42,406 research outputs found
Quantum computation with linear optics
We present a constructive method to translate small quantum circuits into
their optical analogues, using linear components of present-day quantum optics
technology only. These optical circuits perform precisely the computation that
the quantum circuits are designed for, and can thus be used to test the
performance of quantum algorithms. The method relies on the representation of
several quantum bits by a single photon, and on the implementation of universal
quantum gates using simple optical components (beam splitters, phase shifters,
etc.). The optical implementation of Brassard et al.'s teleportation circuit, a
non-trivial 3-bit quantum computation, is presented as an illustration.Comment: LaTeX with llncs.cls, 11 pages with 5 postscript figures, Proc. of
1st NASA Workshop on Quantum Computation and Quantum Communication (QCQC 98
Minimal Universal Two-qubit Quantum Circuits
We give quantum circuits that simulate an arbitrary two-qubit unitary
operator up to global phase. For several quantum gate libraries we prove that
gate counts are optimal in worst and average cases. Our lower and upper bounds
compare favorably to previously published results. Temporary storage is not
used because it tends to be expensive in physical implementations.
For each gate library, best gate counts can be achieved by a single universal
circuit. To compute gate parameters in universal circuits, we only use
closed-form algebraic expressions, and in particular do not rely on matrix
exponentials. Our algorithm has been coded in C++.Comment: 8 pages, 2 tables and 4 figures. v3 adds a discussion of asymetry
between Rx, Ry and Rz gates and describes a subtle circuit design problem
arising when Ry gates are not available. v2 sharpens one of the loose bounds
in v1. Proof techniques in v2 are noticeably revamped: they now rely less on
circuit identities and more on directly-computed invariants of two-qubit
operators. This makes proofs more constructive and easier to interpret as
algorithm
ZH: A Complete Graphical Calculus for Quantum Computations Involving Classical Non-linearity
We present a new graphical calculus that is sound and complete for a
universal family of quantum circuits, which can be seen as the natural
string-diagrammatic extension of the approximately (real-valued) universal
family of Hadamard+CCZ circuits. The diagrammatic language is generated by two
kinds of nodes: the so-called 'spider' associated with the computational basis,
as well as a new arity-N generalisation of the Hadamard gate, which satisfies a
variation of the spider fusion law. Unlike previous graphical calculi, this
admits compact encodings of non-linear classical functions. For example, the
AND gate can be depicted as a diagram of just 2 generators, compared to ~25 in
the ZX-calculus. Consequently, N-controlled gates, hypergraph states,
Hadamard+Toffoli circuits, and diagonal circuits at arbitrary levels of the
Clifford hierarchy also enjoy encodings with low constant overhead. This
suggests that this calculus will be significantly more convenient for reasoning
about the interplay between classical non-linear behaviour (e.g. in an oracle)
and purely quantum operations. After presenting the calculus, we will prove it
is sound and complete for universal quantum computation by demonstrating the
reduction of any diagram to an easily describable normal form.Comment: In Proceedings QPL 2018, arXiv:1901.0947
Optimal quantum circuit synthesis from Controlled-U gates
From a geometric approach, we derive the minimum number of applications
needed for an arbitrary Controlled-Unitary gate to construct a universal
quantum circuit. A new analytic construction procedure is presented and shown
to be either optimal or close to optimal. This result can be extended to
improve the efficiency of universal quantum circuit construction from any
entangling gate. Specifically, for both the Controlled-NOT and Double-CNOT
gates, we develop simple analytic ways to construct universal quantum circuits
with three applications, which is the least possible.Comment: 4 pages, 3 figure
Universal Quantum Circuits
We define and construct efficient depth-universal and almost-size-universal
quantum circuits. Such circuits can be viewed as general-purpose simulators for
central classes of quantum circuits and can be used to capture the
computational power of the circuit class being simulated. For depth we
construct universal circuits whose depth is the same order as the circuits
being simulated. For size, there is a log factor blow-up in the universal
circuits constructed here. We prove that this construction is nearly optimal.Comment: 13 page
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