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arXiv:cond-mat/0606627 · Physical Review B

Universal quantum computing with correlated spin-charge states

Jordan Kyriakidis, Guido Burkard

Published Mar 26, 2007• 21 citations
arXivHTMLPDF

Abstract

We propose a universal quantum computing scheme in which the orthogonal qubit states \ensuremath{\mid}0⟩ and \ensuremath{\mid}1⟩ are identical in their single-particle spin and charge properties. Each qubit is contained in a single quantum dot, and gate operations are induced all electrically by changes in the confinement potential. Within the computational space, these qubits are robust against environmental influences that couple to the system through single-particle channels. Due to the identical spin and charge properties of the \ensuremath{\mid}0⟩, \ensuremath{\mid}1⟩ states, the lowest-order relaxation and decoherence rates $1∕{T}_{1}$ and $1∕{T}_{2}$, within the Born-Markov approximation, both vanish for a large class of environmental couplings. We give explicit pulse sequences for a universal set of gates (phase, $\ensuremath{\pi}∕8$, Hadamard, and CNOT) and discuss state preparation, manipulation, and detection.

DOI
10.1103/physrevb.75.115324

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We propose a universal quantum computing scheme in which the orthogonal qubit states \ensuremath{\mid}0⟩ and \ensuremath{\mid}1⟩ are identical in their single-particle spin and charge properties. Each qubit is contained in a single quantum dot, and gate operations are induced all electrically by changes in the confinement potential. Within the computational space, these qubits are robust against environmental influences that couple to the system through single-particle channels. Due to the identical spin and charge properties of the \ensuremath{\mid}0⟩, \ensuremath{\mid}1⟩ states, the lowest-order relaxation and decoherence rates 1∕T11∕{T}_{1}1∕T1​ and 1∕T21∕{T}_{2}1∕T2​, within the Born-Markov approximation, both vanish for a large class of environmental couplings. We give explicit pulse sequences for a universal set of gates (phase, \ensuremathπ∕8\ensuremath{\pi}∕8\ensuremathπ∕8, Hadamard, and CNOT) and discuss state preparation, manipulation, and detection.
We investigate a two-electron double quantum dot with both spin and valley degrees of freedom as they occur in graphene, carbon nanotubes or silicon and regard the 16-dimensional space with one electron per dot as a four-qubit logic space. In the spin-only case, it is well known that the exchange coupling between the dots combined with arbitrary single-qubit operations is sufficient for universal quantum computation. The presence of valley degeneracy in the electronic band structure alters the form of the exchange coupling and, in general, leads to spin–valley entanglement. Here, we show that universal quantum computation can still be performed by exchange interaction and single-qubit gates in the presence of an additional (valley) degree of freedom. We present an explicit pulse sequence for a spin-only controlled-NOT consisting of the generalized exchange coupling and single-electron spin and valley rotations. We also propose state preparations and projective measurements with the use of adiabatic transitions between states with (1,1) and (0,2) charge distributions similar to the spin-only case, but with the additional requirement of controlling the spin and valley Zeeman energies by an external magnetic field. Finally, we demonstrate a universal two-qubit gate between a spin and a valley qubit, allowing universal gate operations on the combined spin and valley quantum register.
We propose a set of universal gate operations for the singlet-triplet qubit realized by two-electron spins in a double quantum dot, in the presence of a fixed inhomogeneous magnetic field. All gate operations are achieved by switching the potential offset between the two dots with an electrical bias, and do not require time-dependent control of the tunnel coupling between the dots. We analyze the two-electron dynamics and calculate the effective qubit rotation angle as a function of the applied electric bias. We present explicit gate sequences for single-qubit rotations about two orthogonal axes, and a CNOT gate sequence, completing the universal gate set.
A crucial requirement for scalable quantum-information processing is the realization of multiple-qubit quantum gates. Universal multiple-qubit gates can be implemented by a set of universal single qubit gates and any one kind of two-qubit gate, such as a controlled-NOT (CNOT) gate. Semiconductor quantum dot qubits are a leading approach for the physical implementation of quantum computation, due to their potential for large-scale integration. Two-qubit gate operations have been so far only demonstrated in individual electron spin-based quantum dot systems. Due to the relatively short de-coherence time, charge qubits in quantum dots are generally considered to be inferior for going beyond single qubit level. Here, we demonstrate the benchmarking CNOT gate in two capacitively coupled charge qubits, each consisting of an electron confined in a GaAs/AlGaAs double quantum dot. Owing to the strong inter-qubit coupling strength, gate operations with a clock speed up to 5GHz has been realized. A processing tomography shows encouragingly that the universal two-qubit gate operations have comparable fidelities to that of spin-based two-qubit gates. Our results suggest that semiconductor charge qubits have a considerable potential for scalable quantum computing and may stimulate the use of long-range Coulomb interaction for coherent quantum control in other devices.
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.
Reliable quantum information processing requires high-fidelity universal manipulation of quantum systems within the characteristic coherence times. Non-adiabatic holonomic quantum computation offers a promising approach to implement fast, universal, and robust quantum logic gates particularly useful in nano-fabricated solid-state architectures, which typically have short coherence times. Here, we propose an experimentally feasible scheme to realize high-speed universal geometric quantum gates in nano-engineered pseudo-spin charge qubits. We use a system of three coupled quantum dots containing a single electron, where two computational states of a double quantum dot charge qubit interact through an intermediate quantum dot. The additional degree of freedom introduced into the qubit makes it possible to create a geometric model system, which allows robust and efficient single-qubit rotations through careful control of the inter-dot tunneling parameters. We demonstrate that a capacitive coupling between two charge qubits permits a family of non-adiabatic holonomic controlled two-qubit entangling gates, and thus provides a promising procedure to maintain entanglement in charge qubits and a pathway toward fault-tolerant universal quantum computation. We estimate the feasibility of the proposed structure by analyzing the gate fidelities to some extent.