A new form of qubit control can increase the time of steady operation of a quantum computer.

The Heisenberg Limit cannot be overcome, but if you carefully calculate, you can approach it

Quantum computing is based on controlling quantum states. Recently, more and more news about how quantum computers are calculating something, and the ability to control such computers is taken for granted. But in fact, this control still serves as a limiting factor for the development of quantum computers.

At the heart of this whole topic are qubits , quantum objects used to encode information. Some of the capabilities of a quantum computer come from the fact that a qubit can be transferred to a state of superposition, which makes it possible to organize parallel computing. The goal of quantum algorithms is such a manipulation of the qubit superposition states, so that when a qubit is measured, it returns a binary value corresponding to the correct answer.

This means control over the state of superposition, in which highly precise and very expensive equipment is involved. Improvements usually mean that equipment becomes cheaper. But a new study suggests that we may be able to improve control 1000 times using existing equipment and ingenious tricks.

To understand the problem of control, you need a little to understand the superposition. Describing the states of quantum superposition, we usually use some conventions and say something like: “this means that the particle is in two states at the same time”.

But for our purposes this is not enough, and it seems to me that in any case it is confusing. A quantum object has several measurable properties. And while this property, for example, position, is not measured, it has no value. We have to think in terms of probabilities: if we took a measurement, what is the probability of getting a certain value?

This is in general. And in particular, an extremely unusual concept of “wave function” is revealed, it is also called “amplitude of probability”. The probability is always positive or zero and real, but the amplitude can be positive, negative or even complex. And it changes everything.

Suppose we have a separate particle, and we shoot it at the screen with two slits. The particle can pass through any of the slots or get into the screen. On the other side of the screen, we place the detector and ask ourselves the question: “What is the probability of detecting a particle?”

To do this, we need to add the wave functions of each path that a particle can travel to the detector. The amplitudes may be positive or negative, so their sum will not always be greater. It may even become zero.

If we calculate for many different possible positions of the detector, we find many places where the probability is zero, and many places with equal probability. If you conduct such an experiment, that’s what you measure. After a thousand individual particles pass through the cracks, places will open where they have never been found, and places where they are found regularly.

What am I leading to? In quantum mechanics, in order to accurately predict results, it is necessary to know all the possible ways in which a particle can reach a certain place. So in our example we have to consider both ways to our detector. Because of this, people often say that a particle goes through both slots at the same time.

But the addition of wave functions determines where the particle can be found and where it cannot be found. So if you change one of the ways a particle can go, then you change the amplitudes and thereby move the places where the particle can be detected.

Using superposition

So the probability of measuring the value depends on the history of the probability wave. This includes all possible paths. And this can be turned into a wonderful sensor. And we really use this scheme to measure the flow of time with extreme sensitivity. It also works well for measuring other properties.

A common example is a magnetic field sensor. An electron can be considered a tiny magnet. The electron magnet will line up in a magnetic field, either in the direction of the lines or against them. Therefore, we can bring the electron into a state of superposition, where it is aligned along and against the lines. The magnetic field changes the wave function of the two states, and the strength of the changes depends on the strength of the magnetic field.

Passing through a magnetic field, we measure the orientation of the electron magnet. The only measurement tells us nothing, but after a thousand electrons we will have relative probabilities of two orientations. Based on this, we can calculate the strength of the magnetic field.

In principle, it can work very accurate sensor. Only one thing interferes: noise. The value of the wave functions depends on the path they choose (but not necessarily on the distance they travel). This path changes unpredictably under the influence of the local environment, so each electron will actually be a measure of the influence of the magnetic field that interests us, plus the contribution of noise. And this contribution is different for each electron. If the noise is quite strong, then everything will even out and the two measurements will have the same probabilities.

Noise can not be reduced. Therefore, to obtain a good measurement, it is necessary to make the electron less sensitive to random fluctuations and more sensitive to the signal.

Increase sensitivity

In the case of measuring time-dependent signals, it is necessary to periodically kick an electron very periodically. In the absence of kicks or any noise, the probability for an electron changes smoothly with time. Noise adds leaps to these changes. It looks as if the wave jumps forward or backward in time imperceptibly to you.

