15 research outputs found
Power-law spin correlations in a perturbed honeycomb spin model
We consider spin- model on the honeycomb lattice~\cite{Kitaev06}
in presence of a weak magnetic field . Such a perturbation
destroys exact integrability of the model in terms of gapless fermions and
\textit{static} fluxes. We show that it results in appearance of a
long-range tail in the irreducible dynamic spin correlation function: , where is
proportional to the density polarization function of fermions
Fermionic quantum computation
We define a model of quantum computation with local fermionic modes (LFMs) --
sites which can be either empty or occupied by a fermion. With the standard
correspondence between the Foch space of LFMs and the Hilbert space of
qubits, simulation of one fermionic gate takes qubit gates and vice
versa. We show that using different encodings, the simulation cost can be
reduced to and a constant, respectively. Nearest-neighbors
fermionic gates on a graph of bounded degree can be simulated at a constant
cost. A universal set of fermionic gates is found. We also study computation
with Majorana fermions which are basically halves of LFMs. Some connection to
qubit quantum codes is made.Comment: 18 pages, Latex; one reference adde
Layered architecture for quantum computing
We develop a layered quantum computer architecture, which is a systematic
framework for tackling the individual challenges of developing a quantum
computer while constructing a cohesive device design. We discuss many of the
prominent techniques for implementing circuit-model quantum computing and
introduce several new methods, with an emphasis on employing surface code
quantum error correction. In doing so, we propose a new quantum computer
architecture based on optical control of quantum dots. The timescales of
physical hardware operations and logical, error-corrected quantum gates differ
by several orders of magnitude. By dividing functionality into layers, we can
design and analyze subsystems independently, demonstrating the value of our
layered architectural approach. Using this concrete hardware platform, we
provide resource analysis for executing fault-tolerant quantum algorithms for
integer factoring and quantum simulation, finding that the quantum dot
architecture we study could solve such problems on the timescale of days.Comment: 27 pages, 20 figure
Suppressing quantum errors by scaling a surface code logical qubit
Practical quantum computing will require error rates that are well below what
is achievable with physical qubits. Quantum error correction offers a path to
algorithmically-relevant error rates by encoding logical qubits within many
physical qubits, where increasing the number of physical qubits enhances
protection against physical errors. However, introducing more qubits also
increases the number of error sources, so the density of errors must be
sufficiently low in order for logical performance to improve with increasing
code size. Here, we report the measurement of logical qubit performance scaling
across multiple code sizes, and demonstrate that our system of superconducting
qubits has sufficient performance to overcome the additional errors from
increasing qubit number. We find our distance-5 surface code logical qubit
modestly outperforms an ensemble of distance-3 logical qubits on average, both
in terms of logical error probability over 25 cycles and logical error per
cycle ( compared to ). To investigate
damaging, low-probability error sources, we run a distance-25 repetition code
and observe a logical error per round floor set by a single
high-energy event ( when excluding this event). We are able
to accurately model our experiment, and from this model we can extract error
budgets that highlight the biggest challenges for future systems. These results
mark the first experimental demonstration where quantum error correction begins
to improve performance with increasing qubit number, illuminating the path to
reaching the logical error rates required for computation.Comment: Main text: 6 pages, 4 figures. v2: Update author list, references,
Fig. S12, Table I
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
Higher-Order Pattern Complement 37 Pfenning, F. 2001b. Intensionality, extensionality, and proof irrelevance in modal type theory
A new type of local-check additive quantum code is presented. Qubits are associated with edges of a 2-dimensional lattice whereas the stabilizer operators correspond to the faces and the vertices. The boundary of the lattice consists of alternating pieces with two different types of boundary conditions. Logical operators are described in terms of relative homology groups. Since Shorâs discovery of the quantum error correcting codes [1], a large number of examples have been constructed. Most of them belong to the class of additive codes [2]. More specifically, codewords of an additive code form a common eigenspace of several commuting stabilizer operators, each of which is a product of Pauli matrices acting on different qubits. A peculiar property of toric codes [3, 4, 5] is that the stabilizer operators are local: each of them involves only 4 qubits, each qubit is involved only in 4 stabilizer operators, while the code distance goes to infinity. (The number 4 is not a matter of principle; it could be any constant). Furthermore, this locality is geometric while the codeword subspace and error correction properties are related to the topology of the torus. Operators acting on codewords are associated with 1-dimensional homology and cohomology classes of the torus (with Z2 coefficients). Similar codes can be defined for lattices on an arbitrary closed 2-D surface. In this paper we extend this definition to surfaces with boundary. A similar construction has been proposed by M. Freedman and D. Meyer [6]. Let us briefly recall the definition and the properties of the toric codes. In a toric code, qubits are associated with edges of an n Ă n square lattice on the torus T 2. To each vertex s and each face p we assign a stabilizer operator of the form: As = ïżœ jâstar(s) Ï x j, Bp = ïżœ Ï jâboundary(p) z