Session W38: Control and Characterization Tools for Quantum Error Mitigation

Demonstrating error rate homogenization using dynamically corrected gates in a trapped ion system

High quality, error-robust gates are a fundamental element of scalable quantum computing architectures; however, their performance is often limited by their high sensitivity to external perturbations and imperfections in the control field. We experimentally demonstrate that replacing “primitive” physical gates with error-suppressing, dynamically corrected gates (DCGs) can homogenize error rates across a qubit register in both space and time, in addition to reducing net error rates.
We perform parallel single-qubit operations on a multi-qubit register of ¹⁷¹Yb⁺ ions using a microwave field. We achieve a best case single-qubit average error rate of 1.9e-5 using primitive gates, although inhomogeneous fields lead to an order of magnitude variation across the 10 qubit register. By using DCGs, we observe an 8.5x reduction in the spread of error rates across the register, and a 2.4x improvement of the average value. Furthermore, DCGs provide an added robustness to slow drifts in the control, reducing the overhead required for regular calibrations.
Finally, we discuss a microwave synthesis chain using a cryogenic sapphire oscillator and an arbitrary waveform generator, aimed at improving the control-field phase noise and reducing the calibration requirements compared to traditional I/Q.   

Error Mitigation Via Simulated Measurement of Stabilizers

While closed-loop control is the ideal for quantum error correction, open-loop techniques are more accessible given current technologies. Dynamical decoupling is the go-to error mitigation technique, but many of the noise mechanisms encountered in experimental implementations, such as microwave cross-talk or coherent gate errors, are not amenable to simple dynamical decoupling schemes. An alternative technique for these errors is to simulate measurement of stabilizer operators via the stochastic application of gates from the set of stabilizers. We demonstrate the error-mitigating effects of this simulated quantum measurement protocol on a small superconducting qubit processor.   

SPAM Error Correction: Transition Matrix versus Quasiprobabilities

State preparation and measurement (SPAM) errors limit the performance
of noisy intermediate-scale quantum computers and their potential for
practical application. Two techniques have been used to partially
mitigate these SPAM errors. Both approaches build approximate models
of the errors via tomography and then attempt to invert it. The first
technique is to measure the transition matrix between all initial and
final classical states, and to use this information to classically
correct subsequently measured data. The second technique recently proposed
by Temme, Bravyi, and Gambetta decomposes an ideal circuit into a
quasiprobabilistic mixture of noisy measured ones. While neither approach
is scalable, it would be useful to know their effectiveness when applied
to real SPAM errors. Here apply both methods to online IBM qubits, and
find very similar predictions for one- and two-qubit corrected Pauli
expectation values, with some indication that the simpler transition
matrix method performs slightly better than the quasiprobability
representation, at least for the SPAM errors encountered in superconducting
qubits.   

Experimental Realization of Randomized Compiling for in-situ Error Reduction

We present work on reducing the average error during the operation of an algorithm through randomized compiling (RC) [1], which tailors arbitrary Markovian noise into stochastic Pauli errors. By compiling random single-qubit twirling gates into the bare sequence of an algorithm and averaging over many initializations of an RC circuit, the total error of an algorithm is reduced because the error per single qubit gate has been averaged into a stochastic noise channel that is independent of the gate itself. Here, we demonstrate experimental work towards implementing RC in both random circuits and quantum protocols for optimization problems. We show that RC suppresses coherent errors in a circuit and that it increases the probability of measuring the correct solution of an algorithm.

[1] J.J. Wallman and J. Emerson, Noise tailoring for scalable quantum computation via randomized compiling, Phys Rev A 94, 052325 (2016).
  

Optimizing stability and performance of cloud-based quantum systems

Since the launch of the first five-qubit device on the IBM Q Experience platform in 2016, we have made steady increases in the number of devices available for cloud access, as well as their fidelity, stability, speed and uptime. Here we will discuss some of the challenges encountered, lessons learned, and best practices adopted in the bring-up, operation, and maintenance of these devices.   

Fidelity of sequences of SWAP operations in chains of multiple coupled qubits

We investigate the swapping of qubit states between neighboring qubits in a chain of multiple qubits with quasistatic noise both in the (nearest-neighbor) couplings between them and in fields applied to the individual qubits. We will assume no intentionally applied fields, so that all such fields that appear are due entirely to noise. We consider chains of several different lengths and different sequences of SWAP operations (i.e., different pairs of neighboring qubits to perform the operation on and different lengths). We determine the fidelity of these sequences as a function of sequence and qubit chain length for different noise strengths.   

