29 research outputs found
Time-reversed two-photon interferometry for phase super-resolution
We observed two-photon phase super-resolution in an unbalanced Michelson
interferometer with classical Gaussian laser pulses. Our work is a
time-reversed version of a two-photon interference experiment using an
unbalanced Michelson interferometer. A measured interferogram exhibits
two-photon phase super-resolution with a high visibility of 97.9% \pm 0.4%. Its
coherence length is about 22 times longer than that of the input laser pulses.
It is a classical analogue to the large difference between the one- and
two-photon coherence lengths of entangled photon pairs.Comment: 6 pages, 4 figure
Observation of nonlinear variations in three-vertex geometric phase in two-photon polarization qutrit
We experimentally observed nonlinear variations in the three-vertex geometric
phase in a two- photon polarization qutrit. The three-vertex geometric phase is
defined by three quantum states, which generally forms a three-state (qutrit)
system. By changing one of the three constituent states, we observed two rapid
increases in the three-vertex geometric phase. The observed variations are
inherent in a three-state system and cannot be observed in a two-state system.
We used a time-reversed two-photon interferometer to measure the geometric
phase with much more intense signals than those of a typical two-photon
interferometer.Comment: 6 pages, 5 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
Bloch sphere representation of three-vertex geometric phases
The properties of the geometric phases between three quantum states are
investigated in a high-dimensional Hilbert space using the Majorana
representation of symmetric quantum states. We found that the geometric phases
between the three quantum states in an N-state quantum system can be
represented by N-1 spherical triangles on the Bloch sphere. The parameter
dependence of the geometric phase was analyzed based on this picture. We found
that the geometric phase exhibits rich nonlinear behavior in a high-dimensional
Hilbert space.Comment: 5 pages, 4 figure
ZZ-Interaction-Free Single-Qubit-Gate Optimization in Superconducting Qubits
Overcoming the issue of qubit-frequency fluctuations is essential to realize
stable and practical quantum computing with solid-state qubits. Static ZZ
interaction, which causes a frequency shift of a qubit depending on the state
of neighboring qubits, is one of the major obstacles to integrating
fixed-frequency transmon qubits. Here we propose and experimentally demonstrate
ZZ-interaction-free single-qubit-gate operations on a superconducting transmon
qubit by utilizing a semi-analytically optimized pulse based on a perturbative
analysis. The gate is designed to be robust against slow qubit-frequency
fluctuations. The robustness of the optimized gate spans a few MHz, which is
sufficient for suppressing the adverse effects of the ZZ interaction. Our
result paves the way for an efficient approach to overcoming the issue of ZZ
interaction without any additional hardware overhead.Comment: 6 pages, 2 figures plus Supplementary Information (4 pages, 2
figures