arXiv subjects

T. F. Havel

Publications and source records attributed to T. F. Havel.

14 recordsLinked to original sources

arXiv2006

Experimental Implementation of Logical Bell State Encoding

Liquid phase NMR is a general purpose test-bed for developing methods of coherent control relevant to quantum information processing. Here we extend these studies to the coherent control of logical qubits and in particular to the unitary gates necessary to create entanglement between logical qubits. We report an experimental implementation of a conditional logical gate between two logical qubits that are each in decoherence free subspaces that protect the quantum information from fully correlated dephasing.

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arXiv2006

Subsystem Pseudo-pure States

A critical step in experimental quantum information processing (QIP) is to implement control of quantum systems protected against decoherence via informational encodings, such as quantum error correcting codes, noiseless subsystems and decoherence free subspaces. These encodings lead to the promise of fault tolerant QIP, but they come at the expense of resource overheads. Part of the challenge in studying control over multiple logical qubits, is that QIP test-beds have not had sufficient resources to analyze encodings beyond the simplest ones. The most relevant resources are the number of available qubits and the cost to initialize and control them. Here we demonstrate an encoding of logical information that permits the control over multiple logical qubits without full initialization, an issue that is particularly challenging in liquid state NMR. The method of subsystem pseudo-pure state will allow the study of decoherence control schemes on up to 6 logical qubits using liquid state NMR implementations.

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arXiv2006

Principles of Control for Decoherence-Free Subsystems

Decoherence-Free Subsystems (DFS) are a powerful means of protecting quantum information against noise with known symmetry properties. Although Hamiltonians theoretically exist that can implement a universal set of logic gates on DFS encoded qubits without ever leaving the protected subsystem, the natural Hamiltonians that are available in specific implementations do not necessarily have this property. Here we describe some of the principles that can be used in such cases to operate on encoded qubits without losing the protection offered by the DFS. In particular, we show how dynamical decoupling can be used to control decoherence during the unavoidable excursions outside of the DFS. By means of cumulant expansions, we show how the fidelity of quantum gates implemented by this method on a simple two-physical-qubit DFS depends on the correlation time of the noise responsible for decoherence. We further show by means of numerical simulations how our previously introduced "strongly modulating pulses" for NMR quantum information processing can permit high-fidelity operations on multiple DFS encoded qubits in practice, provided that the rate at which the system can be modulated is fast compared to the correlation time of the noise. The principles thereby illustrated are expected to be broadly applicable to many implementations of quantum information processors based on DFS encoded qubits.

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arXiv2004

Incoherent Noise and Quantum Information Processing

Incoherence in the controlled Hamiltonian is an important limitation on the precision of coherent control in quantum information processing. Incoherence can typically be modelled as a distribution of unitary processes arising from slowly varying experimental parameters. We show how it introduces artifacts in quantum process tomography and we explain how the resulting estimate of the superoperator may not be completely positive. We then go on to attack the inverse problem of extracting an effective distribution of unitaries that characterizes the incoherence via a perturbation theory analysis of the superoperator eigenvalue spectra.

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arXiv2003

A Method for Modeling Decoherence on a Quantum Information Processor

We develop and implement a method for modeling decoherence processes on an N-dimensional quantum system that requires only an $N^2$-dimensional quantum environment and random classical fields. This model offers the advantage that it may be implemented on small quantum information processors in order to explore the intermediate regime between semiclassical and fully quantum models. We consider in particular $σ_zσ_z$ system-environment couplings which induce coherence (phase) damping, though the model is directly extendable to other coupling Hamiltonians. Effective, irreversible phase-damping of the system is obtained by applying an additional stochastic Hamiltonian on the environment alone, periodically redressing it and thereby irreversibliy randomizing the system phase information that has leaked into the environment as a result of the coupling. This model is exactly solvable in the case of phase-damping, and we use this solution to describe the model's behavior in some limiting cases. In the limit of small stochastic phase kicks the system's coherence decays exponentially at a rate which increases linearly with the kick frequency. In the case of strong kicks we observe an effective decoupling of the system from the environment. We present a detailed implementation of the method on an nuclear magnetic resonance quantum information processor.

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arXiv2002

A Robust Method for Estimating the Lindblad Operators of a Dissipative Quantum Process from Measurements of the Density Operator at Multiple Time Points

We present a robust method for quantum process tomography, which yields a set of Lindblad operators that optimally fit the measured density operators at a sequence of time points. The benefits of this method are illustrated using a set of liquid-state Nuclear Magnetic Resonance (NMR) measurements on a molecule containing two coupled hydrogen nuclei, which are sufficient to fully determine its relaxation superoperator. It was found that the complete positivity constraint, which is necessary for the existence of the Lindblad operators, was also essential for obtaining a robust fit to the measurements. The general approach taken here promises to be broadly useful in studying dissipative quantum processes in many of the diverse experimental systems currently being developed for quantum information processing purposes.

