---
title: "Numerically Controlled Oscillators: How OPX1000 Generates Multitone Signals"
date: "2026-09-03T14:48:11+00:00"
url: "https://www.quantum-machines.co/resources/blog/numerically-controlled-oscillators-opx1000-multitone/"
description: "How OPX1000's numerically controlled oscillators generate precise multitone signals in real time — from qubit drive to atom sorting."
---

# Numerically Controlled Oscillators: How OPX1000 Generates Multitone Signals

Writers

         ![Unnati Akhouri](https://www.quantum-machines.co/wp-content/uploads/2026/05/Unnati-150x150.webp)#### Unnati Akhouri

Unnati Akhouri is a Product Solutions Physicist at Quantum Machines, specializing in the intersection of quantum theory and hardware control. She holds a PhD from Penn State and a Master’s from Oxford, with deep expertise in open quantum systems and qubit decoherence. As a dedicated science communicator, she is the creator of the “Bit, Byte, and Nibble” series and the “Fatal Physics” comics, which aim to simplify complex concepts of quantum computing and fundamental physics into easily understandable and entertaining content.

 Blog September 2026 | 8 min read

![](https://www.quantum-machines.co/wp-content/uploads/2026/09/0926_Blog-Post_1680x420_Numerically-1-1024x256.webp)# Numerically Controlled Oscillators: How OPX1000 Generates Multitone Signals

We often talk about continuous‑time signals, but almost every real digital system works with sampled numbers. At each instant, the system samples a single number that is mapped to an amplitude. If these are sampled fast enough, we can generate smooth waveforms.

A good controller is one that can faithfully represent the continuous output we want from a sequence of sampled values.

Qubit experiments, for example, need time‑dependent signals whose frequency, phase, and amplitude can all change with high precision at nano-second time scales. This makes the task of turning digital samples into a clean, coherent waveform much more challenging.

Numerically controlled oscillators (NCOs) in Direct Digital Synthesis offer a solution by producing digital sinusoidal waves with precise, tunable frequency and phase. The OPX1000 uses such NCOs to generate multitone in real time, rather than storing millions of sample points, making them scalable and adaptable.

So, whether you are working with a frequency-multiplexed readout tones for superconducting qubits or a full multitone trajectory for atom sorting, the OPX1000 can generate the frequency content parametrically rather than from stored samples.

### Inside the NCO: Phase Accumulator, Lookup Table, and Digital-to-Analog Conversion

NCOs are made up of two key elements: a phase accumulator and a phase-to-amplitude converter (PAC).

   ![](https://www.quantum-machines.co/wp-content/uploads/2026/09/IMAGE-2026-09-02-180551.webp)

*The animation illustrates how a reference clock drives the phase accumulator (PA), lookup table (LUT), and DAC to synthesize a digitally controlled waveform, ultimately generating precise tones.*

The phase accumulator is a running counter that adds a fixed numerical value called the phase increment every clock cycle. This determines how quickly the phase advances and therefore sets the output frequency. The accumulated phase value represents the instantaneous phase of the signal.

The phase‑to‑amplitude converter then maps this digital phase to a corresponding waveform amplitude, typically using a lookup table that stores precomputed values.

Because the waveform is represented digitally as samples, operations such as rapid frequency switching, phase adjustment, and repeatable signal generation become straightforward digital manipulations. Rapid frequency switching is needed, for example when a controller must jump from a qubit drive frequency to a different frequency in low latency. Such scenarios that demand frequency agility and accuracy are where NCOs can be helpful. But an NCO alone cannot produce smooth output.

An NCO’s accuracy is limited by the resolution of the lookup table and the system clock, and because the waveform is generated in discrete digital steps, it produces small unwanted spectral components called spurs. This matters in quantum control because spurs can leak into neighboring qubit transitions and cause crosstalk. The spurious‑free dynamic range (SFDR) quantifies this by comparing the main signal to the strongest spur.

When an NCO is paired with a Digital‑to‑Analog Converter (DAC), the DAC converts each digital amplitude sample into a corresponding analog voltage level at the clock rate. A low‑pass anti-aliasing filter then removes spectral images above the Nyquist frequency, leaving a clean, continuous waveform. This combined system is known as a Direct Digital Synthesizer (DDS).

![](https://www.quantum-machines.co/wp-content/uploads/2026/09/image-for-blog-1024x397.webp)OPX1000 enables parametric waveforms, reducing memory usage by reusing a single pulse definition with real-time shaping. Variations in amplitude, phase, and frequency are applied on the fly, eliminating the need to store each pulse variant separately.### How OPX1000 Turns Digital Samples into Waveforms

Because everything downstream of the phase accumulator is digital, a [DDS-based system](https://www.quantum-machines.co/resources/blog/direct-digital-synthesis-for-large-scale-quantum-computers/) needs no analog local oscillator, no mixer, and no calibration. And because every NCO on the OPX1000 is derived from the same reference clock, channels playing simultaneously stay phase coherent by construction, rather than depending on the noise of separate synthesizers.

