12 research outputs found
Overfitting in quantum machine learning and entangling dropout
The ultimate goal in machine learning is to construct a model function that
has a generalization capability for unseen dataset, based on given training
dataset. If the model function has too much expressibility power, then it may
overfit to the training data and as a result lose the generalization
capability. To avoid such overfitting issue, several techniques have been
developed in the classical machine learning regime, and the dropout is one such
effective method. This paper proposes a straightforward analogue of this
technique in the quantum machine learning regime, the entangling dropout,
meaning that some entangling gates in a given parametrized quantum circuit are
randomly removed during the training process to reduce the expressibility of
the circuit. Some simple case studies are given to show that this technique
actually suppresses the overfitting.Comment: 7 pages, 8 figure
Measurement optimization of variational quantum simulation by classical shadow and derandomization
Simulating large quantum systems is the ultimate goal of quantum computing.
Variational quantum simulation (VQS) gives us a tool to achieve the goal in
near-term devices by distributing the computation load to both classical and
quantum computers. However, as the size of the quantum system becomes large,
the execution of VQS becomes more and more challenging. One of the most severe
challenges is the drastic increase in the number of measurements; for example,
the number of measurements tends to increase by the fourth power of the number
of qubits in a quantum simulation with a chemical Hamiltonian. This work aims
to dramatically decrease the number of measurements in VQS by recently proposed
shadow-based strategies such as classical shadow and derandomization. Even
though previous literature shows that shadow-based strategies successfully
optimize measurements in the variational quantum optimization (VQO), how to
apply them to VQS was unclear due to the gap between VQO and VQS in measuring
observables. In this paper, we bridge the gap by changing the way of measuring
observables in VQS and propose an algorithm to optimize measurements in VQS by
shadow-based strategies. Our theoretical analysis not only reveals the
advantage of using our algorithm in VQS but theoretically supports using
shadow-based strategies in VQO, whose advantage has only been given
numerically. Additionally, our numerical experiment shows the validity of using
our algorithm with a quantum chemical system
Expressive Quantum Supervised Machine Learning using Kerr-nonlinear Parametric Oscillators
Quantum machine learning with variational quantum algorithms (VQA) has been
actively investigated as a practical algorithm in the noisy intermediate-scale
quantum (NISQ) era. Recent researches reveal that the data reuploading, which
repeatedly encode classical data into quantum circuit, is necessary for
obtaining the expressive quantum machine learning model in the conventional
quantum computing architecture. However, the data reuploding tends to require
large amount of quantum resources, which motivates us to find an alternative
strategy for realizing the expressive quantum machine learning efficiently. In
this paper, we propose quantum machine learning with Kerr-nonlinear Parametric
Oscillators (KPOs), as another promising quantum computing device. The key idea
is that we use not only the ground state and first excited state but also use
higher excited states, which allows us to use a large Hilbert space even if we
have a single KPO. Our numerical simulations show that the expressibility of
our method with only one mode of the KPO is much higher than that of the
conventional method with six qubits. Our results pave the way towards resource
efficient quantum machine learning, which is essential for the practical
applications in the NISQ era.Comment: 13 pages, 8 figure
Inverse Problem of Cosmic-Ray Electron/Positron from Dark Matter
We discuss the possibility of solving the inverse problem of the cosmic-ray
electron/positron from decaying/annihilating dark matter, and show simple
analytic formulae to reconstruct the source spectrum of the electron/positron
from the observed flux. We also illustrate our approach by applying the
obtained formula to the just released Fermi data as well as the new HESS data.Comment: 16 pages, 6 figure
Identifying the Origin of Longevity of Metastable Stau at the LHC
In the framework of the supersymmetric standard model, the lighter stau often
becomes long-lived. Such longevity of the stau is realized in three
well-motivated scenarios: (A) the stau is the next-to-lightest supersymmetric
particle (NLSP) and the gravitino is the lightest supersymmetric particle
(LSP), (B) the stau is the LSP and R-parity is slightly violated, and (C) the
stau is NLSP, the neutralino is the LSP, and the their masses are degenerate.
We study the event topology and the decay of the stopping stau at the hadron
calorimeter at the LHC, and show that it is possible to identify the reason why
the stau becomes long-lived.Comment: 14 pages, 3 figures, 1 tabl
The generative quantum eigensolver (GQE) and its application for ground state search
We introduce the generative quantum eigensolver (GQE), a novel method for
applying classical generative models for quantum simulation. The GQE algorithm
optimizes a classical generative model to produce quantum circuits with desired
properties. Here, we develop a transformer-based implementation, which we name
the generative pre-trained transformer-based (GPT) quantum eigensolver
(GPT-QE), leveraging both pre-training on existing datasets and training
without any prior knowledge. We demonstrate the effectiveness of training and
pre-training GPT-QE in the search for ground states of electronic structure
Hamiltonians. GQE strategies can extend beyond the problem of Hamiltonian
simulation into other application areas of quantum computing.Comment: 16 pages, 7 figure
Probing High Reheating Temperature Scenarios at the LHC with Long-Lived Staus
We investigate the possibility of probing high reheating temperature
scenarios at the LHC, in supersymmetric models where the gravitino is the
lightest supersymmetric particle, and the stau is the next-to-lightest
supersymmetric particle. In such scenarios, the big-bang nucleosynthesis and
the gravitino abundance give a severe upper bound on the gluino mass. We find
that, if the reheating temperature is \sim 10^8 GeV or higher, the scenarios
can be tested at the LHC with an integrated luminosity of O(1 fb^{-1}) at
\sqrt{s}=7 TeV in most of the parameter space.Comment: 17 pages, 5 figures, minor modification
Approximate amplitude encoding in shallow parameterized quantum circuits and its application to financial market indicators
Efficient methods for loading given classical data into quantum circuits are essential for various quantum algorithms. In this paper, we propose an algorithm called Approximate Amplitude Encoding that can effectively load all the components of a given real-valued data vector into the amplitude of quantum state, while the previous proposal can load only the absolute values of those components. The key of our algorithm is to variationally train a shallow parameterized quantum circuit, using the results of two types of measurement: the standard computational-basis measurement plus the measurement in the Hadamard-transformed basis, introduced in order to handle the sign of the data components. The variational algorithm changes the circuit parameters so as to minimize the sum of two costs corresponding to those two measurement basis, both of which are given by the efficiently computable maximum mean discrepancy. We also consider the problem of constructing the singular value decomposition entropy via the stock market data set to give a financial market indicator; a quantum algorithm (the variational singular value decomposition algorithm) is known to produce a solution faster than classical, which yet requires the sign-dependent amplitude encoding. We demonstrate, with an in-depth numerical analysis, that our algorithm realizes loading of time series of real stock prices on quantum state with small approximation error, and thereby it enables constructing an indicator of the financial market based on the stock prices