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arXiv:cond-mat/0109100 · Physical review. B, Condensed matter

Single- and double-qubit gates by manipulating fourfold degeneracy

Tugrul Hakioglu, J. R. Anderson, F. C. Wellstood

Published Sep 30, 2002• 2 citations
arXivHTMLPDF

Abstract

We propose a mechanism for single- and double-qubit state manipulations in quantum computation with an inseparable double-qubit structure. The principle is based on manipulating the degeneracy of the four energy levels. The degeneracy of levels is allowed to be fourfold, doubly degenerate in pairs and nondegenerate, and these configurations are tuned by two coupling parameters. The quantum gate operations are performed at the nondegenerate whereas the data are stored in the degenerate configurations. The fact that the center of the four energy levels is invariant at all parameter values is exploited, and this particularly increases the performance of the controlled operations. A particular realization of the proposed mechanism is suggested by using the recently proposed inductively coupled rf superconducting quantum interference device loops in the macroscopic quantum tunneling regime where the energy eigenlevels are directly connected with the measurable flux states. This very fact also allows precise read-in and read-out operations by measurement of the flux which can also be done by existing techniques. That other physical realizations of the mechanism than that examined here are likely to exist is also discussed briefly.

DOI
10.1103/physrevb.66.115324

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We propose a mechanism for single- and double-qubit state manipulations in quantum computation with an inseparable double-qubit structure. The principle is based on manipulating the degeneracy of the four energy levels. The degeneracy of levels is allowed to be fourfold, doubly degenerate in pairs and nondegenerate, and these configurations are tuned by two coupling parameters. The quantum gate operations are performed at the nondegenerate whereas the data are stored in the degenerate configurations. The fact that the center of the four energy levels is invariant at all parameter values is exploited, and this particularly increases the performance of the controlled operations. A particular realization of the proposed mechanism is suggested by using the recently proposed inductively coupled rf superconducting quantum interference device loops in the macroscopic quantum tunneling regime where the energy eigenlevels are directly connected with the measurable flux states. This very fact also allows precise read-in and read-out operations by measurement of the flux which can also be done by existing techniques. That other physical realizations of the mechanism than that examined here are likely to exist is also discussed briefly.
We demonstrate that in a coupled two-qubit system any single-qubit gate can be decomposed into \ensuremath{\mid}0⟩-controlled and \ensuremath{\mid}1⟩-controlled two-qubit gates which can be implemented by manipulations analogous to that used for a controlled NOT (CNOT) gate. Based on this we present a unified approach to implement universal single-qubit and two-qubit gates in a coupled two-qubit system with fixed always-on coupling. This approach requires neither supplementary circuit or additional physical qubits to control the coupling nor extra hardware to adjust the energy level structure. The feasibility of this approach is demonstrated by numerical simulation of single-qubit gates and creation of two-qubit Bell states in rf-driven inductively coupled two superconducting quantum interference device flux qubits with realistic device parameters and constant always-on coupling.
Abstract Universal quantum computing relies on high-fidelity entangling operations. Here, we demonstrate that four coupled qubits can operate as a quantum gate, where two qubits control the operation on two target qubits (a four-qubit gate). This configuration can implement four different controlled two-qubit gates: two different entangling swap and phase operations, a phase operation distinguishing states of different parity, and the identity operation (idle quantum gate), where the choice of gate is set by the state of the control qubits. The device exploits quantum interference to control the operation on the target qubits by coupling them to each other via the control qubits. By connecting several four-qubit devices in a two-dimensional lattice, one can achieve a highly connected quantum computer. We consider an implementation of the four-qubit gate with superconducting qubits, using capacitively coupled qubits arranged in a diamond-shaped architecture.
