We construct short analytical quantum circuits for the exact evolution of a spin triangle with Dzyaloshinskii--Moriya (DM) interaction. We consider pure DM interaction with arbitrary real couplings and two Hamiltonian families with uniform Heisenberg exchange. For pure DM, a change of basis reduces the evolution to two single-qubit rotations. The circuits reproduce the full evolution operator at arbitrary time with a fixed gate count and admit implementations with both triangular and linear qubit connectivity. Experiments on a superconducting IBM quantum processor demonstrate directional quantum-state transfer and reproduce the amplitude and phase of transverse magnetization. In these experiments, the exact circuits reduce distortions relative to circuits based on the second-order Trotter formula. On a 12-spin kagome cluster, exact triangle blocks reduce the gate count at a prescribed accuracy. We also investigate the reduction of coherent errors by adjusting circuit angles and applying echo pulses to neighboring qubits.
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47 pages, 17 figures, including Supplemental Material. v2 adds exact chain circuits, IBM Quantum experiments, and coherent-error compensation examples. Code and data: https://doi.org/10.5281/zenodo.23007728
We construct short analytical quantum circuits for the exact evolution of a spin triangle with Dzyaloshinskii--Moriya (DM) interaction. We consider pure DM interaction with arbitrary real couplings and two Hamiltonian families with uniform Heisenberg exchange. For pure DM, a change of basis reduces the evolution to two single-qubit rotations. The circuits reproduce the full evolution operator at arbitrary time with a fixed gate count and admit implementations with both triangular and linear qubit connectivity. Experiments on a superconducting IBM quantum processor demonstrate directional quantum-state transfer and reproduce the amplitude and phase of transverse magnetization. In these experiments, the exact circuits reduce distortions relative to circuits based on the second-order Trotter formula. On a 12-spin kagome cluster, exact triangle blocks reduce the gate count at a prescribed accuracy. We also investigate the reduction of coherent errors by adjusting circuit angles and applying echo pulses to neighboring qubits.
In the present paper, an influence of the anisotropic antisymmetric exchange interaction, the Dzialoshinskii–Moriya (DM) interaction, on entanglement of two qubits in various magnetic spin models, including the pure DM model and the most general XYZ model, are studied. We find that the time evolution generated by DM interaction can implement the SWAP gate and discuss realistic quasi-one-dimensional magnets where it can be realized. It is shown that inclusion of the DM interaction to any Heisenberg model creates, when it does not exist, or strengthens, when it exists, the entanglement. We give physical explanation of these results by studying the ground state of the systems at T = 0. Nonanalytic dependence of the concurrence on the DM interaction and its relation with quantum phase transition is indicated. Our results show that spin models with the DM coupling have some potential applications in quantum computations and the DM interaction could be an efficient control parameter of entanglement.
In the present paper an influence of the anisotropic antisymmetric exchange interaction, the Dzialoshinskii-Moriya (DM) interaction, on entanglement of two qubits in various magnetic spin models, including the pure DM model and the most general XYZ model are studied. We find that the time evolution generated by DM interaction can implement the SWAP gate and discuss realistic quasi-one-dimensional magnets where it can be realized. It is shown that inclusion of the DM interaction to any Heisenberg model creates, when it does not exist, or strengthens, when it exists, the entanglement. We give physical explanation of these results by studying the ground state of the systems at T=0. Nonanalytic dependence of the concurrence on the DM interaction and its relation with quantum phase transition is indicated. Our results show that spin models with the DM coupling have some potential applications in quantum computations and the DM interaction could be an efficient control parameter of entanglement.
Abstract Motivated by the ability of triangular spin ladders to implement quantum information processing, we propose a type of such systems whose Hamiltonian includes the XX Heisenberg interaction on the rungs and Dzyaloshinskii–Moriya (DM) coupling over the legs. In this work, we discuss how tuning the magnetic interactions between elements of a nanomagnetic cell which contains four qubits influences on the dynamical behavior of entanglement shared between any pairs of the system. In this work, we make use of concurrence for monitoring entanglement. It is realized that the generation of quantum W states is an important feature of the present model when the system evolves unitarily with time. In general, coincidence with the emergence of W states, the concurrences of all pairs are equal to 2/ N , where N is the number of system’s qubits. We also obtain the precise relationship between the incidence of such states and the value of DM interaction as well as the time of entanglement transfer. Finally, by studying the two-point quantum correlations and expectation values of different spin variables, we find that xx and yy correlations bring the entanglement to a maximum value for W states, whereas for these states, zz correlation between any pairs completely quenches. Our results reveal that although S ˆ tot z does not commute with the system’s Hamiltonian, its expectation value remains constant during time evolution which is a generic property of quantum W states.
Controlled time-evolution circuits select forward or backward Hamiltonian time evolution according to the state of an ancilla qubit. They are fundamental building blocks in quantum eigenvalue transformation of unitaries, Hamiltonian filtering, and related quantum algorithms. A direct realization adds ancilla control to the elementary gates of the time-evolution circuit and therefore increases the two-qubit gate count, compiled T depth and CX depth. We develop an efficient recursive algorithm that, for an arbitrary Pauli-sum Hamiltonian, partitions the input Pauli terms into groups and assigns to each group a sign-flip Pauli string that anti-commutes with the in-group terms, thereby removing ancilla control from the grouped time-evolution blocks. Numerical benchmarks on random Hamiltonians and structured spin Hamiltonians show reductions in compiled T depth and compiled CX depth. For a Kagome Hamiltonian with 24 spins under full connectivity, the proposed construction reduces the compiled T depth by 85.2% and the compiled CX depth by 68.9%, compared with a conventional implementation that decomposes the Hamiltonian into individual Pauli terms and implements the controlled time evolution of each term by directly adding the ancilla qubit to the corresponding Pauli-rotation circuit.
We investigate the exact entanglement dynamics of a two-qubit Heisenberg XXZ chain with Dzyaloshinskii-Moriya (DM) interactions, interacting with an anisotropic spin bath in thermal equi- librium at a temperature T, driven by an external magnetic field B along the z-axis. We establish that, for an initially entangled qubit pair, the DM interactions generate entanglement and enhance the entanglement in the revival region. The effects of the DM interaction are also seen to be very important at high temperatures and for weak coupling between the two qubits where it is seen to preserve entanglement. These effects are weakened when the magnetic field B and the Heisenberg coupling are switched on. If the two-qubits are prepared in an initially separable state, the DM in- teraction instead has a negative effect on their entanglement. On a whole entanglement can better be preserve in the spin chain even at high temperatures by increases the external magnetic field B and the Heisenberg couplings, and by tuning the strength of the DM interaction.
We investigate the exact entanglement dynamics of a two-qubit Heisenberg XXZ chain with Dzyaloshinskii-Moriya (DM) interactions, interacting with an anisotropic spin bath in thermal equi- librium at a temperature T, driven by an external magnetic field B along the z-axis. We establish that, for an initially entangled qubit pair, the DM interactions generate entanglement and enhance the entanglement in the revival region. The effects of the DM interaction are also seen to be very important at high temperatures and for weak coupling between the two qubits where it is seen to preserve entanglement. These effects are weakened when the magnetic field B and the Heisenberg coupling are switched on. If the two-qubits are prepared in an initially separable state, the DM in- teraction instead has a negative effect on their entanglement. On a whole entanglement can better be preserve in the spin chain even at high temperatures by increases the external magnetic field B and the Heisenberg couplings, and by tuning the strength of the DM interaction.