Fault tolerance is the study of reliable computation using unreliable components. With a given noise model, can one still reliably compute? For example, one can run many copies of a classical calculation in parallel, periodically using majority gates to catch and correct faults. Von Neumann showed in 1956 that if each gate fails independently with probability p, flipping its output bit 0 $ 1, then such a fault tolerance scheme still allows for arbitrarily reliable computation provided that p is below some constant threshold (whose value depends on the model details) [10]. In a quantum computer, the basic gates are much more vulnerable to noise than classical transistors – after all, depending on the implementation, they are manipulating single electron spins, photon polarizations, and similarly fragile subatomic particles. It might not be possible to engineer systems with noise rates less than 10 , or perhaps 10 , per gate. Additionally, the phenomenon of entanglement makes quantum systems inherently fragile. For example, in Schrödinger’s cat state – an equal superposition between a living cat and a dead cat, often idealized as 1= p 2.j0ni C j1ni/ – an interaction with just one quantum bit (“qubit”) can collapse, or decohere, the entire system. Fault tolerance techniques will therefore be essential for achieving the considerable potential of quantum computers. Practical fault tolerance techniques will need to control high noise rates and do so with low overhead, since qubits are expensive. Quantum systems are continuous, not discrete, so there are many possible noise models. However, the essential features of quantum noise for fault tolerance results can be captured by a simple discrete model similar to the one Von Neumann used. The main difference is that, in addition to bit-flip X errors which swap 0 and 1, there can also be phase-flip Z errors which swap jCi 1=p2.j0i C j1i/ and j i 1=p2.j0i j1i/ (Fig. 1). A noisy gate is modeled as a perfect gate followed by independent introduction of X, Z, or Y (which is both X and Z) errors with respective probabilities pX; pZ; pY. One popular model is independent depolarizing noise .pX D pZ D pY p=3/; a depolarized qubit is completely randomized. Faulty measurements and preparations of single-qubit states must additionally be modeled, and there can be memory noise on resting qubits. It is often assumed that measurement results can

Fault-Tolerant Quantum Computation.

By using the dry etching process of tantalum (Ta) film, we had obtained transmon qubit with the best lifetime (T1) 503 us, suggesting that the dry etching process can be adopted in the following multi-qubit fabrication with Ta film. We also compared the relaxation and coherence times of transmons made with different materials (Ta, Nb and Al) with the same design and fabrication processes of Josephson junction, we found that samples prepared with Ta film had the best performance, followed by those with Al film and Nb film. We inferred that the reason for this difference was due to the different loss of oxide materials located at the metal-air interface. 

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Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds

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We report on long-term measurements of a highly coherent, nontunable superconducting transmon qubit, revealing low-frequency burst noise in coherence times and qubit transition frequency. We achieve this through a simultaneous measurement of the qubit's relaxation and dephasing rate as well as its resonance frequency. The analysis of correlations between these parameters yields information about the microscopic origin of the intrinsic decoherence mechanisms in Josephson qubits. Our results are consistent with a small number of microscopic two-level systems located at the edges of the superconducting film, which is further confirmed by a spectral noise analysis.

Correlating decoherence in transmon qubits:Low frequency noise by single fluctuators

The control and handling of errors arising from cross talk and unwanted interactions in multiqubit systems is an important issue in quantum information processing architectures. We introduce a benchmarking protocol that provides information about the amount of addressability present in the system and implement it on coupled superconducting qubits. The protocol consists of randomized benchmarking experiments run both individually and simultaneously on pairs of qubits. A relevant figure of merit for the addressability is then related to the differences in the measured average gate fidelities in the two experiments. We present results from two similar samples with differing cross talk and unwanted qubit-qubit interactions. The results agree with predictions based on simple models of the classical cross talk and Stark shifts.

http://absimage.aps.org/image/MAR13/MWS_MAR13-2012-002923.pdf

Characterization of addressability by simultaneous randomized benchmarking

High fidelity two-qubit gates are fundamental for scaling up the superconducting number. We use two qubits coupled via a frequency-tunable coupler which can adjust the coupling strength, and demonstrate the CZ gate using two different schemes, adiabatic and diabatic methods. The Clifford based Randomized Benchmarking (RB) method is used to assess and optimize the CZ gate fidelity. The fidelity of adiabatic and diabatic CZ gates are 99.53(8)% and 98.72(2)%, respectively. We also analyze the errors induced by the decoherence. Comparing to 30 ns duration time of adiabatic CZ gate, the duration time of diabatic CZ gate is 19 ns, revealing lower incoherence error rate $r'_{\rm{incoherent, int}}$ = 0.0197(5) than $r_{\rm{incoherent, int}}$ = 0.0223(3).

Realisation of adiabatic and diabatic CZ gates in superconducting qubits coupled with a tunable coupler.

Significant progress has been made in building large-scale superconducting quantum processors based on flip-chip technology. In this work, we use flip-chip technology to realize a modified transmon qubit, denoted as the “flipmon,” whose large shunt capacitor is replaced by a vacuum-gap parallel plate capacitor. We place one of the qubit pads and a single Josephson junction on the bottom chip and the other pad on the top chip, which is galvanically connected with the junction through an indium bump. The electric field energy participation ratio can arrive at nearly 53% in air when the vacuum-gap is about 5 μm, thus potentially leading to a lower dielectric loss. The coherence times of the flipmons are obtained in the range of 30–60 μs, which are comparable with that of conventional transmons with similar fabrication processes. The electric field simulation indicates that the metal-air interface's energy participation ratio increases significantly and may dominate the flipmon's decoherence. This suggests that more careful surface treatment needs to be considered. No evidence shows that the indium bumps inside the flipmons cause significant decoherence. With well-designed geometry and good surface treatment, the coherence of the flipmons can be further improved.

Jingning Zhang

Papers

Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds

Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds

Realisation of adiabatic and diabatic CZ gates in superconducting qubits coupled with a tunable coupler.

Vacuum-gap transmon qubits realized using flip-chip technology

Realization of adiabatic and diabatic CZ gates in superconducting qubits coupled with a tunable coupler