16,926 research outputs found
An Arbitrary Two-qubit Computation In 23 Elementary Gates
Quantum circuits currently constitute a dominant model for quantum
computation. Our work addresses the problem of constructing quantum circuits to
implement an arbitrary given quantum computation, in the special case of two
qubits. We pursue circuits without ancilla qubits and as small a number of
elementary quantum gates as possible. Our lower bound for worst-case optimal
two-qubit circuits calls for at least 17 gates: 15 one-qubit rotations and 2
CNOTs. To this end, we constructively prove a worst-case upper bound of 23
elementary gates, of which at most 4 (CNOT) entail multi-qubit interactions.
Our analysis shows that synthesis algorithms suggested in previous work,
although more general, entail much larger quantum circuits than ours in the
special case of two qubits. One such algorithm has a worst case of 61 gates of
which 18 may be CNOTs. Our techniques rely on the KAK decomposition from Lie
theory as well as the polar and spectral (symmetric Shur) matrix decompositions
from numerical analysis and operator theory. They are related to the canonical
decomposition of a two-qubit gate with respect to the ``magic basis'' of
phase-shifted Bell states, published previously. We further extend this
decomposition in terms of elementary gates for quantum computation.Comment: 18 pages, 7 figures. Version 2 gives correct credits for the GQC
"quantum compiler". Version 3 adds justification for our choice of elementary
gates and adds a comparison with classical library-less logic synthesis. It
adds acknowledgements and a new reference, adds full details about the 8-gate
decomposition of topC-V and stealthily fixes several minor inaccuracies.
NOTE: Using a new technique, we recently improved the lower bound to 18 gates
and (tada!) found a circuit decomposition that requires 18 gates or less.
This work will appear as a separate manuscrip
Propagating large open quantum systems towards their steady states: cluster implementation of the time-evolving block decimation scheme
Many-body quantum systems are subjected to the Curse of Dimensionality: The
dimension of the Hilbert space , where these systems live in,
grows exponentially with systems' 'size' (number of their components,
"bodies"). It means that, in order to specify a state of a quantum system, we
need a description whose length grows exponentially with the system size.
However, with some systems it is possible to escape the curse by using low-rank
tensor approximations known as `matrix-product state/operator (MPS/O)
representation' in the quantum community and `tensor-train decomposition' among
applied mathematicians. Motivated by recent advances in computational quantum
physics, we consider chains of spins coupled by nearest-neighbor
interactions. The spins are subjected to an action coming from the environment.
Spatially disordered interaction and environment-induced decoherence drive
systems into non-trivial asymptotic states. The dissipative evolution is
modeled with a Markovian master equation in the Lindblad form. By implementing
the MPO technique and propagating system states with the time-evolving block
decimation (TEBD) scheme (which allows to keep the length of the state
descriptions fixed), it is in principle possible to reach the corresponding
steady states. We propose and realize a cluster implementation of this idea.
The implementation on four nodes allowed us to resolve steady states of the
model systems with spins
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