Tomographic measurements on superconducting qubit states

Liu, Yu-xi; Wei, L. F.; Nori, Franco

doi:10.1103/physrevb.72.014547

Cited by 77 publications

(94 citation statements)

References 83 publications

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“…Tomographic measurements on the quantum states of superconducting charge qubits, either single or multiple qubits, were proposed in [60]. Recently, there were many experiments on the quantum state tomography of single superconducting phase qubits [61,62] and of two coupled superconducting phase [63] and charge [64] qubits.…”

Section: Electromagnetically Induced Transparencymentioning

confidence: 99%

Atomic physics and quantum optics using superconducting circuits

You

Nori

2011

Nature

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1,255

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Superconducting circuits based on Josephson junctions exhibit macroscopic quantum coherence and can behave like artificial atoms. Recent technological advances have made it possible to implement atomic-physics and quantum-optics experiments on a chip using these artificial atoms. This review presents a brief overview of the progress achieved so far in this rapidly advancing field. We not only discuss phenomena analogous to those in atomic physics and quantum optics with natural atoms, but also highlight those not occurring in natural atoms. In addition, we summarize several prospective directions in this emerging interdisciplinary field.Superconducting circuits with Josephson junctions can behave as artificial atoms. In these quantum circuits, the Josephson junctions act as nonlinear circuit elements (see Box 1). Such nonlinearity in a circuit ensures an unequal spacing between energy levels, so that the lowest levels can be individually addressed by using external fields (see, e.g., [1][2][3][4][5][6][7][8][9]). Experimentally, these circuits are fabricated on a micrometer scale and operated at mK temperatures. Because of the reduced dimensionality and thanks to the superconductivity, the environmentinduced dissipation and noise are greatly suppressed, so the circuits can behave quantum mechanically.Superconducting circuits based on Josephson junctions have recently become subjects of intense research because they can be used as qubits-controllable quantum two-level system-for quantum computing (see, e.g., [1-4] for reviews). Even though the typical decoherence times of these circuits fall short of the requirements for quantum computation, their macroscopic quantum coherence is sufficient for them to exhibit striking quantum behaviors. These circuits can have a number of superconducting eigenstates with discrete eigenvalues lower than the energy levels of the quasi-particle excitations that involve breaking Cooper pairs. This property allows these circuits to behave like superconducting artificial atoms. Indeed, there is a deep analogy between natural atoms and the artificial atoms made from superconducting circuits (see Box 2). Both have discrete energy levels and can exhibit coherent quantum oscillations between these levels. Whereas natural atoms may be controlled using visible or microwave photons that excite electrons from one state to another, the artificial atoms in the circuits are driven by currents, voltages and microwave photons that excite the system from one macroscopic quantum state to another.Differences between superconducting circuits and natural atoms include the different energy scales in the two systems, and how strongly each system couples to its environment; the coupling is weak for atoms and strong for circuits. In contrast to naturally occurring atoms, artificial atoms can be designed with specific characteristics and fabricated on a chip using standard lithographical technologies. With a view to applications, this degree of tunability is an important advantage over natural atoms. Thus, ...

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Section: Electromagnetically Induced Transparencymentioning

confidence: 99%

Atomic physics and quantum optics using superconducting circuits

You

Nori

2011

Nature

Self Cite

1,255

1,081

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“…Figure 4E shows ↑ L and ↑ R measured after the CNOT gate acts on different input states with angle R . These data show that the target qubit follows the state of the control qubit, as needed for a universal CNOT gate.We next use the CNOT gate (17) to create the Bell stateThe Bell state fidelity is extracted by performing two qubit state tomography (23,24). By appending single qubit rotations after the CNOT we measure the expectation value for all two qubit Pauli operators (for example, by applying a π/2x rotation to the left qubit and π/2y rotation to the right we measure the YX two qubit operator).…”