Noise-resistant Landau-Zener sweeps from geometrical curves

The decoherence of a qubit due to environmental noise is a long-standing problem in quantum information science. Recent work provided a new recipe for designing dynamically corrected gates analytically using a simple geometric formalism. By adapting that formalism, we demonstrate how to design noise-resistant Landau-Zener sweeps through an avoided crossing. In the case where the avoided crossing is created purely from noise, we demonstrate identity gates and phase gates that are robust against error up to second order. In the more general case where the avoided crossing exists in the absence of noise, we show that robust sweeping protocols are in one-to-one correspondence with curves lying on a sphere that obey certain constraints. We show how to exploit this correspondence to systematically construct noise-resistant Landau-Zener sweeps for generic avoided crossings.   

High-performance nonlinear optimization module for quantum control

Precise manipulation of quantum systems via shaped control pulses has emerged as a key area of development for quantum physics and chemistry. In near-term quantum computers, for example, substitution of primitive operations with optimized noise-robust controls can yield improved fidelities for single- and multi-qubit gates without hardware modifications. However, for all but the most basic of systems, identifying ideal control pulses via analytic approaches is intractable, motivating an approach based on numerical optimization. In this talk we introduce a custom GPU-compatible optimization toolkit purpose-built for rapidly creating high-fidelity, noise-robust quantum controls in high-dimensional Hilbert spaces. We describe the design of the toolkit, provide examples of standard and custom workflows, and present benchmarking results that demonstrate the speedup enabled by the GPU-compatible graph architecture.   

Implementation of a canonical phase measurement with quantum feedback

In many sectors of modern metrology and communication technology, information is encoded in electromagnetic waves, typically as an amplitude or phase. While current hardware can perform near-ideal measurements of photon number or field amplitude, a device that can perform an ideal phase measurement is elusive. In this work, we implement a single-shot canonical phase measurement on a one-photon wave packet which surpasses the current standard of heterodyne detection and is optimal for single-shot phase estimation. By applying quantum feedback to a Josephson parametric amplifier, our system adaptively changes its measurement basis during photon arrival and allows us to validate the detector’s performance by tracking the quantum state of the photon source. These results demonstrate that quantum feedback can both enhance the precision of a detector and enable it to measure new classes of physical observables.   

Two-qubit Pauli-frame randomization in a superconducting system

Coherent noise and non-Markovianity are projected to be significant sources of non-ideal behavior in large scale quantum computers. One approach to dealing with such noise sources is called Randomized Compiling where quantum circuits are permuted by the insertion of random gates whose effect is tracked and inverted at the end of the circuit on a shot-by-shot basis. While this technique effectively removes coherent error and significantly reduces non-Markovianity, it can be quite challenging to implement experimentally due to the large number of random circuits that need to be generated and data that needs to be post processed. To remove some of the experimental overhead, we have implemented control system firmware that randomizes quantum circuits on-the-fly using custom control electronics. Here we build on previous work accomplishing this in a single qubit system extending it to circuits with two qubit gates.

“This document does not contain technology or technical data controlled under either the ITAR or the EAR.”   

Deep Reinforcement Learning for Quantum Control: Learning to Optimally Navigate in Complex Noisy Environments

Quantum control seeks to establish control over a quantum system in such a way so that logical operations are implemented while simultaneously mitigating unwanted interactions between the system and its environment. From the point of view of quantum computation, quantum control can potentially provide significant improvements in computational accuracy when quantum logic operations are tailored for the particular noise plaguing the hardware. Specifically tailoring each controlled operation can be quite demanding if one wishes to perform this task for every instantiation of a quantum algorithm. Here, we examine how one can leverage reinforcement learning to learn and predict quantum gates in the presence of temporally correlated noise. We discuss how this information provides knowledge about optimal gate construction for noise-tailored quantum algorithms, as well as how this approach potentially informs noise characterization.   

Assigning Hamiltonians to Open Quantum Systems

Building on recent efforts illustrating that one may characterize a closed system of k-local interacting particles, we study the task of identifying a local-Hamiltonian in the presence of additional environmental interactions. Beginning with a candidate system consisting of an XX-interacting spin chain subject to thermal relaxation noise, we show how both the Hamiltonian and the underlying Lindbladian can models can be inferred. Moreover, we study open-systems learning in the settings where one is given i) access to steady states, ii) dynamical information, as well as iii) in the presence of stochastic noise on the measurement output.