I am going to post here all newly submitted articles on the arXiv related to superconducting circuits. If your article has been accidentally forgotten, feel free to contact me

07
Mai
2021

# Quantify the Non-Markovian Process with Intermediate Projections in a Superconducting Processor

The physical system is commonly considered memoryless to simplify its dynamics, which is called a Markov assumption. However, memory effect is a fundamental phenomenon in the universe.

In the quantum regime, this effect is roughly attributed to the correlated noise. With quantum measurements often collapsing the quantum state, it is hard to characterize non-Markovianity of quantum dynamics. Based on the recently developed framework by Pollock et al., we design a 2-step quantum process, where one qubit is the system and another ancilla serves as its environment. In a superconducting processor, the restricted quantum process tensor is determined using a set of sequential projective measurements, and the result is then used to predict the output state of the process. When the environment has memory, we have achieved very high fidelity in predicting the final state of the system (99.86%±1.1‰). We further take a closer look at the cause of the memory effect and quantify the non-Markovianity of the quantum process conditioned on the historical operations.

06
Mai
2021

# Injection locking and synchronization in Josephson photonics devices

Injection locking can stabilize a source of radiation, leading to an efficient suppression of noise-induced spectral broadening and therefore, to a narrow spectrum. The technique is

well established in laser physics, where a phenomenological description due to Adler is usually sufficient. Recently, locking experiments were performed in Josephson photonics devices, where microwave radiation is created by inelastic Cooper pair tunneling across a dc-biased Josephson junction connected in-series with a microwave resonator. An in-depth theory of locking for such devices, accounting for the Josephson non-linearity and the specific engineered environments, is lacking.
Here, we study injection locking in a typical Josephson photonics device where the environment consists of a single mode cavity, operated in the classical regime. We show that an in-series resistance, however small, is an important ingredient in describing self-sustained Josephson oscillations and enables the locking region. We derive a dynamical equation describing locking, similar to an Adler equation, from the specific circuit equations. The effect of noise on the locked Josephson phase is described in terms of phase slips in a modified washboard potential. For weak noise, the spectral broadening is reduced exponentially with the injection signal. When this signal is provided from a second Josephson device, the two devices synchronize. In the linearized limit, we recover the Kuramoto model of synchronized oscillators. The picture of classical phase slips established here suggests a natural extension towards a theory of locking in the quantum regime.

# Compiling Arbitrary Single-Qubit Gates Via the Phase-Shifts of Microwave Pulses

Realizing an arbitrary single-qubit gate is a precursor for many quantum computational tasks, including the conventional approach to universal quantum computing. For superconducting

qubits, single-qubit gates are usually realized by microwave pulses along drive or flux lines. These pulses are calibrated to realize a particular single-qubit gate. However, it is clearly impractical to calibrate a pulse for every possible single-qubit gate in SU(2). On the other hand, compiling arbitrary gates using a finite universal gate set will lead to unacceptably low fidelities. Here, we provide a compilation scheme for arbitrary single-qubit gates for which the three real parameters of the gate directly correspond to the phase shifts of microwave pulses, which can be made extremely accurate experimentally, that is also compatible with any two-qubit gate. Furthermore, we only require the calibration of the Xπ and Xπ2 pulses, gates that are already necessary for tasks such as Clifford-based randomized benchmarking as well as measuring the T1 and T2 decoherence parameters.

05
Mai
2021

# Lindblad Tomography of a Superconducting Quantum Processor

As progress is made towards the first generation of error-corrected quantum computers, careful characterization of a processor’s noise environment will be crucial to designing

tailored, low-overhead error correction protocols. While standard coherence metrics and characterization protocols such as T1 and T2, process tomography, and randomized benchmarking are now ubiquitous, these techniques provide only partial information about the dynamic multi-qubit loss channels responsible for processor errors, which can be described more fully by a Lindblad operator in the master equation formalism. Here, we introduce and experimentally demonstrate Lindblad Tomography, a hardware-agnostic characterization protocol for tomographically reconstructing the Hamiltonian and Lindblad operators of a quantum channel from an ensemble of time-domain measurements. Performing Lindblad Tomography on a small superconducting quantum processor, we show that this technique characterizes and accounts for state-preparation and measurement (SPAM) errors and allows one to place strong bounds on the degree of non-Markovianity in the channels of interest. Comparing the results of single- and two-qubit measurements on a superconducting quantum processor, we demonstrate that Lindblad Tomography can also be used to identify and quantify sources of crosstalk on quantum processors, such as the presence of always-on qubit-qubit interactions.

