
Span Program for Nonbinary Functions
Span programs characterize the quantum query complexity of binary functi...
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Span Programs and Quantum Space Complexity
While quantum computers hold the promise of significant computational sp...
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Leveraging Unknown Structure in Quantum Query Algorithms
Quantum span program algorithms for function evaluation commonly have re...
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Quantum Algorithms for Connectivity and Related Problems
An important family of span programs, stconnectivity span programs, hav...
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A Practical Algorithm for the Computation of the Genus
We describe a practical algorithm to compute the (oriented) genus of a g...
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QRMW: Quantum representation of multi wavelength images
In this study, we propose quantum representation of multi wavelength ima...
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Verifying Asymptotic Time Complexity of Imperative Programs in Isabelle
We present a framework in Isabelle for verifying asymptotic time complex...
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Span programs and quantum time complexity
Span programs are an important model of quantum computation due to their tight correspondence with quantum query complexity. For any decision problem f, the minimum complexity of a span program for f is equal, up to a constant factor, to the quantum query complexity of f. Moreover, this correspondence is constructive. A span program for f with complexity C can be compiled into a bounded error quantum algorithm for f with query complexity O(C), and vice versa. In this work, we prove an analogous connection for quantum time complexity. In particular, we show how to convert a quantum algorithm for f with time complexity T into a span program for f such that it compiles back into a quantum algorithm for f with time complexity O(T). While the query complexity of quantum algorithms obtained from span programs is wellunderstood, it is not generally clear how to implement certain queryindependent operations in a timeefficient manner. We show that for span programs derived from algorithms with a timeefficient implementation, we can preserve the time efficiency when implementing the span program. This means in particular that span programs not only fully capture quantum query complexity, but also quantum time complexity. One practical advantage of being able to convert quantum algorithms to span programs in a way that preserves time complexity is that span programs compose very nicely. We demonstrate this by improving Ambainis's variabletime quantum search result using our construction through a span program composition for the OR function.
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