534 research outputs found
Quantum Circuits for Incompletely Specified Two-Qubit Operators
While the question ``how many CNOT gates are needed to simulate an arbitrary
two-qubit operator'' has been conclusively answered -- three are necessary and
sufficient -- previous work on this topic assumes that one wants to simulate a
given unitary operator up to global phase. However, in many practical cases
additional degrees of freedom are allowed. For example, if the computation is
to be followed by a given projective measurement, many dissimilar operators
achieve the same output distributions on all input states. Alternatively, if it
is known that the input state is |0>, the action of the given operator on all
orthogonal states is immaterial. In such cases, we say that the unitary
operator is incompletely specified; in this work, we take up the practical
challenge of satisfying a given specification with the smallest possible
circuit. In particular, we identify cases in which such operators can be
implemented using fewer quantum gates than are required for generic completely
specified operators.Comment: 15 page
Economic Analysis of Traditional and Sri Method of Paddy Cultivation
The conventional paddy growing tracts are in worst crisis due to social, biological and technical setbacks. Well acclaimed rice bowls in several part of the nation is facing a decline in area, production and productivity. In India, there is a growing demand for rice due to ever escalating population. Rice is consumed both in urban and rural area and its consumption is growing due to high-income elasticity of demand. To meet the growing demand, a rapid income in paddy production is needed. But there is little scope to increase the area; hence increase in production and productivity with an improvement in efficiency of production to act as a technological breakthrough to meet the growing demand
Towards optimization of quantum circuits
Any unitary operation in quantum information processing can be implemented
via a sequence of simpler steps - quantum gates. However, actual implementation
of a quantum gate is always imperfect and takes a finite time. Therefore,
seeking for a short sequence of gates - efficient quantum circuit for a given
operation, is an important task. We contribute to this issue by proposing
optimization of the well-known universal procedure proposed by Barenco et.al
[1]. We also created a computer program which realizes both Barenco's
decomposition and the proposed optimization. Furthermore, our optimization can
be applied to any quantum circuit containing generalized Toffoli gates,
including basic quantum gate circuits.Comment: 10 pages, 11 figures, minor changes+typo
Synthesis of Quantum Logic Circuits
We discuss efficient quantum logic circuits which perform two tasks: (i)
implementing generic quantum computations and (ii) initializing quantum
registers. In contrast to conventional computing, the latter task is nontrivial
because the state-space of an n-qubit register is not finite and contains
exponential superpositions of classical bit strings. Our proposed circuits are
asymptotically optimal for respective tasks and improve published results by at
least a factor of two.
The circuits for generic quantum computation constructed by our algorithms
are the most efficient known today in terms of the number of expensive gates
(quantum controlled-NOTs). They are based on an analogue of the Shannon
decomposition of Boolean functions and a new circuit block, quantum
multiplexor, that generalizes several known constructions. A theoretical lower
bound implies that our circuits cannot be improved by more than a factor of
two. We additionally show how to accommodate the severe architectural
limitation of using only nearest-neighbor gates that is representative of
current implementation technologies. This increases the number of gates by
almost an order of magnitude, but preserves the asymptotic optimality of gate
counts.Comment: 18 pages; v5 fixes minor bugs; v4 is a complete rewrite of v3, with
6x more content, a theory of quantum multiplexors and Quantum Shannon
Decomposition. A key result on generic circuit synthesis has been improved to
~23/48*4^n CNOTs for n qubit
Efficient quantum algorithm for preparing molecular-system-like states on a quantum computer
We present an efficient quantum algorithm for preparing a pure state on a
quantum computer, where the quantum state corresponds to that of a molecular
system with a given number of electrons occupying a given number of
spin orbitals. Each spin orbital is mapped to a qubit: the states and
of the qubit represent, respectively, whether the spin orbital is
occupied by an electron or not. To prepare a general state in the full Hilbert
space of qubits, which is of dimension %, controlled-NOT
gates are needed, i.e., the number of gates scales \emph{exponentially} with
the number of qubits. We make use of the fact that the state to be prepared
lies in a smaller Hilbert space, and we find an algorithm that requires at most
gates, i.e., scales \emph{polynomially} with the number
of qubits , provided . The algorithm is simulated numerically for
the cases of the hydrogen molecule and the water molecule. The numerical
simulations show that when additional symmetries of the system are considered,
the number of gates to prepare the state can be drastically reduced, in the
examples considered in this paper, by several orders of magnitude, from the
above estimate.Comment: 11 pages, 8 figures, errors are corrected, Journal information adde
Speed limits for quantum gates in multi-qubit systems
We use analytical and numerical calculations to obtain speed limits for
various unitary quantum operations in multiqubit systems under typical
experimental conditions. The operations that we consider include single-, two-,
and three-qubit gates, as well as quantum-state transfer in a chain of qubits.
We find in particular that simple methods for implementing two-qubit gates
generally provide the fastest possible implementations of these gates. We also
find that the three-qubit Toffoli gate time varies greatly depending on the
type of interactions and the system's geometry, taking only slightly longer
than a two-qubit controlled-NOT (CNOT) gate for a triangle geometry. The speed
limit for quantum-state transfer across a qubit chain is set by the maximum
spin-wave speed in the chain.Comment: 7 pages (two-column), 2 figures, 2 table
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