10 research outputs found
Tight Limits on Nonlocality from Nontrivial Communication Complexity; a.k.a. Reliable Computation with Asymmetric Gate Noise
It has long been known that the existence of certain superquantum nonlocal
correlations would cause communication complexity to collapse. The absurdity of
a world in which any nonlocal binary function could be evaluated with a
constant amount of communication in turn provides a tantalizing way to
distinguish quantum mechanics from incorrect theories of physics; the statement
"communication complexity is nontrivial" has even been conjectured to be a
concise information-theoretic axiom for characterizing quantum mechanics. We
directly address the viability of that perspective with two results. First, we
exhibit a nonlocal game such that communication complexity collapses in any
physical theory whose maximal winning probability exceeds the quantum value.
Second, we consider the venerable CHSH game that initiated this line of
inquiry. In that case, the quantum value is about 0.85 but it is known that a
winning probability of approximately 0.91 would collapse communication
complexity. We show that the 0.91 result is the best possible using a large
class of proof strategies, suggesting that the communication complexity axiom
is insufficient for characterizing CHSH correlations. Both results build on new
insights about reliable classical computation. The first exploits our
formalization of an equivalence between amplification and reliable computation,
while the second follows from a rigorous determination of the threshold for
reliable computation with formulas of noise-free XOR gates and
-noisy AND gates.Comment: 64 pages, 6 figure
Learning Irreducible Representations of Noncommutative Lie Groups
Recent work has constructed neural networks that are equivariant to
continuous symmetry groups such as 2D and 3D rotations. This is accomplished
using explicit group representations to derive the equivariant kernels and
nonlinearities. We present two contributions motivated by frontier applications
of equivariance beyond rotations and translations. First, we relax the
requirement for explicit Lie group representations, presenting a novel
algorithm that finds irreducible representations of noncommutative Lie groups
given only the structure constants of the associated Lie algebra. Second, we
demonstrate that Lorentz-equivariance is a useful prior for object-tracking
tasks and construct the first object-tracking model equivariant to the
Poincar\'e group.Comment: 15 pages, 5 figure
Low-Bandwidth Recovery of Linear Functions of Reed-Solomon-Encoded Data
We study the problem of efficiently computing on encoded data. More specifically, we study the question of low-bandwidth computation of functions F:F^k ? F of some data ? ? F^k, given access to an encoding ? ? F? of ? under an error correcting code. In our model - relevant in distributed storage, distributed computation and secret sharing - each symbol of ? is held by a different party, and we aim to minimize the total amount of information downloaded from each party in order to compute F(?). Special cases of this problem have arisen in several domains, and we believe that it is fruitful to study this problem in generality.
Our main result is a low-bandwidth scheme to compute linear functions for Reed-Solomon codes, even in the presence of erasures. More precisely, let ? > 0 and let ?: F^k ? F? be a full-length Reed-Solomon code of rate 1 - ? over a field F with constant characteristic. For any ? ? [0, ?), our scheme can compute any linear function F(?) given access to any (1 - ?)-fraction of the symbols of ?(?), with download bandwidth O(n/(? - ?)) bits. In contrast, the naive scheme that involves reconstructing the data ? and then computing F(?) uses ?(n log n) bits. Our scheme has applications in distributed storage, coded computation, and homomorphic secret sharing
Overcoming leakage in scalable quantum error correction
Leakage of quantum information out of computational states into higher energy
states represents a major challenge in the pursuit of quantum error correction
(QEC). In a QEC circuit, leakage builds over time and spreads through
multi-qubit interactions. This leads to correlated errors that degrade the
exponential suppression of logical error with scale, challenging the
feasibility of QEC as a path towards fault-tolerant quantum computation. Here,
we demonstrate the execution of a distance-3 surface code and distance-21
bit-flip code on a Sycamore quantum processor where leakage is removed from all
qubits in each cycle. This shortens the lifetime of leakage and curtails its
ability to spread and induce correlated errors. We report a ten-fold reduction
in steady-state leakage population on the data qubits encoding the logical
state and an average leakage population of less than
throughout the entire device. The leakage removal process itself efficiently
returns leakage population back to the computational basis, and adding it to a
code circuit prevents leakage from inducing correlated error across cycles,
restoring a fundamental assumption of QEC. With this demonstration that leakage
can be contained, we resolve a key challenge for practical QEC at scale.Comment: Main text: 7 pages, 5 figure
Measurement-induced entanglement and teleportation on a noisy quantum processor
Measurement has a special role in quantum theory: by collapsing the
wavefunction it can enable phenomena such as teleportation and thereby alter
the "arrow of time" that constrains unitary evolution. When integrated in
many-body dynamics, measurements can lead to emergent patterns of quantum
information in space-time that go beyond established paradigms for
characterizing phases, either in or out of equilibrium. On present-day NISQ
processors, the experimental realization of this physics is challenging due to
noise, hardware limitations, and the stochastic nature of quantum measurement.
Here we address each of these experimental challenges and investigate
measurement-induced quantum information phases on up to 70 superconducting
qubits. By leveraging the interchangeability of space and time, we use a
duality mapping, to avoid mid-circuit measurement and access different
manifestations of the underlying phases -- from entanglement scaling to
measurement-induced teleportation -- in a unified way. We obtain finite-size
signatures of a phase transition with a decoding protocol that correlates the
experimental measurement record with classical simulation data. The phases
display sharply different sensitivity to noise, which we exploit to turn an
inherent hardware limitation into a useful diagnostic. Our work demonstrates an
approach to realize measurement-induced physics at scales that are at the
limits of current NISQ processors
Non-Abelian braiding of graph vertices in a superconducting processor
Indistinguishability of particles is a fundamental principle of quantum
mechanics. For all elementary and quasiparticles observed to date - including
fermions, bosons, and Abelian anyons - this principle guarantees that the
braiding of identical particles leaves the system unchanged. However, in two
spatial dimensions, an intriguing possibility exists: braiding of non-Abelian
anyons causes rotations in a space of topologically degenerate wavefunctions.
Hence, it can change the observables of the system without violating the
principle of indistinguishability. Despite the well developed mathematical
description of non-Abelian anyons and numerous theoretical proposals, the
experimental observation of their exchange statistics has remained elusive for
decades. Controllable many-body quantum states generated on quantum processors
offer another path for exploring these fundamental phenomena. While efforts on
conventional solid-state platforms typically involve Hamiltonian dynamics of
quasi-particles, superconducting quantum processors allow for directly
manipulating the many-body wavefunction via unitary gates. Building on
predictions that stabilizer codes can host projective non-Abelian Ising anyons,
we implement a generalized stabilizer code and unitary protocol to create and
braid them. This allows us to experimentally verify the fusion rules of the
anyons and braid them to realize their statistics. We then study the prospect
of employing the anyons for quantum computation and utilize braiding to create
an entangled state of anyons encoding three logical qubits. Our work provides
new insights about non-Abelian braiding and - through the future inclusion of
error correction to achieve topological protection - could open a path toward
fault-tolerant quantum computing