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confidence: 99%

Resonantly driven CNOT gate for electron spins

Zajac

Sigillito

Russ

et al. 2018

Science

547

587

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Abstract:Single qubit rotations and two-qubit CNOT operations are crucial ingredients for universal quantum computing. While high fidelity single qubit operations have been achieved using the electron spin degree of freedom, realizing a robust CNOT gate has been a major challenge due to rapid nuclear spin dephasing and charge noise. We demonstrate an efficient resonantly-driven CNOT gate for electron spins in silicon. Our platform achieves single-qubit rotations with fidelities >99%, as verified by randomized benchmarking. Gate control of the exchange coupling allows a quantum CNOT gate to be implemented with resonant driving in ~200 ns. We use the CNOT gate to generate a Bell state with 75% fidelity, limited by quantum state readout. Our quantum dot device architecture opens the door to multi-qubit algorithms in silicon.Main Text: Gate defined semiconductor quantum dots are a powerful platform for isolating and coherently controlling single electron spins (1, 2). Silicon quantum dots can leverage state-ofthe-art industrial nanofabrication capabilities for scalability, and support some of the longest quantum coherence times measured in the solid-state (3-5). By engineering local magnetic field gradients, electron spins can be electrically controlled (6, 7) with single qubit gate fidelities exceeding 99% (8). Despite this progress, demonstrations of two-qubit gates with quantum dot spins are scarce due to technological and materials challenges (9, 10). While exchange control of spins was demonstrated as early as 2005, high fidelity exchange gates have been difficult to achieve due to nuclear spin dephasing and charge noise (10, 11). A demonstration of an efficient CNOT gate for spins in silicon will open a path for multi-qubit algorithms in a scalable semiconductor system.Here we demonstrate a ~200 ns CNOT gate in a silicon semiconductor double quantum dot (DQD), nearly an order of magnitude faster than the previously demonstrated composite CNOT gate (9). The gate is implemented by turning on an exchange interaction, which results in a state-selective electron spin resonance (ESR) transition that is used to implement a CNOT gate with a single microwave (MW) pulse. Local magnetic field gradients allow for all-electrical control of the spin states with single qubit gate fidelities exceeding 99%, enabled by the largely nuclear-spin-free environment of the silicon host lattice. In contrast with previous DQD implementations of the exchange gate, our CNOT gate is implemented at a symmetric operating point, where the exchange coupling J is first-order insensitive to charge noise (12,13). By combining the CNOT with single qubit gates we create a Bell state with a fidelity F = 75%, limited primarily by the qubit readout visibility (14). Our demonstration of a universal set of fast quantum gates for spins in silicon paves the way for the first multi-qubit algorithms with semiconductor spin qubits (15).The spin of a single electron is used to encode a qubit (16). A gate-defined DQD (Fig. 1A) is used to isolate two electron...

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“…To demonstrate the GHZ state, we could use the well developed quantum state tomography technique in superconducting qubits 42 to reconstruct the density matrix of the final state 15,43 . After the GHZ state is generated, we can tune the transition frequencies of the qubits such that the interactions between all qubits and the TLRs are switched off.…”

Section: Discussion and Summarymentioning

confidence: 99%

Fast generation of multiparticle entangled state for flux qubits in a circle array of transmission line resonators with tunable coupling

et al. 2012

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We study a one-step approach to the fast generation of Greenberger-Horne-Zeilinger (GHZ) states in a circuit QED system with superconducting flux qubits. The GHZ state can be generated in about 10 ns, which is much shorter than the coherence time of flux qubits and comparable with the time of single-qubit operation. In our proposal, a time-dependent microwave field is applied to a superconducting transmission line resonator (TLR) and displaces the resonator in a controlled manner, thus inducing indirect qubit-qubit coupling without residual entanglement between the qubits and the resonator. The design of a tunably coupled TLR circle array provides us with the potential for extending this one-step scheme to the case of many qubits coupled via several TLRs.

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Tomographic measurements on superconducting qubit states

Cited by 77 publications

References 83 publications

Atomic physics and quantum optics using superconducting circuits

Atomic physics and quantum optics using superconducting circuits

Resonantly driven CNOT gate for electron spins

Fast generation of multiparticle entangled state for flux qubits in a circle array of transmission line resonators with tunable coupling

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