20 research outputs found
symmetry breaking in Projected Entangled Pair State models
We consider Projected Entangled Pair State (PEPS) models with a global
symmetry, which are constructed from -symmetric
tensors and are thus -invariant wavefunctions, and study the
occurence of long-range order and symmetry breaking in these systems. First, we
show that long-range order in those models is accompanied by a degeneracy in
the so-called transfer operator of the system. We subsequently use this
degeneracy to determine the nature of the symmetry broken states, i.e., those
stable under arbitrary perturbations, and provide a succinct characterization
in terms of the fixed points of the transfer operator (i.e.\ the different
boundary conditions) in the individual symmetry sectors. We verify our findings
numerically through the study of a -symmetric model, and show that
the entanglement Hamiltonian derived from the symmetry broken states is
quasi-local (unlike the one derived from the symmetric state), reinforcing the
locality of the entanglement Hamiltonian for gapped phases.Comment: 11 page
Dynamical subset sampling of quantum error correcting protocols
Quantum error correcting (QEC) stabilizer codes enable protection of quantum
information against errors during storage and processing. Simulation of noisy
QEC codes is used to identify the noise parameters necessary for advantageous
operation of logical qubits in realistic quantum computing architectures.
Typical quantum error correction techniques contain intermediate measurements
and classical feedback that determine the actual noisy circuit sequence in an
instance of performing the protocol. Dynamical subset sampling enables
efficient simulation of such non-deterministic quantum error correcting
protocols for any type of quantum circuit and incoherent noise of low strength.
As an importance sampling technique, dynamical subset sampling allows one to
effectively make use of computational resources to only sample the most
relevant sequences of quantum circuits in order to estimate a protocol's
logical failure rate with well-defined error bars. We demonstrate the
capabilities of dynamical subset sampling with examples from fault-tolerant
(FT) QEC. We show that, in a typical stabilizer simulation with incoherent
Pauli noise of strength , our method can reach a required sampling
accuracy on the logical failure rate with two orders of magnitude fewer samples
than direct Monte Carlo simulation. Furthermore, dynamical subset sampling
naturally allows for efficient simulation of realistic multi-parameter noise
models describing faulty quantum processors. It can be applied not only for QEC
in the circuit model but any noisy quantum computing framework with incoherent
fault operators including measurement-based quantum computation and quantum
networks.Comment: 33 pages, 26 figure
Towards a realistic GaAs-spin qubit device for a classical error-corrected quantum memory
Based on numerically-optimized real-device gates and parameters we study the
performance of the phase-flip (repetition) code on a linear array of Gallium
Arsenide (GaAs) quantum dots hosting singlet-triplet qubits. We first examine
the expected performance of the code using simple error models of circuit-level
and phenomenological noise, reporting, for example, a circuit-level
depolarizing noise threshold of approximately 3%. We then perform
density-matrix simulations using a maximum-likelihood and minimum-weight
matching decoder to study the effect of real-device dephasing, read-out error,
quasi-static as well as fast gate noise. Considering the trade-off between
qubit read-out error and dephasing time (T2) over measurement time, we identify
a sub-threshold region for the phase-flip code which lies within experimental
reach.Comment: 22 page
Computational Capabilities and Compiler Development for Neutral Atom Quantum Processors: Connecting Tool Developers and Hardware Experts
Neutral Atom Quantum Computing (NAQC) emerges as a promising hardware
platform primarily due to its long coherence times and scalability.
Additionally, NAQC offers computational advantages encompassing potential
long-range connectivity, native multi-qubit gate support, and the ability to
physically rearrange qubits with high fidelity. However, for the successful
operation of a NAQC processor, one additionally requires new software tools to
translate high-level algorithmic descriptions into a hardware executable
representation, taking maximal advantage of the hardware capabilities.
Realizing new software tools requires a close connection between tool
developers and hardware experts to ensure that the corresponding software tools
obey the corresponding physical constraints. This work aims to provide a basis
to establish this connection by investigating the broad spectrum of
capabilities intrinsic to the NAQC platform and its implications on the
compilation process. To this end, we first review the physical background of
NAQC and derive how it affects the overall compilation process by formulating
suitable constraints and figures of merit. We then provide a summary of the
compilation process and discuss currently available software tools in this
overview. Finally, we present selected case studies and employ the discussed
figures of merit to evaluate the different capabilities of NAQC and compare
them between two hardware setups.Comment: 32 pages, 13 figures, 2 table
Spontaneous symmetry breaking in projected entangled pair state models
In this thesis, we consider projected entangled pair state (PEPS) models as a framework for two-dimensional strongly-correlated quantum many body systems, where the global properties of the system are concisely encoded in one local tensor. While it was well known how to construct PEPS models with desired symmetries by manifestly encoding the symmetry in the local tensor, our goal in this work is to investigate whether this manifestly encoded symmetry can be spontaneously broken. By defining long-range order as a good criterion for symmetry breaking in a finite volume PEPS, we answer this question in the affirmative. A particularly attractive feature of PEPS models is that they have an exact holographic mapping, which is to say that the large system behavior is described by the ''PEPS boundary'', given by the fixed point(s) of the so called transfer operator. We investigate the implications of long-range order and prove that it leads to a particular symmetry breaking pattern in the fixed point space. We find this pattern by first proving that long-range order implies an asymptotic degeneracy in the transfer operator and then identifying the symmetry breaking mechanism as the one which, from all possible boundary (-matrix) configurations, selects the configurations that correspond to positive-semi-definite matrices, i.e. one-dimensional virtual quantum states. We prove that these correspond to boundary configurations that do not mix under arbitrary perturbations and are thus stable. We study the entanglement properties of these virtual quantum states and show that they can be described by local entanglement Hamiltonians, establishing that also in phases with symmetry breaking, gapped quantum phases have an associated local entanglement Hamiltonian