Suppressing errors in quantum computers
Researchers at the National Institute of Standards and Technology (NIST) have demonstrated a technique for efficiently suppressing errors in quantum computersResearchers at the National Institute of Standards and Technology (NIST) have demonstrated a technique for efficiently suppressing errors in quantum computers. The advance could eventually make it much easier to build useful versions of these potentially powerful but highly fragile machines, which theoretically could solve important problems that are intractable using today's computers.
The new error-suppression method, described in the April 23 issue of Nature, was demonstrated using an array of about 1,000 ultra cold beryllium ions (electrically charged atoms) trapped by electric and magnetic fields. Each ion can act as a quantum bit (qubit) for storing information in a quantum computer. These ions form neatly ordered crystals, similar to arrays of qubits being fabricated by other researchers using semiconducting and superconducting circuitry. Arrays like this potentially could be used as multi-bit quantum memories.
Engineer Live spoke with Mike Biercuk, the lead author of the study.
1. As it stands now, what are some issues that potentially contribute to the fragility of today's quantum computers?
Quantum computing utilises the quantum mechanical phenomenon of superposition as a fundamental tool for performing operations in parallel. Unlike classical digital computers, quantum computers represent information in a manner more similar to analogue computers, ie the information representation for a single bit is continuous, instead of only being allowed to take the values 0 or 1. In a 'superposition state', a quantum bit, or qubit, is able to simultaneously represent the values 0 and 1 with any relative weight between the two, and with any arbitrary phase between the two basis states (the phase being similar to the classical phase of an RF or microwave signal). Information is encoded in the exact phase and amplitude relationships present in the superposition state. These relationships and the way they evolve in time are determined, in part, by the characteristics of the physical system, which forms the qubit. These characteristics can be perturbed by environmental factors such as stray electric and magnetic fields. As such, the phase and amplitude relationships - and hence the quantum information - can be disturbed by simple environmental noise. This is a process known asdecoherence, and is fundamental to essentially all quantum information systems. Unfortunately, the very quantum mechanical property, which allows for the potential benefits associated with quantum computers, also opens them up to significant fragility.
2. How do errors arise?
Errors arise due to decoherence as described above (the superposition state becomes disturbed), and by imprecise control operations. The effects of decoherence are often considered to be the more insidious of the two, as even when a qubit is nominally being 'left alone’, quantum information can still be disturbed by coupling to the environment. Further, a process known as dephasing, where the phase relationship in a superposition state is disturbed by environmental coupling, is quite common and serves as a limiting source of errors in many quantum information experiments today.
3. By what means can these errors be avoided? Several general methods exist to avoid errors.
First, when implementing a quantum operation, one wishes to have very precise control - this is generally considered an 'engineering' problem and isn’t fundamental to quantum information (eg precision of D/A converters, timing resolution of a pulse generator, etc). Regarding decoherence, one may physically shield an experiment from its environment using, for example, magnetic shields to mitigate the effects of ambient magnetic field fluctuations. This is common at high-level, but environmental coupling can be extremely localized, and this kind of approach has limited benefits. Next, one may use as a qubit basis special states which have some intrinsic immunity to the dominant source of environmental fluctuations. This may be accomplished using special symmetries in nature, or special configurations of a qubit device which have small coupling to the environment. These strategies are emerging in the field, but the states which have high immunity to environmental fluctuations are often inconvenient to employ as the same weak environmental coupling makes them difficult or slow to control. Finally, a general procedure to mitigate the effects of decoherence is known as dynamical decoupling in which special sequences of control operations may eliminate the effects of environmental coupling. Because of its generality across all qubit types and implementations, we study this final approach.