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arXiv2001

An NMR Analog of the Quantum Disentanglement Eraser

We report the implementation of a three-spin quantum disentanglement eraser on a liquid-state NMR quantum information processor. A key feature of this experiment was its use of pulsed magnetic field gradients to mimic projective measurements. This ability is an important step towards the development of an experimentally controllable system which can simulate any quantum dynamics, both coherent and decoherent.

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arXiv2000

NMR Based Quantum Information Processing: Achievements and Prospects

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 but large enough for observing and better understanding the complexity of the quantum world. While liquid state NMR is the only present-day technology about to reach this number of qubits, further increases in complexity will require new methods. We sketch one direction leading towards a scalable quantum computer using spin 1/2 particles. The next step of which is a solid state NMR-based QIP capable of reaching 10-30 qubits.

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arXiv1999

Quantum simulation of a three-body interaction Hamiltonian on an NMR quantum computer

Extensions of average Hamiltonian theory to quantum computation permit the design of arbitrary Hamiltonians, allowing rotations throughout a large Hilbert space. In this way, the kinematics and dynamics of any quantum system may be simulated by a quantum computer. A basis mapping between the systems dictates the average Hamiltonian in the quantum computer needed to implement the desired Hamiltonian in the simulated system. The flexibility of the procedure is illustrated with NMR on 13-C labelled Alanine by creating the non-physical Hamiltonian ZZZ corresponding to a three body interaction.

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arXiv1999

Principles and Demonstrations of Quantum Information Processing by NMR Spectroscopy

This paper surveys our recent research on quantum information processing by nuclear magnetic resonance (NMR) spectroscopy. We begin with a geometric introduction to the NMR of an ensemble of indistinguishable spins, and then show how this geometric interpretation is contained within an algebra of multispin product operators. This algebra is used throughout the rest of the paper to demonstrate that it provides a facile framework within which to study quantum information processing more generally. The implementation of quantum algorithms by NMR depends upon the availability of special kinds of mixed states, called pseudo-pure states, and we consider a number of different methods for preparing these states, along with analyses of how they scale with the number of spins. The quantum-mechanical nature of processes involving such macroscopic pseudo-pure states also is a matter of debate, and in order to discuss this issue in concrete terms we present the results of NMR experiments which constitute a macroscopic analogue Hardy's paradox. Finally, a detailed product operator description is given of recent NMR experiments which demonstrate a three-bit quantum error correcting code, using field gradients to implement a precisely-known decoherence model.

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arXiv1999

Observations of Quantum Dynamics by Solution-State NMR Spectroscopy

NMR is emerging as a valuable testbed for the investigation of foundational questions in quantum mechanics. The present paper outlines the preparation of a class of mixed states, called pseudo-pure states, that emulate pure quantum states in the highly mixed environment typically used to describe solution-state NMR samples. It also describes the NMR observation of spinor behavior in spin 1/2 nuclei, the simulation of wave function collapse using a magnetic field gradient, the creation of entangled (or Bell) pseudo-pure states, and a brief discussion of quantum computing logic gates, including the Quantum Fourier Transform. These experiments show that liquid-state NMR can be used to demonstrate quantum dynamics at a level suitable for laboratory exercises.

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arXiv1999

Quantum Simulations on a Quantum Computer

We present a general scheme for performing a simulation of the dynamics of one quantum system using another. This scheme is used to experimentally simulate the dynamics of truncated quantum harmonic and anharmonic oscillators using nuclear magnetic resonance. We believe this to be the first explicit physical realization of such a simulation.

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arXiv1998

The effective Hamiltonian of the Pound-Overhauser controlled-NOT gate

In NMR-based quantum computing, it is known that the controlled-NOT gate can be implemented by applying a low-power, monochromatic radio-frequency field to one peak of a doublet in a weakly-coupled two-spin system. This is known in NMR spectroscopy as Pound-Overhauser double resonance. The ``transition'' Hamiltonian that has been associated with this procedure is however only an approximation, which ignores off-resonance effects and does not correctly predict the associated phase factors. In this paper, the exact effective Hamiltonian for evolution of the spins' state in a rotating frame is derived, both under irradiation of a single peak (on-transition) as well as between the peaks of the doublet (on-resonance). The accuracy of these effective Hamiltonians is validated by comparing the observable product operator components of the density matrix obtained by simulation to those obtained by fitting the corresponding experiments. It is further shown how both the on-transition and on-resonance fields can be used to implement the controlled-NOT gate exactly up to conditional phases, and analytic expressions for these phases are derived. In Appendices, the on-resonance Hamiltonian is analytically diagonalized, and proofs are given that, in the weak-coupling approximation, off-resonance effects can be neglected whenever the radio-frequency field power is small compared to the difference in resonance frequencies of the two spins.

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arXiv1998

Experimental Quantum Error Correction

Quantum error correction is required to compensate for the fragility of the state of a quantum computer. We report the first experimental implementations of quantum error correction and confirm the expected state stabilization. In NMR computing, however, a net improvement in the signal-to-noise would require very high polarization. The experiment implemented the 3-bit code for phase errors in liquid state state NMR.

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