
Revisiting the simulation of quantum Turing machines by quantum circuits
Yao (1993) proved that quantum Turing machines and uniformly generated q...
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Quantum Logarithmic Space and Postselection
Postselection, the power of discarding all runs of a computation in whi...
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A Schematic Definition of Quantum Polynomial Time Computability
In the past four decades, the notion of quantum polynomialtime computab...
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Multiway Turing Machines
Multiway Turing machines (also known as nondeterministic Turing machines...
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On the Universality of Memcomputing Machines
Universal memcomputing machines (UMMs) [IEEE Trans. Neural Netw. Learn. ...
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Quantum Random SelfModifiable Computation
Among the fundamental questions in computer science, at least two have a...
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A Simple Elementary Proof of P=NP based on the Relational Model of E. F. Codd
The P versus NP problem is studied under the relational model of E. F. C...
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Quantum Random Access StoredProgram Machines
Random access machines (RAMs) and random access storedprogram machines (RASPs) are models of computing that are closer to the architecture of realworld computers than Turing machines (TMs). They are also convenient in complexity analysis of algorithms. The relationships between RAMs, RASPs and TMs are wellstudied. However, a clear relationships between their quantum counterparts are still missing in the literature. We fill in this gap by formally defining the models of quantum random access machines (QRAMs) and quantum random access storedprogram machines (QRASPs) and clarifying the relationships between QRAMs, QRASPs and quantum Turing machines (QTMs). In particular, we prove: 1. A T(n)time QRAM (resp. QRASP) can be simulated by an O(T(n))time QRASP (resp. QRAM). 2. A T(n)time QRAM under the logarithmic (resp. constant) cost criterion can be simulated by an Õ(T(n)^4)time (resp. Õ(T(n)^8)time) QTM. 3. A T(n)time QTM can be simulated within error ε > 0 by an O(T(n)^2 polylog(T(n), 1/ε))time QRAM (under both the logarithmic and constant cost criterions). As a corollary, we have: P⊆EQRAMP⊆EQP⊆BQP = BQRAMP, where EQRAMP and BQRAMP stand for the sets of problems that can be solved by polynomialtime QRAMs with certainty and boundederror, respectively.
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