706 research outputs found
Quantum state reduction for universal measurement based computation
Measurement based quantum computation (MBQC), which requires only single
particle measurements on a universal resource state to achieve the full power
of quantum computing, has been recognized as one of the most promising models
for the physical realization of quantum computers. Despite considerable
progress in the last decade, it remains a great challenge to search for new
universal resource states with naturally occurring Hamiltonians, and to better
understand the entanglement structure of these kinds of states. Here we show
that most of the resource states currently known can be reduced to the cluster
state, the first known universal resource state, via adaptive local
measurements at a constant cost. This new quantum state reduction scheme
provides simpler proofs of universality of resource states and opens up plenty
of space to the search of new resource states, including an example based on
the one-parameter deformation of the AKLT state studied in [Commun. Math. Phys.
144, 443 (1992)] by M. Fannes et al. about twenty years ago.Comment: 5 page
No-go Theorem for One-way Quantum Computing on Naturally Occurring Two-level Systems
One-way quantum computing achieves the full power of quantum computation by
performing single particle measurements on some many-body entangled state,
known as the resource state. As single particle measurements are relatively
easy to implement, the preparation of the resource state becomes a crucial
task. An appealing approach is simply to cool a strongly correlated quantum
many-body system to its ground state. In addition to requiring the ground state
of the system to be universal for one-way quantum computing, we also want the
Hamiltonian to have non-degenerate ground state protected by a fixed energy
gap, to involve only two-body interactions, and to be frustration-free so that
measurements in the course of the computation leave the remaining particles in
the ground space. Recently, significant efforts have been made to the search of
resource states that appear naturally as ground states in spin lattice systems.
The approach is proved to be successful in spin-5/2 and spin-3/2 systems. Yet,
it remains an open question whether there could be such a natural resource
state in a spin-1/2, i.e., qubit system. Here, we give a negative answer to
this question by proving that it is impossible for a genuinely entangled qubit
states to be a non-degenerate ground state of any two-body frustration-free
Hamiltonian. What is more, we prove that every spin-1/2 frustration-free
Hamiltonian with two-body interaction always has a ground state that is a
product of single- or two-qubit states, a stronger result that is interesting
independent of the context of one-way quantum computing.Comment: 5 pages, 1 figur
Tensor product representation of topological ordered phase: necessary symmetry conditions
The tensor product representation of quantum states leads to a promising
variational approach to study quantum phase and quantum phase transitions,
especially topological ordered phases which are impossible to handle with
conventional methods due to their long range entanglement. However, an
important issue arises when we use tensor product states (TPS) as variational
states to find the ground state of a Hamiltonian: can arbitrary variations in
the tensors that represent ground state of a Hamiltonian be induced by local
perturbations to the Hamiltonian? Starting from a tensor product state which is
the exact ground state of a Hamiltonian with topological order,
we show that, surprisingly, not all variations of the tensors correspond to the
variation of the ground state caused by local perturbations of the Hamiltonian.
Even in the absence of any symmetry requirement of the perturbed Hamiltonian,
one necessary condition for the variations of the tensors to be physical is
that they respect certain symmetry. We support this claim by
calculating explicitly the change in topological entanglement entropy with
different variations in the tensors. This finding will provide important
guidance to numerical variational study of topological phase and phase
transitions. It is also a crucial step in using TPS to study universal
properties of a quantum phase and its topological order.Comment: 10 pages, 6 figure
Conversational Speech Recognition by Learning Audio-textual Cross-modal Contextual Representation
Automatic Speech Recognition (ASR) in conversational settings presents unique
challenges, including extracting relevant contextual information from previous
conversational turns. Due to irrelevant content, error propagation, and
redundancy, existing methods struggle to extract longer and more effective
contexts. To address this issue, we introduce a novel Conversational ASR
system, extending the Conformer encoder-decoder model with cross-modal
conversational representation. Our approach leverages a cross-modal extractor
that combines pre-trained speech and text models through a specialized encoder
and a modal-level mask input. This enables the extraction of richer historical
speech context without explicit error propagation. We also incorporate
conditional latent variational modules to learn conversational level attributes
such as role preference and topic coherence. By introducing both cross-modal
and conversational representations into the decoder, our model retains context
over longer sentences without information loss, achieving relative accuracy
improvements of 8.8% and 23% on Mandarin conversation datasets HKUST and
MagicData-RAMC, respectively, compared to the standard Conformer model.Comment: Submitted to TASL
Quantum codes give counterexamples to the unique pre-image conjecture of the N-representability problem
It is well known that the ground state energy of many-particle Hamiltonians
involving only 2-body interactions can be obtained using constrained
optimizations over density matrices which arise from reducing an N-particle
state. While determining which 2-particle density matrices are "N-
representable" is a computationally hard problem, all known extreme
N-representable 2-particle reduced density matrices arise from a unique
N-particle pre-image, satisfying a conjecture established in 1972. We present
explicit counterexamples to this conjecture through giving Hamiltonians with
2-body interactions which have degenerate ground states that cannot be
distinguished by any 2-body operator. We relate the existence of such
counterexamples to quantum error correction codes and topologically ordered
spin systems.Comment: 4 pages, 1 figur
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