In Phys. Rev. A 100, 062317 (2019), the authors reported an algorithm to implement, in a circuit-based quantum computer, a general quantum measurement (GQM) of a two-level quantum system, a qubit. Even though their algorithm seems right, its application involves the solution of an intricate nonlinear system of equations to obtain the angles determining the quantum circuit to be implemented for the simulation. In this article, we identify and discuss a simple way to circumvent this issue and implement GQMs on any $d$-level quantum system through quantum state preparation algorithms. Using some examples for one qubit, one qutrit, and two qubits, we illustrate the easy of application of our protocol. In addition, we show how one can utilize our protocol for simulating quantum instruments, for which we also give an example. All our examples are demonstrated using IBM's quantum processors.
In Phys. Rev. A 100, 062317 (2019), the authors reported an algorithm to implement, in a circuit-based quantum computer, a general quantum measurement (GQM) of a two-level quantum system, a qubit. Even though their algorithm seems right, its application involves the solution of an intricate nonlinear system of equations to obtain the angles determining the quantum circuit to be implemented for the simulation. In this article, we identify and discuss a simple way to circumvent this issue and implement GQMs on any d-level quantum system through quantum state preparation algorithms. Using some examples for one qubit, one qutrit, and two qubits, we illustrate the easy of application of our protocol. In addition, we show how one can utilize our protocol for simulating quantum instruments, for which we also give an example. All our examples are demonstrated using IBM's quantum processors.
Abstract In Xin et al (2017 Phys. Rev. A 96 062303) and Wei et al (2018 Sci. China Phys. Mech. Astron. 61 70311), the authors reported an algorithm to simulate, in a circuit-based quantum computer, a general quantum channel (QC). However, the application of their algorithm is limited because it entails the solution of intricate non-linear systems of equations in order to obtain the quantum circuit to be implemented for the simulation. Motivated by this issue, in this article we identify and discuss a simple way to implement the simulation of QCs on any d -level quantum system through quantum state preparation algorithms, that have received much attention in the quantum information science literature lately. We exemplify the versatility of our protocol applying it to most well known qubit QCs, to some qudit QCs, and to simulate the effect of Lorentz transformations on spin states. We also regard the application of our protocol for initial mixed states. Most of the given application examples are demonstrated using IBM’s quantum computers.
This work presents a new protocol for simulating quantum systems based on quantum state preparation, with various applications such as the simulation of quantum channels and the implementation of general measurements. In general, these applications are modeled by quantum operations and involve completely positive trace-preserving (CPTP) maps. These maps correspond to sets of operators known as Kraus operators, when applied to the simulation of quantum channels, and general measurement operators, when applied to the implementation of non-selective measurements. In the literature, especially when the experimental platform is circuit-based quantum computing, these operators are employed to adjust the parameters of unitary matrices, which are the ones that actually operate in the experiment. To do this, it is necessary to solve a system of nonlinear equations numerically. The new protocol avoids these complications by applying the operators directly over the analytical description of the quantum systems to be simulated. Through the use of isometries and purifications, it models the quantum operations of interest to the experimentalist, whether they are quantum channels or general measurements, enabling the use of software libraries for symbolic algebra to perform exact and automated manipulation of the state vector, with complex amplitudes, to be prepared for simulation. The algebraic manipulation of the state vector provides greater flexibility in experimental planning, as it can be used on any quantum simulation platform. More specifically, it is not restricted to circuit-based quantum computing. Finally, the use of the new protocol is illustrated in the simulation of one-qubit channels, qudits, Lorentz transformations, mixed-state simulations, POVM implementation, and the certification of quantum contextuality via POVMs.
Abstract The preparation of quantum states is a fundamental subroutine for a broad class of quantum information protocols and is critical for both quantum communication and quantum computation. Building upon the quantum algorithms introduced in previous works [M. B. Pozzobom and J. Maziero, Quantum Inf. Process. 18, 142 (2019)] and [E. R. Gårding et al., Entropy 23, 797 (2021)], the authors of [F. Shahbeigi, M. Karimi and V. Karimipour, Phys. Scr. 97, 025101 (2022)] demonstrated the capability to prepare mixed two-qubit X-real states on quantum computers by extending the methodology originally devised for mixed two-qubit Bell-diagonal states. In this article, we delve into an overlooked pattern within these quantum circuits, allowing us to present a modular algorithm for the preparation of general d -dimensional mixed quantum states using quantum information processors. Our general algorithm has a modular structure, encompassing eigenvalue encoding, entropy injection, and eigenvector preparation. To validate our algorithm, we conduct tests on quantum computers utilizing both X- and non-X-states for two mixed-state qubits, two-ququart Bell-diagonal states, as well as arbitrary random density matrices spanning one, two, and three qubits.
