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Navigating Dogma and Heresy in Quantum Computing: Exploring New Paradigms

This paper delves into the established and emergent theories surrounding quantum computing, challenging conventional dogmas while exploring heretical ideas in the field. It discusses the physical implementations required for scalable quantum systems, including qubit initialization, decoherence times, and universal gates. The work emphasizes the importance of questioning established rules and exploring alternative methods, such as quantum teleportation and cluster-state entanglement, to advance the understanding and realization of quantum computation. With the evolving nature of quantum models, new insights into quantum gates and their precise execution are presented, calling for ongoing theoretical and experimental work.

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Navigating Dogma and Heresy in Quantum Computing: Exploring New Paradigms

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  1. Dogma and Heresy in Quantum Computing DoRon Motter February 18, 2002

  2. Introduction • dog·ma ('dog-m&, 'däg-) • something held as an established opinion • a point of view or tenet put forth as authoritative without adequate grounds • her·e·sy('her-&-sE) • an opinion or doctrine contrary to dogma • dissent or deviation from a dominant theory, opinion, or practice

  3. Physical Implementation • Scalable system with well characterized qubits • Ability to initialize the state to a ‘simple’ state • ‘Long’ decoherence times • A “universal” set of quantum gates • Qubit-specific measurementcapability • Ability to interconvert stationary and flying quibits • Ability to faithfully transmit flying qubits between locations

  4. Heresy • Tenets have been laid out for physical implementation of quantum computation • Recognize these rules as simply a start • Attempt to explore their validity and reinterpret them • Remainder of talk: • Implementations which sidestep some accepted notions

  5. Universal Gates • What set of gates is “universal?”

  6. Universal Gates • What set of gates is “universal?” • CNOT + {one-bit gates}?

  7. Universal Gates • What set of gates is “universal?” • CNOT + {one-bit gates}? • CNOT might be difficult to realize physically

  8. Universal Gates • [Gottesman Chuang 99] No two-qubit interactions need take place after the start of computation. • Ideas • Use quantum teleportation as a primitive • Use measurement as a primitive • Use of measurement in gates was also explored (“programmable gates”)

  9. Universal Gates • [Gottesman Chuang 99] CNOT can be performed using classically controlled single qubit operations, prior entanglement, and Bell basis measurements.

  10. Universal Gates • We have replaced CNOT with Bell basis measurements • Some form of two-qubit interaction is necessary during execution of a quantum computer

  11. Universal Gates • We have replaced CNOT with Bell basis measurements

  12. Universal Gates • We have replaced CNOT with Bell basis measurements • [Raussendorf Briegel] cluster-state entanglement

  13. Cluster-State Entanglement • Entire resource for computation is provided initially in the form of a cluster state • Information is processed using one particle measurements only • A physical realization of cluster states is outlined

  14. Exchange-Only QC • Heisenburg interaction known to be “nice” for implementation • Accurate functional form • Strong interaction (fast gates • Not universal • Cannot generate an arbitrary Unitary over spin-1/2 qubits

  15. Exchange-Only QC • Can encode qubits into states for which the spin number remains the same • In principle a solved problem • In practice, constant factor overhead

  16. Precision in Gates • Relatively many schemes have been introduced which add new perspective on computation • However, each “gate” as the result of some Hamiltonian action must be done in a highly precise manner

  17. Precision in Gates • Relatively many schemes have been introduced which add new perspective on computation

  18. Geometric Phases • Even if gates are the result of interaction, it need not depend sensitively on H(t) • Sensitive effects are those that depend on dynamical phase • Change of state is linked to a change of energy as a function of time • Transformations based on geometric phase are insensitive to time profile of H(t)

  19. Conclusions • Theoretical and experimental work must progress for realization of QC • From a Computer Science perspective • Accept quantum circuits as a model of computation • This stems from it being close to what a physical realization of QC might be • Other equivalent models of computation (QTM) are more abstract (and have few other advantages) • Changes in the way quantum computers will be realized may have an effect on the model of computation used to describe them

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