03
Mai
2021

# Improving qubit coherence using closed-loop feedback

Superconducting qubits are a promising platform for building a larger-scale quantum processor capable of solving otherwise intractable problems. In order for the processor to reach

practical viability, the gate errors need to be further suppressed and remain stable for extended periods of time. With recent advances in qubit control, both single- and two-qubit gate fidelities are now in many cases limited by the coherence times of the qubits. Here we experimentally employ closed-loop feedback to stabilize the frequency fluctuations of a superconducting transmon qubit, thereby increasing its coherence time by 26\% and reducing the single-qubit error rate from (8.5±2.1)×10−4 to (5.9±0.7)×10−4. Importantly, the resulting high-fidelity operation remains effective even away from the qubit flux-noise insensitive point, significantly increasing the frequency bandwidth over which the qubit can be operated with high fidelity. This approach is helpful in large qubit grids, where frequency crowding and parasitic interactions between the qubits limit their performance.

# Experimental Deep Reinforcement Learning for Error-Robust Gateset Design on a Superconducting Quantum Computer

Quantum computers promise tremendous impact across applications — and have shown great strides in hardware engineering — but remain notoriously error prone. Careful design

of low-level controls has been shown to compensate for the processes which induce hardware errors, leveraging techniques from optimal and robust control. However, these techniques rely heavily on the availability of highly accurate and detailed physical models which generally only achieve sufficient representative fidelity for the most simple operations and generic noise modes. In this work, we use deep reinforcement learning to design a universal set of error-robust quantum logic gates on a superconducting quantum computer, without requiring knowledge of a specific Hamiltonian model of the system, its controls, or its underlying error processes. We experimentally demonstrate that a fully autonomous deep reinforcement learning agent can design single qubit gates up to 3× faster than default DRAG operations without additional leakage error, and exhibiting robustness against calibration drifts over weeks. We then show that ZX(−π/2) operations implemented using the cross-resonance interaction can outperform hardware default gates by over 2× and equivalently exhibit superior calibration-free performance up to 25 days post optimization using various metrics. We benchmark the performance of deep reinforcement learning derived gates against other black box optimization techniques, showing that deep reinforcement learning can achieve comparable or marginally superior performance, even with limited hardware access.

29
Apr
2021

# Variational tight-binding method for simulating large superconducting circuits

We generalize solid-state tight-binding techniques for the spectral analysis of large superconducting circuits. We find that tight-binding states can be better suited for approximating

the low-energy excitations than charge-basis states, as illustrated for the interesting example of the current-mirror circuit. The use of tight binding can dramatically lower the Hilbert space dimension required for convergence to the true spectrum, and allows for the accurate simulation of larger circuits that are out of reach of charge basis diagonalization.

# Quantum and thermal fluctuations in the dynamics of a RCSJ junction

We theoretically investigate the phase and voltage correlation dynamics under a current noise including thermal and quantum fluctuations in a resistively and capacitively shunted Josephson

(RCSJ) junction. Within the linear regime, an external current is found to shift and intensify the deterministic contributions in phase and voltage. In addition to the deterministic contribution, we observe the relaxation of autocorrelation functions of phase and voltage to finite values due to the current noise. We also find an earlier decay of coherence at a higher temperature in which thermal fluctuations dominate over quantum ones.

24
Apr
2021

# Optimization of Controlled-Z Gate with Data-Driven Gradient Ascent Pulse Engineering in a Superconducting Qubit System

The experimental optimization of a two-qubit controlled-Z (CZ) gate is realized following two different data-driven gradient ascent pulse engineering (GRAPE) protocols in the aim of

optimizing the gate operator and the output quantum state, respectively. For both GRAPE protocols, the key computation of gradients utilizes mixed information of the input Z-control pulse and the experimental measurement. With an imperfect initial pulse in a flattop waveform, our experimental implementation shows that the CZ gate is quickly improved and the gate fidelities subject to the two optimized pulses are around 99%. Our experimental study confirms the applicability of the data-driven GRAPE protocols in the problem of the gate optimization.

23
Apr
2021

# Ghost Factors in Gauss Sum Factorization with Transmon Qubits

A challenge in the Gauss sums factorization scheme is the presence of ghost factors – non-factors that behave similarly to actual factors of an integer – which might lead

to the misidentification of non-factors as factors or vice versa, especially in the presence of noise. We investigate Type II ghost factors, which are the class of ghost factors that cannot be suppressed with techniques previously laid out in the literature. The presence of Type II ghost factors and the coherence time of the qubit set an upper limit for the total experiment time, and hence the largest factorizable number with this scheme. Discernability is a figure of merit introduced to characterize this behavior. We introduce preprocessing as a strategy to increase the discernability of a system, and demonstrate the technique with a transmon qubit. This can bring the total experiment time of the system closer to its decoherence limit, and increase the largest factorizable number.