But small jumps we do not need, they will interfere with the signal. Instead, it is necessary to hit an electron with a quantum baseball bat, creating a fairly large jump, able to swap the wave functions of two possible outcomes (this is called π-pulse). If you do so at regular intervals, the effect cancels all changes that occurred during this interval due to noise.

So if there is no signal, and there is only noise, you will not find changes in the probabilities. But if the magnetic field oscillates with a constant frequency (or, more precisely, causes the qubit to oscillate with this frequency), the changes in the wave function will accumulate.

This only works if the signals change over a period equal to the intervals between the kicks. In fact, we have a very narrow filter (people who are interested in electronics could recognize a synchronous amplifier in this description).

Although the filter is narrow enough to be used, it cannot be smoothly changed in frequency, so we cannot scan different frequencies. The problem is technology. In the role of a quantum baseball bat is often a microwave pulse. These pulses must somehow be created, and a good signal generator can update the output signals every nanosecond. This means that the interval between pulses (and the length of each pulse) can be changed only by one nanosecond.

Imagine that you need to measure the frequency and amplitude of an alternating magnetic field. You know that the magnetic field changes with a frequency of about 5 MHz (this means that in 100 ns the field changes from a completely positive to a completely negative value). But you do not know its exact frequency. To find a magnetic field, you increment the pulse interval to cover the entire gap of interest. And find nothing. Why? Because the frequency of changes in the magnetic field lay between the smallest of your possible steps.

The same problem occurs when controlling qubits. In a device with several qubits, each is slightly different and must be controlled with a slightly different set of microwave pulses. And the resolution of our tool does not allow it to optimize well enough.

To get around this, it turns out, you need to treat the electron a little more politely. Instead of constantly using a baseball bat, we gently push the electron. A gentle microwave pulse has an interesting effect of increasing the temporal resolution of the pulses. As a result, we get higher frequency resolution (and better control over qubits).

Rounding the corners of the square

In the on / off pulse, the generator amplitude has only two values. In a continuously increasing and decreasing pulse, the entire amplitude scale of the generator can be used to change the central position of each pulse by an amount much smaller than one nanosecond. In fact, nature calculates the center of the pulse using interpolation, even if its generator does not produce a central value.

As a result, a pulse generator with a 14-bit digital-analog converter and a 1 ns time resolution can change the time passing between the centers of the pulses by 1 picosecond. And this improvement is a thousand times.

Researchers have shown that this works by performing spectroscopy of magnetic fields applied to superconducting loops. Then they applied the same technology to measure the frequency of nuclear magnetic resonance of a single carbon atom ( ¹³ C heavy isotope) in diamond. In both cases, they were able to measure quantities with much higher resolution than it should have been possible with their equipment.

Isn't nature strange?

This achievement is quite amazing. In fact, the researchers took a piece of equipment that can be found in any laboratory, and used it a little differently. The result is what could be done only with the impulse generators of the future.

But although I get results and understand the argument, I still do not fully understand how it works. Nature does not interpolate as we do — at least I don’t think so. An electron or any selected quantum object sends an impulse as it is: a set of discrete voltages increasing and decreasing in fixed steps for fixed periods of time. The center of the impulse cannot be magically discerned by tracing an imaginary line between fixed points.

I think that what is called the “impulse area” (the integral of the impulse, or, literally, the area under the curve) plays the role. The center of the pulse can be defined as the time over which the integral reaches half. In a pulse with a smoothly varying amplitude, small changes in the shape of the pulse can vary, and this half-way value can be achieved in a controlled manner.

But I am not convinced that everything works that way. The key is contained in the area, and, for a rectangular impulse, the area can still change continuously, even if the time steps are rather coarse. You just need to change the amplitude of the "on" value of the rectangular pulse.

But this technology will be useful to many. People studying quantum computing need to be able to control the states of superposition, and this requires just such a technology. And now they should be able to control the quantum states with even greater precision, which means that the stored quantum information will last longer, and more calculations will be possible. In this sense, this technology represents a significant step forward.

And someday I can even understand why it works better than I think it should.