We report a deterministic and exact protocol to reverse any unknown qubit-unitary operation, which simulates the time inversion of a closed qubit system. To avoid known no-go results on universal deterministic exact unitary inversion, we consider the most general class of protocols transforming unknown unitary operations within the quantum circuit model, where the input unitary operation is called multiple times in sequence and fixed quantum circuits are inserted between the calls. In the proposed protocol, the input qubit-unitary operation is called 4 times to achieve the inverse operation, and the output state in an auxiliary system can be reused as a catalyst state in another run of the unitary inversion. We also present the simplification of the semidefinite programming for searching the optimal deterministic unitary inversion protocol for an arbitrary dimension presented by M. T. Quintino and D. Ebler [Quantum 6, 679 (2022)2521-327X10.22331/q-2022-03-31-679]. We show a method to reduce the large search space representing all possible protocols, which provides a useful tool for analyzing higher-order quantum transformations for unitary operations.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1103/PhysRevLett.131.120602 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
An optical waveplate rotating light polarization can be modeled as a single-qubit unitary operator. This analogy can be exploited to experimentally retrieve a polarization transformation within the paradigm of quantum process tomography. Standard approaches to tomographic problems rely on the maximum-likelihood estimation, providing the most likely transformation to yield the same outcomes as a set of experimental projective measurements.
View Article and Find Full Text PDFReversing Unknown Qubit-Unitary Operation, Deterministically and Exactly.
Phys Rev Lett
September 2023
Department of Physics, Graduate School of Science, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan.
We report a deterministic and exact protocol to reverse any unknown qubit-unitary operation, which simulates the time inversion of a closed qubit system. To avoid known no-go results on universal deterministic exact unitary inversion, we consider the most general class of protocols transforming unknown unitary operations within the quantum circuit model, where the input unitary operation is called multiple times in sequence and fixed quantum circuits are inserted between the calls. In the proposed protocol, the input qubit-unitary operation is called 4 times to achieve the inverse operation, and the output state in an auxiliary system can be reused as a catalyst state in another run of the unitary inversion.
View Article and Find Full Text PDFSpecifying the Unitary Evolution of a Qudit for a General Nonstationary Hamiltonian via the Generalized Gell-Mann Representation.
Entropy (Basel)
May 2020
Applied Mathematics Department, National Research University Higher School of Economics, Moscow 101000, Russia.
Optimal realizations of quantum technology tasks lead to the necessity of a detailed analytical study of the behavior of a -level quantum system (qudit) under a time-dependent Hamiltonian. In the present article, we introduce a new general formalism describing the unitary evolution of a qudit ( d ≥ 2 ) in terms of the Bloch-like vector space and specify how, in a general case, this formalism is related to finding time-dependent parameters in the exponential representation of the evolution operator under an arbitrary time-dependent Hamiltonian. Applying this new general formalism to a qubit case ( d = 2 ) , we specify the unitary evolution of a qubit via the evolution of a unit vector in R 4 , and this allows us to derive the precise analytical expression of the qubit unitary evolution operator for a wide class of nonstationary Hamiltonians.
View Article and Find Full Text PDFEntanglement bounds on the performance of quantum computing architectures.
Phys Rev Res
January 2020
Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA.
There are many possible architectures of qubit connectivity that designers of future quantum computers will need to choose between. However, the process of evaluating a particular connectivity graph's performance as a quantum architecture can be difficult. In this paper, we show that a quantity known as the isoperimetric number establishes a lower bound on the time required to create highly entangled states.
View Article and Find Full Text PDFRevising the measurement process in the variational quantum eigensolver: is it possible to reduce the number of separately measured operators?
Chem Sci
April 2019
OTI Lumionics Inc. , 100 College Street 351, Toronto , Ontario M5G 1L5 , Canada.
Current implementations of the Variational Quantum Eigensolver (VQE) technique for solving the electronic structure problem involve splitting the system qubit Hamiltonian into parts whose elements commute within their single qubit subspaces. The number of such parts rapidly grows with the size of the molecule. This increases the computational cost and can increase uncertainty in the measurement of the energy expectation value because elements from different parts need to be measured independently.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!