for quantum mechanics and HV theories. In our experiments, the intensities and the visibilities of the interference are in consistent the theoretical prediction of quantum mechanics. The results imply that a contradiction is appearing when all three assumptions of HV models are combined, though any two of the above assumptions are compatible with it.

Experimental construction of generic three-qubit states and their reconstruction from two-party reduced states on an NMR quantum information processor

We experimentally explore the state space of three qubits on a nuclear magnetic resonance (NMR) quantum-information processor. We construct a scheme to experimentally realize a canonical form for general three-qubit states up to single-qubit unitaries. This form involves a nontrivial combination of Greenberger-Horne-Zeilinger (GHZ) and $W$-type maximally entangled states of three qubits. The general circuit that we have constructed for the generic state reduces to those for GHZ and $W$ states as special cases. The experimental construction of a generic state is carried out for a nontrivial set of parameters and the good fidelity of preparation is confirmed by complete state tomography. The GHZ and $W$ states are constructed as special cases of the general experimental scheme. Further, we experimentally demonstrate a curious fact about three-qubit states, where for almost all pure states, the two-qubit reduced states can be used to reconstruct the full three-qubit state. For the case of a generic state and for the $W$ state, we demonstrate this method of reconstruction by comparing it to the directly tomographed three-qubit state.

Experimental optimal single qubit purification in an NMR quantum information processor.

High quality single qubits are the building blocks in quantum information processing. But they are vulnerable to environmental noise. To overcome noise, purification techniques, which generate qubits with higher purities from qubits with lower purities, have been proposed. Purifications have attracted much interest and been widely studied. However, the full experimental demonstration of an optimal single qubit purification protocol proposed by Cirac, Ekert and Macchiavello [Phys. Rev. Lett. 82, 4344 (1999), the CEM protocol] more than one and half decades ago, still remains an experimental challenge, as it requires more complicated networks and a higher level of precision controls. In this work, we design an experiment scheme that realizes the CEM protocol with explicit symmetrization of the wave functions. The purification scheme was successfully implemented in a nuclear magnetic resonance quantum information processor. The experiment fully demonstrated the purification protocol, and showed that it is an effective way of protecting qubits against errors and decoherence.

Quantum simulation using fidelity-profile optimization

Experimental quantum simulation of a Hamiltonian H requires unitary operator decomposition (UOD) of its evolution unitary U = exp(-iHt) in terms of native unitary operators of the experimental system. Here, using a genetic algorithm, we numerically evaluate the most generic UOD (valid over a continuous range of Hamiltonian parameters) of the unitary operator U, termed fidelity-profile optimization. The optimization is obtained by systematically evaluating the functional dependence of experimental unitary operators (such as single-qubit rotations and time-evolution unitaries of the system interactions) to the Hamiltonian (H) parameters. Using this technique, we have solved the experimental unitary decomposition of a controlled-phase gate (for any phase value), the evolution unitary of the Heisenberg XY interaction, and simulation of the Dzyaloshinskii-Moriya (DM) interaction in the presence of the Heisenberg XY interaction. Using these decompositions, we studied the entanglement dynamics of a Bell state in the DM interaction and experimentally verified the entanglement preservation procedure of Hou et al. Ann. Phys. (N.Y.) 327, 292 (2012)] in a nuclear magnetic resonance quantum information processor.

Experimental realization of quantum algorithm for solving linear systems of equations

Many important problems in science and engineering can be reduced to the problem of solving linear equations. The quantum algorithm discovered recently indicates that one can solve an $N$-dimensional linear equation in $O(logN)$ time, which provides an exponential speedup over the classical counterpart. Here we report an experimental demonstration of the quantum algorithm when the scale of the linear equation is $2\ifmmode\times\else\texttimes\fi{}2$ using a nuclear magnetic resonance quantum information processor. For all sets of experiments, the fidelities of the final four-qubit states are all above 96%. This experiment gives the possibility of solving a series of practical problems related to linear systems of equations and can serve as the basis to realize many potential quantum algorithms.