A two-level quantum system is the building block of a quantum computer. This pair of quantum states defines the computational unit of a quantum computer, and it is called a quantum bit or qubit in analogy to the bit that is the binary unit of a classical computer. The spin of a single electron naturally defines such a two-level quantum system. A quantum dot can be tuned to the single-electron regime, and an array of singly occupied quantum dots provides a multi-qubit register. This thesis describes the multielectron encoding of a spin qubit using a pair or a trio of quantum dots, and it analyzes the coherence properties and manipulation protocols of this system. The singlet-triplet qubit, coded using the singlet state and the spinless triplet state of a pair of singly occupied quantum dots, can be controlled all electrically when applying voltages to gates close to the quantum dot structure. Rapid, subnanosecond modifications of the double quantum dot's charge configuration have been realized successfully. A small magnetic field gradient across the double quantum dot enables universal qubit control. Two modifications of the normal singlet-triplet encoding are introduced. (1) The six-electron configuration of a double quantum dot encodes a singlet-triplet qubit in the same way as for the two-electron double quantum dot. Two electrons at each quantum dot are irrelevant for the qubit manipulations because they are paired in a singlet state; the remaining two electrons encode the qubit. The qubit's wave function is immune to charge noise at moderate out-of-plane magnetic fields. (2) A singlet-triplet qubit encoded using two quantum dots of different sizes has an orbital state degeneracy of the singlet state and the spinless triplet state at finite out-of-plane magnetic fields. Spin-orbit interactions lift this state degeneracy, while the magnitude of the state coupling is determined by the size difference of the QDs. This setup enables the manipulations of singlet-triplet qubits without the need for magnetic field gradients. Finally, two-qubit gates between singlet-triplet qubits are proposed that use mediated exchange interactions via one quantum state. These operations are well controlled and highly noise insensitive. Orbital interactions alone can control spin qubits coded in a three electron Hilbert space. For example, the exchange-only qubit is encoded using three singly occupied quantum dots. The exchange interactions of two quantum dot pairs need to be modified to manipulate this qubit. The noise sensitivity of the exchange-only qubit is discussed. Alternatively, a three-electron qubit at a double quantum dot can be operated when single electrons are transferred between the quantum dots. Fast, subnanosecond manipulations of the double quantum dot's charge configuration are required to realize single-qubit gates. A novel two-qubit pulse gate for the three-electron double quantum dot qubit is proposed.
Universal quantum computing relies on high-fidelity entangling operations. Here, we demonstrate that four coupled qubits can operate as a quantum gate, where two qubits control the operation on two target qubits (a four-qubit gate). This configuration can implement four different controlled two-qubit gates: two different entangling swap and phase operations, a phase operation distinguishing states of different parity, and the identity operation (idle quantum gate), where the choice of gate is set by the state of the control qubits. The device exploits quantum interference to control the operation on the target qubits by coupling them to each other via the control qubits. By connecting several four-qubit devices in a two-dimensional lattice, one can achieve a highly connected quantum computer. We consider an implementation of the four-qubit gate with superconducting qubits, using capacitively coupled qubits arranged in a diamond-shaped architecture.
Two-level system fluctuators in superconducting devices have demonstrated coherent coupling with superconducting qubits. Here, we show that universal quantum logic gates can be realized in these two-level systems solely by tuning a superconducting resonator in which they are imbedded. Because of the large energy separation between the fluctuators, conventional gate schemes in the cavity QED approach that are widely used for solid-state qubits cannot be directly applied to the fluctuators. We study a scheme to perform the gate operations by exploiting the controllability of the superconducting resonator with realistic parameters. Numerical simulation that takes into account the decay of the resonator mode shows that the quantum logic gates can be realized with high fidelity at moderate resonator decay rate. The quantum logic gates can also be realized between fluctuators inside different Josephson junctions that are connected by a superconducting loop. Our scheme can be applied to explore the coupling between two-level system fluctuators and superconducting resonators as well as the coherent properties of the fluctuators.
Superconducting qubits are employed for the practical implementation of scalable quantum information processors. Fault-tolerant quantum computation schemes using superconducting qubits is under intensive study. Among the various kinds of superconducting qubits, flux qubits have a significant advantage in that they can be made insensitive to randomly fluctuating charges in the substrate. Here, the characterization results of a double-loop four-Josephson-junction flux qubit is reported. By varying the magnetic flux in one of the two loops, the energy gap at the classical degeneracy point can be controlled in situ. The basic operation of the system is illustrated by the appearance of a qubit step on a two-dimensional flux map. The energy gap can be indirectly estimated from the shape of the qubit step. The dependence of the shape of the qubit step on the control flux, which is analyzed in terms of the step height and maximum slope, is in good agreement with the simulation results, thereby implicitly indicating that the energy gap is varied from almost zero, less than the thermal energy, to a value higher than 50 GHz. Spectroscopic measurements directly demonstrated the controllability of the energy gap. In addition, doublet splitting due to intercell tunneling was observed for the first time.