Low-cost error mitigation by symmetry verification

We investigate the performance of error mitigation via measurement of conserved symmetries on near-term devices. We present two protocols to measure conserved symmetries during the bulk of an experiment, and develop a zero-cost post-processing protocol which is equivalent to a variant of the quantum subspace expansion. We develop methods for inserting global and local symetries into quantum algorithms, and for adjusting natural symmetries of the problem to boost their mitigation against different error channels. We demonstrate these techniques on two- and four-qubit simulations of the hydrogen molecule (using a classical density-matrix simulator), finding up to an order of magnitude reduction of the error in obtaining the ground state dissociation curve.Comment: Published versio

Calculating energy derivatives for quantum chemistry on a quantum computer

Modeling chemical reactions and complicated molecular systems has been proposed as the `killer application' of a future quantum computer. Accurate calculations of derivatives of molecular eigenenergies are essential towards this end, allowing for geometry optimization, transition state searches, predictions of the response to an applied electric or magnetic field, and molecular dynamics simulations. In this work, we survey methods to calculate energy derivatives, and present two new methods: one based on quantum phase estimation, the other on a low-order response approximation. We calculate asymptotic error bounds and approximate computational scalings for the methods presented. Implementing these methods, we perform the world's first geometry optimization on an experimental quantum processor, estimating the equilibrium bond length of the dihydrogen molecule to within 0.014 Angstrom of the full configuration interaction value. Within the same experiment, we estimate the polarizability of the H2 molecule, finding agreement at the equilibrium bond length to within 0.06 a.u. (2% relative error).Comment: 19 pages, 1 page supplemental, 7 figures. v2 - tidied up and added example to appendice

Chip-to-chip entanglement of transmon qubits using engineered measurement fields

© 2018 American Physical Society. While the on-chip processing power in circuit QED devices is growing rapidly, an open challenge is to establish high-fidelity quantum links between qubits on different chips. Here, we show entanglement between transmon qubits on different cQED chips with 49% concurrence and 73% Bell-state fidelity. We engineer a half-parity measurement by successively reflecting a coherent microwave field off two nearly identical transmon-resonator systems. By ensuring the measured output field does not distinguish |01) from |10), unentangled superposition states are probabilistically projected onto entangled states in the odd-parity subspace. We use in situ tunability and an additional weakly coupled driving field on the second resonator to overcome imperfect matching due to fabrication variations. To demonstrate the flexibility of this approach, we also produce an even-parity entangled state of similar quality, by engineering the matching of outputs for the |00) and |11) states. The protocol is characterized over a range of measurement strengths using quantum state tomography showing good agreement with a comprehensive theoretical model

Time-domain characterization and correction of on-chip distortion of control pulses in a quantum processor

We introduce Cryoscope, a method for sampling on-chip baseband pulses used to dynamically control qubit frequency in a quantum processor. We specifically use Cryoscope to measure the step response of the dedicated flux control lines of two-junction transmon qubits in circuit QED processors with the temporal resolution of the room-temperature arbitrary waveform generator producing the control pulses. As a first application, we iteratively improve this step response using optimized real-time digital filters to counter the linear-dynamical distortion in the control line, as needed for high-fidelity, repeatable one- and two-qubit gates based on dynamical control of qubit frequency

Influence of gestational age at initiation of antihypertensive therapy: secondary analysis of CHIPS trial data (control of hypertension in pregnancy study)

For hypertensive women in CHIPS (Control of Hypertension in Pregnancy Study), we assessed whether the maternal benefits of tight control could be achieved, while minimizing any potentially negative effect on fetal growth, by delaying initiation of antihypertensive therapy until later in pregnancy. For the 981 women with nonsevere, chronic or gestational hypertension randomized to less-tight (target diastolic blood pressure, 100 mm Hg), or tight (target, 85 mm Hg) control, we used mixed-effects logistic regression to examine whether the effect of less-tight (versus tight) control on major outcomes was dependent on gestational age at randomization, adjusting for baseline factors as in the primary analysis and including an interaction term between gestational age at randomization and treatment allocation. Gestational age was considered categorically (quartiles) and continuously (linear or quadratic form), and the optimal functional form selected to provide the best fit to the data based on the Akaike information criterion. Randomization before (but not after) 24 weeks to less-tight (versus tight) control was associated with fewer babies with birth weight 48 hours (Pinteraction=0.354). For the mother, less-tight (versus tight) control was associated with more severe hypertension at all gestational ages but particularly so before 28 weeks (Pinteraction=0.076). In women with nonsevere, chronic, or gestational hypertension, there seems to be no gestational age at which less-tight (versus tight) control is the preferred management strategy to optimize maternal or perinatal outcomes

Developmental trajectories of aggressive behavior in children from ages 8 to 10: The role of sex and hormones

[Objectives] This study explored the developmental trajectory of aggressive behavior from age 8 to age 10 in school-aged children, taking into account possible sex differences, as well as the involvement of certain hormones.[Methods] Participants were 90 children (49 boys and 41 girls) from four schools. At the beginning of the study, the children were 8-year old and were in 3rd grade of primary school. The second data collection phase was carried out two years later (at age 10) when the children were in 5th grade (primary). Their aggressive behavior was measured by the Direct and Indirect Aggression Scale, an instrument which uses peer rating. Hormone levels, testosterone, cortisol and estradiol were analyzed using an enzymoimmunoassay technique in saliva samples.[Results] The results revealed a difference in aggressive behavior between the ages of 8 and 10, in boys only, who were found to be more aggressive at age 10. A regression analysis revealed that cortisol and estradiol contributed to explaining the changes observed in aggressive behavior in boys. Boys whose cortisol levels rose most between the ages of 8 and 10 were also those whose aggressive behavior increased most during the same timeframe. Moreover, boys whose estradiol levels rose most between the ages of 8 and 10 were also those whose aggressive behavior decreased most during the same timeframe.[Conclusions] Our results highlight the importance of studying aggressive behavior from a longitudinal perspective, taking into account sex differences and biological measures

Experimental error mitigation via symmetry verification in a variational quantum eigensolver

Variational quantum eigensolvers offer a small-scale testbed to demonstrate the performance of error mitigation techniques with low experimental overhead. We present successful error mitigation by applying the recently proposed symmetry verification technique to the experimental estimation of the ground-state energy and ground state of the hydrogen molecule. A finely adjustable exchange interaction between two qubits in a circuit QED processor efficiently prepares variational ansatz states in the single-excitation subspace respecting the parity symmetry of the qubit-mapped Hamiltonian. Symmetry verification improves the energy and state estimates by mitigating the effects of qubit relaxation and residual qubit excitation, which violate the symmetry. A full-density-matrix simulation matching the experiment dissects the contribution of these mechanisms from other calibrated error sources. Enforcing positivity of the measured density matrix via scalable convex optimization correlates the energy and state estimate improvements when using symmetry verification, with interesting implications for determining system properties beyond the ground-state energy.QCD/DiCarlo LabQuTechFTQC/Bertels LabComputer EngineeringBusiness DevelopmentQN/DiCarlo La

DiCarloLab-Delft/PycQED_py3: Initial public release

Python3 version of PycQED using QCodes as backen