5,279 research outputs found
Overlapping Qubits
An ideal system of n qubits has 2^n dimensions. This exponential grants power, but also hinders characterizing the system\u27s state and dynamics. We study a new problem: the qubits in a physical system might not be independent. They can "overlap," in the sense that an operation on one qubit slightly affects the others.
We show that allowing for slight overlaps, n qubits can fit in just polynomially many dimensions. (Defined in a natural way, all pairwise overlaps can be <= epsilon in n^{O(1/epsilon^2)} dimensions.) Thus, even before considering issues like noise, a real system of n qubits might inherently lack any potential for exponential power.
On the other hand, we also provide an efficient test to certify exponential dimensionality. Unfortunately, the test is sensitive to noise. It is important to devise more robust tests on the arrangements of qubits in quantum devices
Framework for classifying logical operators in stabilizer codes
Entanglement, as studied in quantum information science, and non-local
quantum correlations, as studied in condensed matter physics, are fundamentally
akin to each other. However, their relationship is often hard to quantify due
to the lack of a general approach to study both on the same footing. In
particular, while entanglement and non-local correlations are properties of
states, both arise from symmetries of global operators that commute with the
system Hamiltonian. Here, we introduce a framework for completely classifying
the local and non-local properties of all such global operators, given the
Hamiltonian and a bi-partitioning of the system. This framework is limited to
descriptions based on stabilizer quantum codes, but may be generalized. We
illustrate the use of this framework to study entanglement and non-local
correlations by analyzing global symmetries in topological order, distribution
of entanglement and entanglement entropy.Comment: 20 pages, 9 figure
Power of Quantum Computation with Few Clean Qubits
This paper investigates the power of polynomial-time quantum computation in
which only a very limited number of qubits are initially clean in the |0>
state, and all the remaining qubits are initially in the totally mixed state.
No initializations of qubits are allowed during the computation, nor
intermediate measurements. The main results of this paper are unexpectedly
strong error-reducible properties of such quantum computations. It is proved
that any problem solvable by a polynomial-time quantum computation with
one-sided bounded error that uses logarithmically many clean qubits can also be
solvable with exponentially small one-sided error using just two clean qubits,
and with polynomially small one-sided error using just one clean qubit. It is
further proved in the case of two-sided bounded error that any problem solvable
by such a computation with a constant gap between completeness and soundness
using logarithmically many clean qubits can also be solvable with exponentially
small two-sided error using just two clean qubits. If only one clean qubit is
available, the problem is again still solvable with exponentially small error
in one of the completeness and soundness and polynomially small error in the
other. As an immediate consequence of the above result for the two-sided-error
case, it follows that the TRACE ESTIMATION problem defined with fixed constant
threshold parameters is complete for the classes of problems solvable by
polynomial-time quantum computations with completeness 2/3 and soundness 1/3
using logarithmically many clean qubits and just one clean qubit. The
techniques used for proving the error-reduction results may be of independent
interest in themselves, and one of the technical tools can also be used to show
the hardness of weak classical simulations of one-clean-qubit computations
(i.e., DQC1 computations).Comment: 44 pages + cover page; the results in Section 8 are overlapping with
the main results in arXiv:1409.677
Test for a large amount of entanglement, using few measurements
Bell-inequality violations establish that two systems share some quantum
entanglement. We give a simple test to certify that two systems share an
asymptotically large amount of entanglement, n EPR states. The test is
efficient: unlike earlier tests that play many games, in sequence or in
parallel, our test requires only one or two CHSH games. One system is directed
to play a CHSH game on a random specified qubit i, and the other is told to
play games on qubits {i,j}, without knowing which index is i.
The test is robust: a success probability within delta of optimal guarantees
distance O(n^{5/2} sqrt{delta}) from n EPR states. However, the test does not
tolerate constant delta; it breaks down for delta = Omega~(1/sqrt{n}). We give
an adversarial strategy that succeeds within delta of the optimum probability
using only O~(delta^{-2}) EPR states.Comment: 17 pages, 2 figures. Journal versio
Decoherence benchmarking of superconducting qubits
We benchmark the decoherence of superconducting qubits to examine the
temporal stability of energy-relaxation and dephasing. By collecting statistics
during measurements spanning multiple days, we find the mean parameters
= 49 s and = 95 s, however,
both of these quantities fluctuate explaining the need for frequent
re-calibration in qubit setups. Our main finding is that fluctuations in qubit
relaxation are local to the qubit and are caused by instabilities of
near-resonant two-level-systems (TLS). Through statistical analysis, we
determine switching rates of these TLS and observe the coherent coupling
between an individual TLS and a transmon qubit. Finally, we find evidence that
the qubit's frequency stability is limited by capacitance noise. Importantly,
this produces a 0.8 ms limit on the pure dephasing which we also observe.
Collectively, these findings raise the need for performing qubit metrology to
examine the reproducibility of qubit parameters, where these fluctuations could
affect qubit gate fidelity.Comment: 15 pages ArXiv version rev
Pairwise quantum and classical correlations in multi-qubits states via linear relative entropy
The pairwise correlations in a multi-qubit state are quantified through a
linear variant of relative entropy. In particular, we derive the explicit
expressions of total, quantum and classical bipartite correlations. Two
different bi-partioning schemes are considered. We discuss the derivation of
closest product, quantum-classical and quantum-classical product states. We
also investigate the additivity relation between the various pairwise
correlations existing in pure and mixed states. As illustration, some special
cases are examined.Comment: 19 pages, To appear in International Journal of Quantum Informatio
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