An active area of research in the fields of machine learning and statistics is the development of causal discovery algorithms, the purpose of which is to infer the causal relations that hold among a set of variables from the correlations that these exhibit . We apply some of these algorithms to the correlations that arise for entangled quantum systems. We show that they cannot distinguish correlations that satisfy Bell inequalities from correlations that violate Bell inequalities, and consequently that they cannot do justice to the challenges of explaining certain quantum correlations causally. Nonetheless, by adapting the conceptual tools of causal inference, we can show that any attempt to provide a causal explanation of nonsignalling correlations that violate a Bell inequality must contradict a core principle of these algorithms, namely, that an observed statistical independence between variables should not be explained by fine-tuning of the causal parameters. In particular, we demonstrate the need for such fine-tuning for most of the causal mechanisms that have been proposed to underlie Bell correlations, including superluminal causal influences, superdeterminism (that is, a denial of freedom of choice of settings), and retrocausal influences which do not introduce causal cycles. 4 Other work in the field of machine learning has appealed to statistical features besides CI relations, but not the features of correlations that are relevant for Bellʼs theorem. Peters et al [8] demonstrate that if one is promised an additive noise model, then features of the joint distribution can often distinguish cause from effect in the case of a distribution on a pair of variables, where there are no CI relations to guide the analysis. Other approaches have appealed to the complexity of conditional distributions [3][4][5]. 5 A defining feature of a common cause is that if the statistical dependence between two variables is to be explained entirely by a common cause, then it must be the case that conditioning on the common cause makes the variables statistically independent. As we will see, this feature is built into the framework of causal models. Statements of Reichenbachʼs principle often assert it explicitly. New J. Phys. 17 (2015) 033002 C J Wood and R W Spekkens New J. Phys. 17 (2015) 033002 C J Wood and R W Spekkens

For superconducting qubits, microwave pulses drive rotations around the Bloch sphere. The phase of these drives can be used to generate zero-duration arbitrary "virtual" Z-gates which, combined with two X π/2 gates, can generate any SU(2) gate. Here we show how to best utilize these virtual Z-gates to both improve algorithms and correct pulse errors. We perform randomized benchmarking using a Clifford set of Hadamard and Z-gates and show that the error per Clifford is reduced versus a set consisting of standard finite-duration X and Y gates. Z-gates can correct unitary rotation errors for weakly anharmonic qubits as an alternative to pulse shaping techniques such as DRAG. We investigate leakage and show that a combination of DRAG pulse shaping to minimize leakage and Z-gates to correct rotation errors (DRAGZ) realizes a 13.3 ns X π/2 gate characterized by low error (1.95[3] × 10 −4 ) and low leakage (3.1[6] × 10 −6 ). Ultimately leakage is limited by the finite temperature of the qubit, but this limit is two orders-of-magnitude smaller than pulse errors due to decoherence.Computers based on quantum bits (qubits) are predicted to outperform classical computers for certain critical problems, e.g., factoring. Unlike a classical bit, which is discretely in the state 0 or 1, a qubit can be in a superposition state |Ψ = cos(θ/2)|0 + e iφ sin(θ/2)|1 where |0 and |1 are the quantum versions of the classical 0 and 1 states. This single-qubit superposition state can be geometrically represented as a point on the surface of a unit-sphere known as the Bloch sphere. Critical to implementing a quantum computer is the ability to control the state of the qubit, i.e., transform the qubit state arbitrarily between two points on the Bloch sphere. This is accomplished by unitary transformations (gates), which correspond to rotations of the state around different axes in the Bloch sphere representation. Physically, X and Y gates (rotations around the X and Y axes) are generated by modulating the coupling between the states |0 and |1 at the frequency difference between these states ω 01 = (E |1 −E |0 )/h. This modulation drive has the general form Ω(t) cos(ω D t − γ) where Ω(t) is the drive strength of the rotation, ω D is the drive frequency (ω D = ω 01 on resonance) and γ is the drive phase. The duration of the gate is set by the desired rotation angle and the drive strength. On-resonance, when γ = 0, the qubit state rotates around the X axis and when γ = π 2 the rotation is around the Y axis. Therefore, the geometric X and Y axes in the Bloch sphere correspond to a real π 2 phase difference between drive fields. Rotations around the remaining axis (Z axis), i.e., Zgates, correspond to a change in the relative phase between the |0 and |1 states. A Z-gate can be implemented by either detuning the frequency of the qubit with respect to the drive field for some finite amount of time (e.g. see Ref.[1]) or by composite X and Y gates. The result is that the qubit state rotates with respect to the X and Y axes. However, it is equivalent t...

We improve the quality of quantum circuits on superconducting quantum computing systems, as measured by the quantum volume (QV), with a combination of dynamical decoupling, compiler optimizations, shorter two-qubit gates, and excited state promoted readout. This result shows that the path to larger QV systems requires the simultaneous increase of coherence, control gate fidelities, measurement fidelities, and smarter software which takes into account hardware details, thereby demonstrating the need to continue to co-design the software and hardware stack for the foreseeable future.

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The quantum circuit model is an abstraction that hides the underlying physical implementation of gates and measurements on a quantum computer. For precise control of real quantum hardware, the ability to execute pulse and readout-level instructions is required. To that end, we introduce Qiskit Pulse, a pulse-level programming paradigm implemented as a module within Qiskit-Terra [1]. To demonstrate the capabilities of Qiskit Pulse, we calibrate both un-echoed and echoed variants of the cross-resonance entangling gate with a pair of qubits on an IBM Quantum system accessible through the cloud. We perform Hamiltonian characterization of both single and two-pulse variants of the cross-resonance entangling gate with varying amplitudes on a cloud-based IBM Quantum system. We then transform these calibrated sequences into a high-fidelity CNOT gate by applying pre and post local-rotations to the qubits, achieving average gate fidelities of F = 0.981 and F = 0.979 for the un-echoed and echoed respectively. This is comparable to the standard backend CNOT fidelity of F CX = 0.984. Furthermore, to illustrate how users can access their results at different levels of the readout chain, we build a custom discriminator to investigate qubit readout correlations. Qiskit Pulse allows users to explore advanced control schemes such as optimal control theory, dynamical decoupling, and error mitigation that are not available within the circuit model.