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Versatile Formal Methods Applied to Quantum Information

Witzel, Wayne W.; Rudinger, Kenneth M.; Sarovar, Mohan S.

Using a novel formal methods approach, we have generated computer-veri ed proofs of major theorems pertinent to the quantum phase estimation algorithm. This was accomplished using our Prove-It software package in Python. While many formal methods tools are available, their practical utility is limited. Translating a problem of interest into these systems and working through the steps of a proof is an art form that requires much expertise. One must surrender to the preferences and restrictions of the tool regarding how mathematical notions are expressed and what deductions are allowed. Automation is a major driver that forces restrictions. Our focus, on the other hand, is to produce a tool that allows users the ability to con rm proofs that are essentially known already. This goal is valuable in itself. We demonstrate the viability of our approach that allows the user great exibility in expressing state- ments and composing derivations. There were no major obstacles in following a textbook proof of the quantum phase estimation algorithm. There were tedious details of algebraic manipulations that we needed to implement (and a few that we did not have time to enter into our system) and some basic components that we needed to rethink, but there were no serious roadblocks. In the process, we made a number of convenient additions to our Prove-It package that will make certain algebraic manipulations easier to perform in the future. In fact, our intent is for our system to build upon itself in this manner.

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TYPE Other Report YEAR 2015
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Optimized pulses for the control of uncertain qubits

Physical Review A - Atomic, Molecular, and Optical Physics

Carroll, Malcolm; Witzel, Wayne W.

The construction of high-fidelity control fields that are robust to control, system, and/or surrounding environment uncertainties is a crucial objective for quantum information processing. Using the two-state Landau-Zener model for illustrative simulations of a controlled qubit, we generate optimal controls for π/2 and π pulses and investigate their inherent robustness to uncertainty in the magnitude of the drift Hamiltonian. Next, we construct a quantum-control protocol to improve system-drift robustness by combining environment-decoupling pulse criteria and optimal control theory for unitary operations. By perturbatively expanding the unitary time-evolution operator for an open quantum system, previous analysis of environment-decoupling control pulses has calculated explicit control-field criteria to suppress environment-induced errors up to (but not including) third order from π/2 and π pulses. We systematically integrate this criteria with optimal control theory, incorporating an estimate of the uncertain parameter to produce improvements in gate fidelity and robustness, demonstrated via a numerical example based on double quantum dot qubits. For the qubit model used in this work, postfacto analysis of the resulting controls suggests that realistic control-field fluctuations and noise may contribute just as significantly to gate errors as system and environment fluctuations.

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TYPE Journal Article YEAR 2012
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Combining dynamical decoupling with optimal control for improved QIP

Carroll, Malcolm; Witzel, Wayne W.

Constructing high-fidelity control pulses that are robust to control and system/environment fluctuations is a crucial objective for quantum information processing (QIP). We combine dynamical decoupling (DD) with optimal control (OC) to identify control pulses that achieve this objective numerically. Previous DD work has shown that general errors up to (but not including) third order can be removed from {pi}- and {pi}/2-pulses without concatenation. By systematically integrating DD and OC, we are able to increase pulse fidelity beyond this limit. Our hybrid method of quantum control incorporates a newly-developed algorithm for robust OC, providing a nested DD-OC approach to generate robust controls. Motivated by solid-state QIP, we also incorporate relevant experimental constraints into this DD-OC formalism. To demonstrate the advantage of our approach, the resulting quantum controls are compared to previous DD results in open and uncertain model systems.

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TYPE Conference YEAR 2010
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55 Results
55 Results