4. Why is more efficient to correct qubit errors prior to occurring as opposed to after the fact?
The theory of Quantum Error Correction (QEC) is a vitally important tool in quantum information science - it provides a means to reduce qubit error probabilities to arbitrarily low levels such that, in principle, large computations may be performed with negligible probability of hardware errors. (This is similar to the concept of bit-error-rate in a digital processor - with a common value of 10^-23,it is extremely unlikely that a hardware error will occur, even during a lengthy computation). QEC is based on both classical error correction, and the specific quirks of quantum mechanics. Despite its theoretical promise for reducing error rates, it is generally quite resource intensive - many qubits and operations are required toper form the error correction procedure in order to reach a desired error rate. Further, the amount of benefit associated with a QEC procedure depends on how low the single-qubit error rate is to begin with. It turns out that by suppressing the single-qubit error rate as much as possible - for instance, by suppressing decoherence - it is possible to achieve the same final qubit error rate after QEC while using far fewer resources than if the single-qubit error rate were higher. This is very important from a practical perspective because after a while it becomes unreasonable to keep adding more and morequbits into a QEC procedure in order to meet a certain error rate.
5. Can you describe the new NIST pulse method and how it works?
The NIST method, known as dynamical decoupling, is based on many decades of research in the nuclear magnetic resonance (NMR) community. The NMR community often employs so-called ‘spin-echo’ techniques which mitigate effects similar to decoherence in bulk spectroscopy measurements. Chaining many of these spin-echo pulses together allows for the effective lifetime of the spin system to be extended. We start with this concept as applied to quantum bits rather than bulk NMR samples, and make one simple change - instead of using a series of evenly spaced spin-echo pulses, we adjust the relative pulse positions in the sequence such that they are no longer evenly spaced. This simple modification -changing the pulse spacing - allows us to modify the effect of the pulse sequence, and allows us to tailor the effect to a particular kind of noise that may be present in an experimental system. Gotz Uhrig, a scientist at Dortmund in Germany used this concept to develop a novel sequence of spin-echo-like pulses which was designed for a particular noise spectrum (noise with particular frequency characteristics). We were able to experimentally demonstrate that his theoretical concepts were correct, in part by artificially engineering the form of environmental noise in our system. We synthesised noise with different frequency characteristics in order to mimic other qubit technologies (eg qubits based in the solid state vs our trapped atomic ion qubits), and tested the ability of Uhrig's sequence to suppress the effects of decoherence.Then we went a bit further, and developed a technique based on measurement feedback that allowed us to suppress qubit error rates due to decoherence far better than other known sequences. In particular, we were able to develop new sequences which were optimised for a given noise environment, but which did not require us to have any knowledge of the noise characteristics. In these experiments the feedback procedure automatically found the best sequences. Using these new techniques we discovered sequences which are in principle able to suppress qubit error rates many orders of magnitude below the best known existing sequences. Using these procedures should allow error rates in a quantum computer to be suppressed significantly, making subsequent error correction techniques considerably more efficient.
6. Finally, what is the next major hurdle in the development of quantum computers and how far off do you envision functional quantum computers?
Our technique provides a means to suppress qubit errors only in the circumstance that we are nominally doing nothing to our qubit - ie a memory operation. However, one also needs the ability to process quantum information, and to suppress decoherence during the processing steps. In the near term we expect that new developments will allow the incorporation of these dynamical decoupling pulse techniques intoactual computationally relevant operations. We also expect that these types of techniques may be extended to so-called entangled states of multiple qubits in which the quantum states of all particles are linked together. Multi qubit entangled states are of fundamental importance for both quantum computation and the quantum error correction procedures which will likely be used in any quantum computer. Preserving entanglement is a significant future challenge(also due to decoherence effects), and we are hopeful that dynamical decoupling may provide a mechanism to suppress decoherence in entangled states as well as individual qubits (as in our experiments).To date, the largest experimental quantum computers consist of only a few qubits. Scaling up will take major advances in quantum control, device engineering, classical electrical engineering, and our understanding of how to mitigate qubit errors. Realising a functional quantum computer will not take long (they're already pretty much there). However, we need to recall that we're competing against very complex and ever-improving classical computers. Realising a functional and USEFUL quantum computer with at least a hundred independently controllable bits (useful for so-called ‘quantum simulations’) may take more than a decade. Building a large-scale machine capable of implementing Shor's factoring algorithm on a large, cryptographically relevant number could take twenty to 30 years or more.
