Research Articles:
PDQP/qpoly=ALL
(pp0901-0909)
Scott
Aaronson
We show that combining two different
hypothetical enhancements to quantum computation---namely, quantum
advice and non-collapsing measurements---would let a quantum computer
solve any decision problem whatsoever in polynomial time, even though
neither enhancement yields extravagant power by itself. This complements
a related result due to Raz.
The proof uses locally decodable
codes.
Universal bound on the cardinality of local hidden variables in networks
(pp0910-0926)
Denis
Rosset, Nicolas Gisin, and Elie Wolfe
We present an algebraic description of
the sets of local correlations in arbitrary networks, when the parties
have finite inputs and outputs. We consider networks generalizing the
usual Bell scenarios by the presence of multiple uncorrelated sources.
We prove a finite upper bound on the
cardinality
of the value sets of the local hidden variables. Consequently, we find
that the sets of local correlations are connected, closed and
semialgebraic,
and bounded by tight polynomial Bell-like inequalities.
Limitations on transversal computation through quantum homomorphic
encryption
(pp0927-0948)
Michael
Newman and Yaoyun Shi
Transversality is a simple and
effective method for implementing quantum computation fault-tolerantly.
However, no quantum error-correcting code (QECC) can transversally
implement a quantum universal gate set (Eastin and Knill,
{\em
Phys. Rev. Lett.}, 102, 110502).
Since reversible classical computation is often a dominating part of
useful quantum computation, whether or not it can be implemented
transversally is an important open problem. We show that, other than a
small set of non-additive codes that we cannot rule out, no binary QECC
can transversally implement a classical reversible universal gate set.
In particular, no such QECC can implement the Toffoli gate
transversally.}{We prove our result by constructing an information
theoretically secure (but inefficient) quantum homomorphic encryption
(ITS-QHE) scheme inspired by Ouyang
{\em
et al.} (arXiv:1508.00938).
Homomorphic encryption allows the implementation of certain functions
directly on encrypted data, i.e. homomorphically. Our scheme
builds on almost any QECC, and implements that code's transversal gate
set homomorphically. We observe a restriction imposed by Nayak's
bound ({\em
FOCS} 1999) on ITS-QHE,
implying that any ITS quantum {\em
fully} homomorphic scheme (ITS-QFHE)
implementing the full set of classical reversible functions must be
highly inefficient. While our scheme incurs exponential overhead,
any such QECC implementing Toffoli transversally would still violate
this lower bound through our scheme.
Is
error detection helpful on IBM 5Q chips?
(pp0949-0964)
Christophe
Vuillot
This paper reports on experiments
realized on several IBM~5Q
chips which show evidence for the advantage of using error detection and
fault-tolerant design of quantum circuits. We show an average
improvement of the task of sampling from states that can be
fault-tolerantly prepared in the
$[[4,2,2]]$ code, when using a
fault-tolerant technique well suited to the layout of the chip. By
showing that fault-tolerant quantum computation is already within our
reach, the author hopes to encourage this approach.
Quantum signaling to the past using P-CTCS
(pp0965-0974)
Soumik
Ghosh, Arnab Adhikary, and Goutam Paul
Closed Timelike Curves (CTCs) are
intriguing relativistic objects that allow for time travel to the past
and can be used as computational resources. In Deutschian Closed
Timelike Curves (D-CTCs), due to the monogamy of entanglement, non-local
correlations between entangled states are destroyed. In contrast, for
Postselected Closed Timelike Curves (P-CTCs), a second variant of CTCs,
the non-local correlations are preserved. P-CTCs can be harnessed for
the signaling of non-orthogonal states to the past without a disruption
of causality. In this paper, we take up signaling to the past and show a
method of sending four non-orthogonal states to the past using P-CTCs.
After constructing our signaling protocol, we study the causality
violations that our protocol results in and put forward two consistency
relations to prevent them.
Weak
measurement for improving the efficiency of remote state preparation in
noisy
(pp0975-0987)
Ming-Ming
Wang and Zhi-Guo Qu
Quantum communication provides a new
way for transmitting highly sensitive information. But the existence of
quantum noise inevitably affects the security and reliability of a
quantum communication system. The technique of weak measurement and its
reversal measurement (WMRM)
has been proposed to suppress the effect of quantum noise, especially,
the amplitude-damping noise. Taking a GHZ based remote state preparation
(RSP)
scheme as an example, we discuss the effect of
WMRM
for suppressing four types of quantum noise that usually encountered in
real-world, i.e., not only the amplitude-damping noise, but also the
bit-flip, phase-flip (phase-damping) and depolarizing noise. And we give
a quantitative study on how much a quantum output state can be improved
by WMRM
in noisy environment. It is shown that the technique of
WMRM
has certain effect for improving the fidelity of the output state in the
amplitude-damping noise, and only has little effect for suppressing the
depolarizing noise, while has no effect for suppressing the bit-flip and
phase-flip (phase-damping) noise. Our result is helpful for improving
the efficiency of entanglement-based quantum communication systems in
real implementation.