64,743 research outputs found
The Encoding and Decoding Complexities of Entanglement-Assisted Quantum Stabilizer Codes
Quantum error-correcting codes are used to protect quantum information from
decoherence. A raw state is mapped, by an encoding circuit, to a codeword so
that the most likely quantum errors from a noisy quantum channel can be removed
after a decoding process.
A good encoding circuit should have some desired features, such as low depth,
few gates, and so on. In this paper, we show how to practically implement an
encoding circuit of gate complexity for an
quantum stabilizer code with the help of pairs of maximally-entangled
states. For the special case of an stabilizer code with , the
encoding complexity is , which is previously known to be
. For this suggests that the benefits from shared
entanglement come at an additional cost of encoding complexity.
Finally we discuss decoding of entanglement-assisted quantum stabilizer codes
and extend previously known computational hardness results on decoding quantum
stabilizer codes.Comment: accepted by the 2019 IEEE International Symposium on Information
Theory (ISIT2019
Universal Programmable Quantum Circuit Schemes to Emulate an Operator
Unlike fixed designs, programmable circuit designs support an infinite number
of operators. The functionality of a programmable circuit can be altered by
simply changing the angle values of the rotation gates in the circuit. Here, we
present a new quantum circuit design technique resulting in two general
programmable circuit schemes. The circuit schemes can be used to simulate any
given operator by setting the angle values in the circuit. This provides a
fixed circuit design whose angles are determined from the elements of the given
matrix-which can be non-unitary-in an efficient way. We also give both the
classical and quantum complexity analysis for these circuits and show that the
circuits require a few classical computations. They have almost the same
quantum complexities as non-general circuits. Since the presented circuit
designs are independent from the matrix decomposition techniques and the global
optimization processes used to find quantum circuits for a given operator, high
accuracy simulations can be done for the unitary propagators of molecular
Hamiltonians on quantum computers. As an example, we show how to build the
circuit design for the hydrogen molecule.Comment: combined with former arXiv:1207.174
Quantum circuit complexity of one-dimensional topological phases
Topological quantum states cannot be created from product states with local
quantum circuits of constant depth and are in this sense more entangled than
topologically trivial states, but how entangled are they? Here we quantify the
entanglement in one-dimensional topological states by showing that local
quantum circuits of linear depth are necessary to generate them from product
states. We establish this linear lower bound for both bosonic and fermionic
one-dimensional topological phases and use symmetric circuits for phases with
symmetry. We also show that the linear lower bound can be saturated by
explicitly constructing circuits generating these topological states. The same
results hold for local quantum circuits connecting topological states in
different phases.Comment: published versio
Quantum Circuits for the Unitary Permutation Problem
We consider the Unitary Permutation problem which consists, given unitary
gates and a permutation of , in
applying the unitary gates in the order specified by , i.e. in
performing . This problem has been
introduced and investigated by Colnaghi et al. where two models of computations
are considered. This first is the (standard) model of query complexity: the
complexity measure is the number of calls to any of the unitary gates in
a quantum circuit which solves the problem. The second model provides quantum
switches and treats unitary transformations as inputs of second order. In that
case the complexity measure is the number of quantum switches. In their paper,
Colnaghi et al. have shown that the problem can be solved within calls in
the query model and quantum switches in the new model. We
refine these results by proving that quantum switches
are necessary and sufficient to solve this problem, whereas calls
are sufficient to solve this problem in the standard quantum circuit model. We
prove, with an additional assumption on the family of gates used in the
circuits, that queries are required, for any
. The upper and lower bounds for the standard quantum circuit
model are established by pointing out connections with the permutation as
substring problem introduced by Karp.Comment: 8 pages, 5 figure
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