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arXiv:1806.07930 · Physical Review Applied

Digital Coherent Control of a Superconducting Qubit

E. Leonard, M. A. Beck, J. Nelson, B.G. Christensen, T. Thorbeck, C. Howington, A. Opremcak, Ivan Pechenezhskiy, K. Dodge, N.P. Dupuis, M.D. Hutchings, J. Ku, F. Schlenker, J. Suttle, C. Wilen, S. Zhu, Maxim Vavilov, B.L.T. Plourde, R. McDermott

Published Jan 7, 2019• 141 citations
arXivHTMLPDF

Abstract

Superconducting qubits are conventionally controlled with shaped microwave pulses from a microwave carrier tone. This works well for small systems, but is difficult to scale up to the millions of qubits needed for a general-purpose quantum computer. Instead, the authors suggest irradiating a qubit with trains of quantized flux pulses derived from single flux quantum (SFQ) digital logic. The pulses are generated by an SFQ driver circuit cofabricated on the qubit chip. This work opens the door to tight integration of a quantum array with a classical coprocessor, to lower wiring heat load, latency, and overall system footprint.

DOI
10.1103/physrevapplied.11.014009

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Superconducting qubits are conventionally controlled with shaped microwave pulses from a microwave carrier tone. This works well for small systems, but is difficult to scale up to the millions of qubits needed for a general-purpose quantum computer. Instead, the authors suggest irradiating a qubit with trains of quantized flux pulses derived from single flux quantum (SFQ) digital logic. The pulses are generated by an SFQ driver circuit cofabricated on the qubit chip. This work opens the door to tight integration of a quantum array with a classical coprocessor, to lower wiring heat load, latency, and overall system footprint.
In the quest to build a fault-tolerant quantum computer, superconducting circuits based on Josephson junctions have emerged as a leading architecture. Coherence times have increased significantly over the last two decades, and processors with ∼ 50 qubits have been experimentally demonstrated. These systems traditionally utilize microwave frequency control signals, and heterodyne based detection schemes for measurement. Both of these techniques rely heavily on room temperature microwave generators, high-bandwidth lines from room temperature to millikelvin temperatures, and bulky non-reciprocal elements such as cryogenic microwave isolators. Reliance on these elements makes it impractical to scale existing devices up a single order of magnitude, let alone the 5-6 orders of magnitude needed for performing fault-tolerant quantum algorithms. Here, I present results that suggesting superconducting digital logic, namely Single Flux Quantum (SFQ) logic, can replace analog control and measurement techniques, avoiding the significant overhead involved. I describe a scheme for measuring qubits with a device known as a Josephson Photomultiplier (JPM), which crucially stores the result of a qubit measurement in a classical circulating supercurrent within the device and allows for integration with SFQ detection circuitry. This technique is experimentally demonstrated, with single-shot measurement fidelity of 92%. Two methods for accessing this measurement result are presented, one utilizing ballistic fluxons, and another utilizing flux comparison. Initial experimental results of the latter are presented. In addition, I describe a scheme for controlling qubits with sequences of digital SFQ pulses. This method is then used to control a qubit without a microwave signal generator, with results of an average single-qubit gate fidelity of around 95%. When combined, these techniques form a nearly fully digital interface to superconducting qubits, which could allow these systems to scale much more easily.
Single-flux-quantum (SFQ) digital logic is an attractive candidate for classical control and monitoring of large-scale quantum processors based on superconducting qubits. The authors describe a control approach based on repeated irradiation of the qubits with short registers of classical bits, which can be stored locally in compact SFQ registers and streamed to the quantum array at a high rate. Numerical simulations show achievable gate fidelity in excess of 99.99%; moreover, the approach allows control of many qubits resonating at different frequencies with a single, global SFQ clock. As a result, the scheme is well matched to the control of a scalable two-dimensional surface code.
In the interest of alleviating qubit coherence constraints and making quantum control circuits more efficient, this paper explores qubit control using superconducting Single-Flux Quantum (SFQ) digital circuits. By using SFQ pulse trains and SFQ switches, we represent qubit state transformations through their equivalent phase changes, where each SFQ pulse represents a phase change of certain degrees. We propose classical-based unitary quantum gates represented by SFQ pulses. We create a classical equivalent model for quantum gates based on an SFQ-based parametric pulse sequence equivalent to quantum Pauli gates. To generate pulse sequences of configurable parameters, we implement a versatile multi-frequency pulse generator that seamlessly integrates with the qubit-resonator cavity.
An approach for scalable quantum computing infrastructure based on the use of low-power digital superconducting single flux quantum (SFQ) circuits is described. Rather than replicating the room-temperature microwave control and measurement infrastructure solutions dominating the current systems, we use the inherent to superconducting technology methods - the use of SFQ pulses directly at the base temperature. For qubit control, we irradiate qubits with the coherent SFQ pulse sequences computed using optical control theory. For qubit measurement, Josephson photon counter performs projective quantum measurement, the result of which is converted to digital SFQ output. These operations are aided by a high-speed digital SFQ coprocessor located at higher temperature stage (e.g., 3 K) to process the measurement results and load new control sequences to 20 mK SFQ quantum-classical interface circuits.
Readout and control of qubits are limiting factors in scaling quantum computers. An ideal solution is to integrate energy-efficient cryogenic circuits close to the qubits to perform control and pre-processing tasks. With orders of magnitude lower power consumption and hence lower noise, Single Flux Quantum (SFQ) and Adiabatic Quantum Flux Parametron (AQFP) superconductor logic families can reach ultimate performance at cryogenic temperatures. We have created a superconductor-based on-chip function generator to control qubits. The generated signal is modulated up to tens of GHz based on the external input waveform applied to the superconductor mixer stage. This circuit works at 4.2K. A radiofrequency (RF) matching circuit transmits the signal to the ~mK stage after digital amplification and noise reduction.
For superconducting quantum processors, microwave signals are delivered to each qubit from room-temperature electronics to the cryogenic environment through coaxial cables. Limited by the heat load of cabling and the massive cost of electronics, such an architecture is not viable for millions of qubits required for fault-tolerant quantum computing. Monolithic integration of the control electronics and the qubits provides a promising solution, which, however, requires a coherent cryogenic microwave pulse generator that is compatible with superconducting quantum circuits. Here, we report such a signal source driven by digital-like signals, generating pulsed microwave emission with well-controlled phase, intensity, and frequency directly at millikelvin temperatures. We showcase high-fidelity readout of superconducting qubits with the microwave pulse generator. The device demonstrated here has a small footprint, negligible heat load, great flexibility to operate, and is fully compatible with today's superconducting quantum circuits, thus providing an enabling technology for large-scale superconducting quantum computers.