Let’s look at the Low-Frequency Front End Module (LF-FEM) of the OPX1000. Each LF-FEM contains 16 independent PPU cores with NCOs (with state-of-art crosstalk isolation between channels). This means that a single LF-FEM can generate up to 16 simultaneous tones up to 750 MHz, each with independent frequency, phase, and amplitude control. For microwave applications, the Microwave-FEM extends this to 50 MHz–10.5 GHz with 8 parallel complex cores.

This differs from the traditional AWG approach, where complete waveforms, carrier and envelope together, are stored and played back directly from memory. While this is manageable at small scale, storing a separate waveform for every frequency, phase, and amplitude combination quickly becomes impractical due to the resulting memory requirements, hardware footprint, power consumption, and waveform transfer overhead. Additionally, compiling all this in mid-circuit becomes impractical.

Instead, the OPX1000 stores compact pulse envelopes and synthesizes the desired signals in real-time. Instructions are sent to the Pulse Processing Unit (PPU), which determines how each waveform should be generated by controlling few parameters like the frequency, phase, and amplitude of the NCOs. The DDS then combines the generated carriers with the stored pulse envelopes to synthesize the final output waveforms with deterministic timing.

QUA, the native pulse-level programming language for OPX1000, allows for rapidly updating the output waveforms. With simple commands, QUA allows for changing amplitude, frequency, and elongating pulses with an in-built interpolation algorithm. The phase is tracked for each NCO, which means that if you jump between phases and return back then you automatically return to the correct phase.

![](https://www.quantum-machines.co/wp-content/uploads/2026/09/image-for-blog-2-1-1-1024x397.webp)OPX1000 preserves phase continuity when switching between frequencies, ensuring deterministic and coherent signal generation across frequency hops.### How does the OPX1000 generate multitone?

A great example of where DDS becomes especially powerful is multitone waveform generation: the ability to produce several precisely controlled frequencies from the same analog output. This matters whenever many independent physical elements need to be addressed at once.

In superconducting systems, for example, multiple tones can be combined on a single line to drive flux lines, tune couplers, or perform frequency-multiplexed readout, where several resonator tones are sent together and separated later on the acquisition side. In these cases, DDS makes the control stack more compact because the tones are generated digitally from few parameters.

   ![initial conditions for Minimal jerk trajectory demonstration](https://www.quantum-machines.co/wp-content/uploads/2026/09/Screenshot-2026-09-02-at-1.33.41-PM.webp)

*Atom sorting into a defect-free array (DFA) using minimal-jerk trajectories. The animation shows selected tones from a multitone comb driving individual optical tweezers toward target sites, assembling a defect-free array at the center. Displayed from top to bottom are the multitone spectrogram with selected tone trajectories, the resulting RF waveform, and a conventional linear chirp for comparison. Minimal-jerk transport suppresses motional excitation while enabling smooth, high-fidelity atom rearrangement.*

With a conventional AWG, adding more tones, channels, or trajectories often means generating and loading more waveform samples before the experiment can run. For large systems, this can create long initialization times and make real-time updates difficult.

In neutral-atom systems, multitone generation is used to independently steer multiple optical tweezers for atom rearrangement and sorting. A standard architecture uses a spatial light modulator to form a static array of tweezers, and a pair of crossed AODs to generate additional, mobile traps that pick atoms up and move them into place. An AOD deflects a laser beam through diffraction, with the deflection angle set by the RF frequency driving it. To move many atoms at once, the AOD needs many simultaneous RF tones.

QUA assigns one core to each tone that is being used to move the atoms. Each oscillator computes its tone frequency and phase directly from a small set of parameters using the NCO-based generation described earlier, rather than reading a stored sample array.

Here, moving translates to chirping the tone. In other words, the frequency of the RF tone sweeps smoothly from a starting value to a target one. The rate of the chirping speeds up and slows back down, so the atom starts and ends at rest.

QUA builds this trajectory as a smooth, minimal-jerk profile from a sequence of short, gapless segments, each with its own chirp rate and duration. Within a segment, the frequency ramps linearly such that the full trajectory tracks a fifth-order polynomial, with zero velocity and acceleration at both endpoints.

Because the trajectory comes from live parameters rather than a stored waveform, the start frequency, target frequency, and chirp rate can all be updated during a running sequence, including from real-time readout data identifying which atoms need to move where.

![spectrogram showing 63 tones for aod for atom movement
](https://www.quantum-machines.co/wp-content/uploads/2026/09/spec_63-1024x628.webp)Spectrogram of a minimal-jerk atom transport trajectory in frequency-time space. Each of the 63 tones follows a smoothly varying frequency trajectory, while color indicates the instantaneous power of each tone.As discussed, each LF-FEM drives up to 16 tones directly. Beyond that, several outputs are combined externally into a single RF signal. For example, in the example above we have been combined 4 LF-FEM here to show 63 tones, chirping over a full millisecond with every tone tracking its minimal jerk trajectory.

Some of our repositories that show this in action are available publicly on [github](https://github.com/qua-platform/qua-libs/tree/main/Quantum-Control-Applications). If you would like to learn how else you could use it for the next big experiment you’re running, [reach out to us for a demo](https://www.quantum-machines.co/request-demo/)!