Direct Digital Synthesis for Large-Scale Quantum Computers

In developing the OPX1000, a controller fit for the ever-growing quantum processors counting 1,000 qubits and beyond, we had to think deeply about every detail that impairs scalability. Our recently unveiled OPX1000 module for microwave generation (MW-FEM) generates pulses up to 10.5 GHz directly, without analog oscillators or mixers. The choice of technology to reach microwave frequencies is not trivial. We choose cutting-edge direct digital synthesis (DDS) for very specific reasons, and we believe it will enable scalability and performance to an even greater degree. In this blog, we dive deeper into the considerations for going this route and existing alternatives. So stick around, whether you like mixers or hate them, this will be an interesting ride. 

Summary of Technologies for Microwave Operation 

The control signals for qubit drive and readout often fall in the microwave range, which is outside the range of baseband controllers. Many qubit labs have solved the issue with solutions based on mixing, including single sideband mixers, IQ-mixers, or more complicated schemes such as double super-heterodyne (DSH) conversion.  

Mixer-based solutions make use of analog local oscillators (LOs) that are multiplied by the signal of a controller or an AWG. IQ-mixers naturally suffer from two main spurs (affectionate name for unwanted signals), the LO leakage and the mixer image, which require non-trivial calibration to be removed. Other schemes, such as double super-heterodyne, offer a zero-calibration solution but use many more components. Additionally, mixing schemes require having an LO source per mixer if different drive frequencies are used. Having a low phase source per mixer is very expensive, and in order to cut prices, will probably include a phase-lock loops (PLL), leading to phase differences between channels, which is detrimental for multi-qubit systems. In other words, while mixers can be useful, we need to be aware of the pros and cons involved.  

Direct Digital Synthesis (DDS) is a more recent technique with clear advantages over its analog counterpart. DDS allows for a much simpler system, with no mixer, no LO, no calibration. A DDS based solution gives a much better frequency agility, improved phase noise and overall precise control over the phase of even multiple channels playing synchronously. Here is a summary of how DDS compares to some alternatives, to be explained in the remainder of this blog post.  

Table – A summary of the main performance considerations when choosing technologies for microwave operation. With its recent advancements, Direct Digital Synthesis (DDS) stands out clearly as the optimal technology for scaling up quantum controllers, such as the OPX1000.

A Deeper Dive on SFDR and Bandwidth 

The first performance indicator for microwave generation or up-conversion modules is the spurious-free dynamic range (SFDR). This tells us how much power difference there is between the signal we want to play and the unwanted signals (spurs) that happen to be generated.  

Because of LO leakage and the generation of an image signal, IQ-mixers require calibration for good SFDR. Quantum Machines’ Octave allows plug-and-play operation up to 18 GHz with an SFDR of 50 dBc, although the calibration process is far from trivial. The Octave’s fast and automated calibration process reduces some of the pain, but not without a price. Mixer calibration is usually narrowly centered around the calibration frequency, which is not great if one needs many frequencies, large bandwidth, or quick switching of frequencies. IQ-mixing solutions require one mixer and one amplifier per channel, but also one LO per channel if multiple frequency carriers are used (see setup in Figure). 

Figure – Different methods of generating microwave for qubit control and readout: IQ-mixing, double super-heterodyne (DSH), and direct digital synthesis (DDS).

More advanced schemes are engineered for high SFDR, such as DSH, and allow for up to 70 dBc, narrowband, and 60 dBc on its operational bandwidth, only using filters and no calibration, at the cost of more components used. Instead, the OPX1000’s new MW-FEM module, operating with DDS without conversion or mixers, gets us an SFDR exceeding 60 dBc on the entire 0.05-10 GHz spectrum. DDS needs no calibration and offers ideal performance with much better phase coherence and fewer components – more on this later. 

The truth is that most qubit chips won’t see a difference between 50 dBc and 70 dBc. The fidelity of even the best currently available qubits is impacted by all sorts of other sources of noise and spurs, from cross-coupling between channels, environmental noise, and more. Thus, the need for better SFDR saturates around 50 dBc, where you can be sure your control system won’t be the fidelity bottleneck any time soon.  

Phase Coherence and a Shared Source of Noise 

Phase coherence and noise are particularly tricky, but also very important to consider for quantum sequences, as they directly impact qubit operational fidelity. When the frequency of a signal wabbles, in the time-domain we get jitter. Jitter on drives acts negatively on qubits, similarly to fluctuating environmental Hamiltonian terms [Ball H., npj Quantum Inf 2, 16033 (2016)]. Additionally, if the jitter of different channels is not correlated, i.e. it does not come from the same LO source, the channels will experience bad phase coherence. 

