800 research outputs found
Verification of Many-Qubit States
Verification is a task to check whether a given quantum state is close to an
ideal state or not. In this paper, we show that a variety of many-qubit quantum
states can be verified with only sequential single-qubit measurements of Pauli
operators. First, we introduce a protocol for verifying ground states of
Hamiltonians. We next explain how to verify quantum states generated by a
certain class of quantum circuits. We finally propose an adaptive test of
stabilizers that enables the verification of all polynomial-time-generated
hypergraph states, which include output states of the
Bremner-Montanaro-Shepherd-type instantaneous quantum polynomial time (IQP)
circuits. Importantly, we do not make any assumption that the identically and
independently distributed copies of the same states are given: Our protocols
work even if some highly complicated entanglement is created among copies in
any artificial way. As applications, we consider the verification of the
quantum computational supremacy demonstration with IQP models, and verifiable
blind quantum computing.Comment: 15 pages, 3 figures, published versio
Merlin-Arthur with efficient quantum Merlin and quantum supremacy for the second level of the Fourier hierarchy
We introduce a simple sub-universal quantum computing model, which we call
the Hadamard-classical circuit with one-qubit (HC1Q) model. It consists of a
classical reversible circuit sandwiched by two layers of Hadamard gates, and
therefore it is in the second level of the Fourier hierarchy. We show that
output probability distributions of the HC1Q model cannot be classically
efficiently sampled within a multiplicative error unless the polynomial-time
hierarchy collapses to the second level. The proof technique is different from
those used for previous sub-universal models, such as IQP, Boson Sampling, and
DQC1, and therefore the technique itself might be useful for finding other
sub-universal models that are hard to classically simulate. We also study the
classical verification of quantum computing in the second level of the Fourier
hierarchy. To this end, we define a promise problem, which we call the
probability distribution distinguishability with maximum norm (PDD-Max). It is
a promise problem to decide whether output probability distributions of two
quantum circuits are far apart or close. We show that PDD-Max is BQP-complete,
but if the two circuits are restricted to some types in the second level of the
Fourier hierarchy, such as the HC1Q model or the IQP model, PDD-Max has a
Merlin-Arthur system with quantum polynomial-time Merlin and classical
probabilistic polynomial-time Arthur.Comment: 30 pages, 4 figure
Quantum computational universality of hypergraph states with Pauli-X and Z basis measurements
Measurement-based quantum computing is one of the most promising quantum
computing models. Although various universal resource states have been proposed
so far, it was open whether only two Pauli bases are enough for both of
universal measurement-based quantum computing and its verification. In this
paper, we construct a universal hypergraph state that only requires and
-basis measurements for universal measurement-based quantum computing. We
also show that universal measurement-based quantum computing on our hypergraph
state can be verified in polynomial time using only and -basis
measurements. Furthermore, in order to demonstrate an advantage of our
hypergraph state, we construct a verifiable blind quantum computing protocol
that requires only and -basis measurements for the client.Comment: 12 pages, 8 figures, 1 table, close to published versio
生物学的線量体積ヒストグラムを用いた食道癌根治的化学放射線療法後の心合併症の検討
内容の要約広島大学(Hiroshima University)博士(医学)Doctor of Philosophy in Medical Sciencedoctora
An Algorithmic Framework for Computing Validation Performance Bounds by Using Suboptimal Models
Practical model building processes are often time-consuming because many
different models must be trained and validated. In this paper, we introduce a
novel algorithm that can be used for computing the lower and the upper bounds
of model validation errors without actually training the model itself. A key
idea behind our algorithm is using a side information available from a
suboptimal model. If a reasonably good suboptimal model is available, our
algorithm can compute lower and upper bounds of many useful quantities for
making inferences on the unknown target model. We demonstrate the advantage of
our algorithm in the context of model selection for regularized learning
problems
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