17 research outputs found
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
Error-mitigated quantum metrology via virtual purification
Quantum metrology with entangled resources aims to achieve sensitivity beyond
the standard quantum limit by harnessing quantum effects even in the presence
of environmental noise. So far, sensitivity has been mainly discussed from the
viewpoint of reducing statistical errors under the assumption of perfect
knowledge of a noise model. However, we cannot always obtain complete
information about a noise model due to coherence time fluctuations, which are
frequently observed in experiments. Such unknown fluctuating noise leads to
systematic errors and nullifies the quantum advantages. Here, we propose an
error-mitigated quantum metrology that can filter out unknown fluctuating noise
with the aid of purification-based quantum error mitigation. We demonstrate
that our protocol mitigates systematic errors and recovers superclassical
scaling in a practical situation with time-inhomogeneous bias-inducing noise.
Our results reveal the usefulness of purification-based error mitigation for
unknown fluctuating noise, thus paving the way not only for practical quantum
metrology but also for quantum computation affected by such noise.Comment: 6+11 pages, 3+4 figure
Generalized quantum subspace expansion
One of the major challenges for erroneous quantum computers is undoubtedly
the control over the effect of noise. Considering the rapid growth of available
quantum resources that are not fully fault-tolerant, it is crucial to develop
practical hardware-friendly quantum error mitigation (QEM) techniques to
suppress unwanted errors. Here, we propose a novel generalized quantum subspace
expansion method which can handle stochastic, coherent, and algorithmic errors
in quantum computers. By fully exploiting the substantially extended subspace,
we can efficiently mitigate the noise present in the spectra of a given
Hamiltonian, without relying on any information of noise. The performance of
our method is discussed under two highly practical setups: the quantum
subspaces are mainly spanned by powers of the noisy state and a set of
error-boosted states, respectively. We numerically demonstrate in both
situations that we can suppress errors by orders of magnitude, and show that
out protocol inherits the advantages of previous error-agnostic QEM techniques
as well as overcoming their drawbacks.Comment: 6+8 pages, 3+5 figure
Dual-GSE: Resource-efficient Generalized Quantum Subspace Expansion
Quantum error mitigation (QEM) is a class of hardware-efficient error
reduction methods through additional modest quantum operations and classical
postprocessing on measurement outcomes. The generalized quantum subspace
expansion (GSE) has been recently proposed as a unified framework of two
distinct QEM methods: quantum subspace expansion (QSE) and purification-based
QEM. GSE takes over the advantages of these two methods, achieving the
mitigation of both coherent and stochastic errors. However, GSE still requires
multiple copies of quantum states and entangled measurements between the
copies, as required in purification-based QEM. This is a significant drawback
under the current situation of the restricted number and connectivity of
qubits. In this work, we propose a resource-efficient implementation of GSE,
which we name "Dual-GSE", circumventing significant overheads of state copies
by constructing an ansatz of error-mitigated quantum states via dual-state
purification. Remarkably, Dual-GSE can further simulate larger quantum systems
beyond the size of available quantum hardware with a suitable ansatz
construction inspired by those divide-and-conquer methods that forge
entanglement classically. This also contributes to a significant reduction of
the measurement overhead because we only need to measure subsystems' Pauli
operators. The proposed method is demonstrated by numerical simulation of the
eight-qubit transverse field Ising model, showing that our method estimates the
ground state energy in high precision under gate noise with low mitigation
overhead and practical sampling cost.Comment: 25 pages, 19 figure