In fact, if multiple frequency carriers are used, mixing solutions have their phase coherence limited by the quality and number of LOs. LOs are often implemented via a phase-lock loop (PLL) circuit that uses voltage-controlled oscillators (VCO) and phase detectors in a feedback loop. In such a loop, the noise of the input reference oscillator directly translates into phase noise of the output, i.e., the LO signal and, later, the qubit drive. This means that for a system with reasonable phase noise we need a large investment in ultra-stable synthesizers as reference oscillators. Assuming each channel working with a different carrier frequency, one such synthesizer might be needed for each PLL, thus one for each qubit (consider that usually drive and readout do not happen with the same carrier frequency). Additionally in such case, each PLLs will experience different noise, making the jitter of different channels uncorrelated, and destroying their phase coherence. This is a very detrimental effect for multi-qubit operation. Finally, every active component such as amplifiers comes with its share of noise, so solutions with a high number of components will generally have worse phase coherence. 

Instead, particularly on matters of phase coherence, DDS really shines. The oscillators generating the signals on the MW-FEM are numerically controlled (NCO), and all share the same reference clock. The clock fractional division reduces the impact of reference phase noise onto the output channels, and most importantly makes them all phase coherent, as they have a single noise source. This means we can invest in a single high-quality clock to generate many drive signals with exceptional phase coherence and very low noise. That is a single high-performance clock for all your OPX1000s. In addition, with everything being digital and controlled by a single brain, the MW-FEM offers complete control of the phase of these NCOs, allowing for resetting their phase in real-time, at will. This is a unique capability, impossible for analog oscillators, while useful for quantum computing protocols, e.g. resetting all phases at the start of each algorithmic run or even within quantum sequences. 

Scalability Considerations 

We considered performance metrics which directly impact fidelity and are important for any one control channel. But the OPX1000 was designed for more than high performance on just one or two qubits. It was meant for the highest fidelities operating thousands of qubits, simultaneously. So, what else do we need to consider for scalability? 

First is the number of components. When scaling to thousands of qubits and beyond, each extra amplifier, LO, and mixer, is one that you must buy, integrate, get space for, and provide power to. They add on cost and limit phase coherence. Furthermore, when thinking about the future of quantum controllers integrated on chip with millions of drive lines, LOs impose hard limitations, as integrating multiple of them on chip is very challenging. The lower number of components for the DDS allows to reduce the cost of scalability and pushes the OPX1000 to have the highest density of channels in the industry, with 80 analog channels in just 3U. As an example, when setting up to control 1,000 superconducting qubits, this amounts to a reduction of roughly a factor of 4 in floor space and power consumption for the data center. Every component matters: a tiny piece replicated thousands of times in a giant puzzle. 

Figure – Thanks to the highest channel density in the industry, the OPX1000 allows controlling 1000 superconducting qubits with just 2.5 racks. This is also thanks to the MW-FEM cutting-edge DDS technology.

Second, it should be clear by now why having a wideband high SFDR is important. Controllers must be flexible to adapt to any technological change, or simply allow to tune to different qubits or system components. Especially when considering controlling many qubits, playing simultaneous pulses of different frequencies from any one port is a great feature. DDS allows each MW-FEM to play up to 8 tones, around 2 different carriers and each with either 800 MHz or 1.6 GHz bandwidth, multiplexed to a single channel. Finally, analog LOs and calibrations prevent mixer-based solutions from switching frequency and reset phase in real-time; all bread and butter for DDS. This comes into play, for example, when we wish to drive and then readout a qubit in a tight time window. Thanks to DDS, the MW-FEM allows not only to switch virtually instantly between frequencies but even to drive many of them simultaneously out of the same channel, with individual control. 

Your Trusted Quantum Control Partner 

These are the main considerations that make us stand behind the cutting-edge DDS for the MW-FEM. DDS allows for the best performance, the highest degree of flexibility, unmatched channel density and scalability, and many unique capabilities. In many cases, a mixer-based solution with a fast and completely automated calibration protocol, such as the Octave, would do the trick. But when thinking about large-scale quantum processing units and future-proof solutions, mixers become a bottleneck. 

The OPX1000 showcasing both the LF-FEM, for baseband operation, and the MW-FEM, for frequencies up to 10.5 GHz, enabled by Direct Digital Synthesis (DDS), with no mixers, no LOs, offering the best performance right out of the box. (Configuration for illustration only). 
Get the product spec sheet here.