Joydip Ghosh

High-Fidelity Single-Shot Toffoli Gate via Quantum Control.

A single-shot Toffoli, or controlled-controlled-not, gate is desirable for classical and quantum information processing. The Toffoli gate alone is universal for reversible computing and, accompanied by the Hadamard gate, forms a universal gate set for quantum computing. The Toffoli gate is also a key ingredient for (nontopological) quantum error correction. Currently Toffoli gates are achieved by decomposing into sequentially implemented single- and two-qubit gates, which require much longer times and yields lower overall fidelities compared to a single-shot implementation. We develop a quantum-control procedure to construct a single-shot Toffoli gate for three nearest-neighbor-coupled superconducting transmon systems such that the fidelity is 99.9% and is as fast as an entangling two-qubit gate under the same realistic conditions. The gate is achieved by a nongreedy quantum control procedure using our enhanced version of the differential evolution algorithm.

High-fidelity controlled-σ Z gate for resonator-based superconducting quantum computers

A possible building block for a scalable quantum computer has recently been demonstrated [M. Mariantoni et al., Science 334, 61 (2011)]. This architecture consists of superconducting qubits capacitively coupled both to individual memory resonators as well as a common bus. In this work we study a natural primitive entangling gate for this and related resonator-based architectures, which consists of a CZ operation between a qubit and the bus. The CZ gate is implemented with the aid of the non-computational qubit |2> state [F. W. Strauch et al., Phys. Rev. Lett. 91, 167005 (2003)]. Assuming phase or transmon qubits with 300 MHz anharmonicity, we show that by using only low frequency qubit-bias control it is possible to implement the qubit-bus CZ gate with 99.9% (99.99%) fidelity in about 17ns (23ns) with a realistic two-parameter pulse profile, plus two auxiliary z rotations. The fidelity measure we refer to here is a state-averaged intrinsic process fidelity, which does not include any effects of noise or decoherence. These results apply to a multi-qubit device that includes strongly coupled memory resonators. We investigate the performance of the qubit-bus CZ gate as a function of qubit anharmonicity, indentify the dominant intrinsic error mechanism and derive an associated fidelity estimator, quantify the pulse shape sensitivity and precision requirements, simulate qubit-qubit CZ gates that are mediated by the bus resonator, and also attempt a global optimization of system parameters including resonator frequencies and couplings. Our results are relevant for a wide range of superconducting hardware designs that incorporate resonators and suggest that it should be possible to demonstrate a 99.9% CZ gate with existing transmon qubits, which would constitute an important step towards the development of an error-corrected superconducting quantum computer.

Controlled-not gate with weakly coupled qubits: Dependence of fidelity on the form of interaction

An approach to the construction of the controlled-not quantum logic gate for a four-dimensional coupled-qubit model with weak but otherwise arbitrary coupling has been given recently [M. R. Geller et al., Phys. Rev. A 81, 012320 (2010)]. How does the resulting fidelity depend on the form of qubit-qubit coupling? In this paper we calculate intrinsic fidelity curves (fidelity in the absence of decoherence versus total gate time) for a variety of qubit-qubit interactions, including the commonly occurring isotropic Heisenberg and XY models, as well as randomly generated ones. For interactions not too close to that of the Ising model, we find that the fidelity curves do not significantly depend on the form of the interaction, and we calculate the resulting interaction-averaged fidelity curve for the non-Ising-like cases and a criterion for determining its applicability.

Simulating Anderson localization via a quantum walk on a one-dimensional lattice of superconducting qubits

Quantum walk (QW) on a disordered lattice leads to a multitude of interesting phenomena, such as Anderson localization. While QW has been realized in various optical and atomic systems, its implementation with superconducting qubits still remains pending. The major challenge in simulating QW with superconducting qubits emerges from the fact that on-chip superconducting qubits cannot hop between two adjacent lattice sites. Here we overcome this barrier and develop a gate-based scheme to realize the discrete time QW by placing a pair of qubits on each site of a one-dimensional (1D) lattice and treating an excitation as a walker. It is also shown that various lattice disorders can be introduced and fully controlled by tuning the qubit parameters in our quantum walk circuit. We observe a distinct signature of transition from the ballistic regime to a localized QW with an increasing strength of disorder. Finally, an eight-qubit experiment is proposed where the signatures of such localized and delocalized regimes can be detected with existing superconducting technology. Our proposal opens up the possibility of exploring various quantum transport processes with promising superconducting qubits.

Understanding the effects of leakage in superconducting quantum-error-detection circuits

The majority of quantum error detection and correction protocols assume that the population in a qubit does not leak outside of its computational subspace. For many existing approaches, however, the physical qubits do possess more than two energy levels and consequently are prone to such leakage events. Analyzing the effects of leakage is therefore essential to devise optimal protocols for quantum gates, measurement, and error correction. In this work, we present a detailed study of leakage in a two-qubit superconducting stabilizer measurement circuit. We simulate the repeated ancilla-assisted measurement of a single

A Leakage-Resilient Approach to Fault-Tolerant Quantum Computing with Superconducting Elements

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Emulating quantum state transfer through a spin-1 chain on a one-dimensional lattice of superconducting qutrits

operator for a data qubit, record the outcome at the end of each measurement cycle, and explore the signature of leakage events in the obtained readout statistics. An analytic model is also developed that closely approximates the results of our numerical simulations. We find that leakage leads to destructive features in the quantum error detection scheme, making additional hardware and software protocols necessary.

Quantum simulation of macro and micro quantum phase transition from paramagnetism to frustrated magnetism with a superconducting circuit

Superconducting qubits, while promising for scalability and long coherence times, contain more than two energy levels, and therefore are susceptible to errors generated by the leakage of population outside of the computational subspace. Such leakage errors constitute a prominent roadblock towards fault-tolerant quantum computing (FTQC) with superconducting qubits. FTQC using topological codes is based on sequential measurements of multiqubit stabilizer operators. Here, we first propose a leakage-resilient procedure to perform repetitive measurements of multiqubit stabilizer operators, and then use this scheme as an ingredient to develop a leakage-resilient approach for surface code quantum error correction with superconducting circuits. Our protocol is based on swap operations between data and ancilla qubits at the end of every cycle, requiring read-out and reset operations on every physical qubit in the system, and thereby preventing persistent leakage errors from occurring.

Measurement-free implementations of small-scale surface codes for quantum-dot qubits

Spin-1 systems, in comparison to spin-

Quantum control for high-fidelity multi-qubit gates

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