Measuring geometric quantum discord using one bit of quantum information

We describe an efficient DQC1-algorithm to quantify the amount of Geometric Quantum Discord present in the output state of a DQC1 computation. DQC1 is a model of computation that utilizes separable states to solve a problem with no known efficient classical algorithm and is known to contain quantum correlations as measured by the discord. For the general case of a (1+n)-qubit DQC1-state we provide an analytical expression for the Geometric Quantum Discord and find that its typical (and maximum) value decreases exponentially with n. This is in contrast to the standard Quantum Discord whose value for typical DQC1-states is known to be independent of n. We experimentally demonstrate the proposed algorithm on a four-qubit liquid-state nuclear magnetic resonance quantum information processor. In the special case of a two-qubit DQC1 model, we also provide an expression for the Quantum Discord that only requires the outcome of the DQC1 algorithm.

Experimental detection of nonclassical correlations in mixed-state quantum computation

We report on an experiment to detect non-classical correlations in a highly mixed state. The correlations are characterized by the quantum discord and are observed using four qubits in a liquid state nuclear magnetic resonance quantum information processor. The state analyzed is the output of a DQC1 computation, whose input is a single quantum bit accompanied by n maximally mixed qubits. This model of computation outperforms the best known classical algorithms, and although it contains vanishing entanglement it is known to have quantum correlations characterized by the quantum discord. This experiment detects non-vanishing quantum discord, ensuring the existence of non-classical correlations as measured by the quantum discord.

Experimental Realization of Braunstein's Weight-Decision Algorithm

Braunstein proposed an algorithm to distinguish the Boolean functions of two different weights. Here we implement the algorithm in a two-qubit nuclear magnetic resonance quantum information processor. The experiment shows that the algorithm could distinguish the Boolean functions of two different weights efficiently.

Experimental Quantum Simulation of Entanglement in Many-Body Systems

We employ a nuclear magnetic resonance (NMR) quantum information processor to simulate the ground state of an XXZ spin chain and measure its NMR analog of entanglement, or pseudoentanglement. The observed pseudoentanglement for a small-size system already displays a singularity, a signature which is qualitatively similar to that in the thermodynamical limit across quantum phase transitions, including an infinite-order critical point. The experimental results illustrate a successful approach to investigate quantum correlations in many-body systems using quantum simulators.

Quantum secret sharing protocol with four state Grover algorithm and its proof-of-principle experimental demonstration

In this article, we propose a three-party quantum secret sharing protocol with four-state Grover algorithm. The protocol has several advantages. It uses only four initial states which simplifies its experimental implementation. It has a higher encoding capacity, each two-qubit state provides two bits of information. We have experimentally demonstrated the protocol in a nuclear magnetic resonance quantum information processor successfully.

Experimental Approximation of the Jones Polynomial with One Quantum Bit

We present experimental results approximating the Jones polynomial using 4 qubits in a liquid state nuclear magnetic resonance quantum information processor. This is the first experimental implementation of a complete problem for the deterministic quantum computation with one quantum bit model of quantum computation, which uses a single qubit accompanied by a register of completely random states. The Jones polynomial is a knot invariant that is important not only to knot theory, but also to statistical mechanics and quantum field theory. The implemented algorithm is a modification of the algorithm developed by Shor and Jordan suitable for implementation in NMR. These experimental results show that for the restricted case of knots whose braid representations have four strands and exactly three crossings, identifying distinct knots is possible 91% of the time.

Simulation of the four-body interaction in a nuclear magnetic resonance quantum information processor

The four-body interaction plays an important role in many-body systems, and it can exhibit interesting phase transition behaviors. In this letter, we report the experimental demonstration of a four-body interaction in a four-qubit nuclear magnetic resonance quantum information processor. The strongly modulating pulse is used to implement spin selective excitation. The results show a good agreement between theory and experiment.

Nuclear magnetic resonance implementation of universal quantum gate with constant Hamiltonian evolution

In this letter, we report an experimental demonstration of single-step realization of universal quantum gate in a nuclear magnetic resonance quantum information processor. The scheme uses a constant Hamiltonian evolution and is robust against decoherence. Our work focuses on the implementation of the controlled-NOT gate. Several sets of parameters are obtained and they provide flexibility to suppress decoherence for quantum computation.