We derive a deterministic protocol to implement a general single-qubit positive operator-valued measure (POVM) on near-term circuit-based quantum computers. The protocol has a modular structure such that an n-element POVM is implemented as a sequence of $(n\ensuremath{-}1)$ circuit modules. Each module performs a two-element POVM. Two variations of the protocol are suggested---one optimal in terms of number of ancilla qubits, the other optimal in terms of number of qubit gate operations and quantum circuit depth. We use the protocol to implement two- and three-element POVMs on two publicly available quantum computing devices. The results we obtain suggest that implementing nontrivial POVMs could be within the reach of the current noisy quantum computing devices.
Quantum computers present a compelling platform for the study of open quantum systems, namely the non-unitary dynamics of a system. Here, we investigate and report digital simulations of Markovian, non-unitary dynamics that converge to a unique steady state. The steady state is programmed as a desired target state, yielding semblance to a quantum state preparation protocol. By delegating ancilla qubits and systems qubits, the system state is driven to the target state by repeatedly performing the following steps: (1) executing a designated system-ancilla entangling circuit, (2) measuring the ancilla qubits, and (3) re-initializing ancilla qubits to known states through active reset. While the ancilla qubits are measured and reinitialized to known states, the system qubits undergo a non-unitary evolution and are steered from arbitrary initial states to desired target states. We show results of the method by preparing arbitrary qubit states and qutrit (three-level) states on contemporary quantum computers. We also demonstrate that the state convergence can be accelerated by utilizing the readouts of the ancilla qubits to guide the protocol in a non-blind manner. Our work serves as a nontrivial example that incorporates and characterizes essential operations such as qubit reuse (qubit reset), entangling circuits, and measurement. These operations are not only vital for near-term noisy intermediate-scale quantum (NISQ) applications but are also crucial for realizing future error-correcting codes.
In this work, the asymmetry properties of quantum states associated with the Hamiltonian generator of the dynamics of the magnetic dipole interaction are investigated and their relationships with the production of entanglement are identified. Are also explored the types of separable or partially entangled quantum states that can be used as a resource in the entanglement distribution protocol, where we use IBM quantum processors to test the results with simulations and experiments performed remotely. Furthermore, a state preparation algorithm is presented that allows simulating and performing experiments with general quantum measurements and quantum instruments, as well as noisy quantum channels. In the topic about the properties of asymmetry and entanglement production, classes of pure and mixed quantum states consisting of 2 qubits evolved under magnetic dipole interaction (MDI) are considered.The asymmetry measure used is based on the Wigner-Yanase skew information between the quantum state and the Hamiltonian of the IDM, whose dependence is provided by the interaction parameters and initial conditions of the system. The local asymmetry associated with the evolved state is investigated, which is characterized by its dependence on the interaction parameters, local and temporal parameters, allowing the establishment of indirect relationships with the entanglement dynamics generated by MDI. The asymmetry related to the element of the unitary group responsible for the dynamics of the MDI is also analyzed, being useful to understand the dynamic character regarding the Wigner-Yanase asymmetry and to establish dynamic links with other properties. On the other hand, regarding the entanglement distribution protocol, the role of separable and partially entangled states are explored in the context of the Bell-diagonal class of states, analyzing the probabilistic entanglement distribution, where it involves selective projective measures, and the deterministic entanglement distribution, where it involves the action of non-selective general quantum measurements. Finally, with the proposal of a state preparation algorithm based on the relationship between the action of quantum channels and isometry, it was possible to carry out simulations and experiments on IBM quantum processors in general quantum measurements, quantum instruments and noisy quantum channels applied to qudits, allowing, in this way, to handle and develop in a simpler way the applications that until then were complex to simulate.