Quantum Gates and trapped-ion Quantum Computers

Quantum logic gates are one of the essential parts of a quantum computer and are the building blocks of all quantum algorithms.

Traditional logic gates

Traditional computers use electrical signals that represent binary 1's and 0's, or bits. Logic gates are the fundamental operations that allow these bits to change between 0 and 1, and a range of examples exists such as ‘AND’, ‘OR’ and ‘NOT’.

For example, a NOT gate changes a bit from a 0 to a 1 (or vice versa). AND and OR gates are two-bit gates that take two bits as inputs and output a single bit, depending on the inputs.

A surprising fact is that all possible processes, from simple addition on a calculator to browsing Facebook, can be constructed from a small set of these gates called a ‘universal gate set’.

This is what allows your computer to carry out such a wide range of seemingly very different tasks. A set consisting of AND, OR and NOT is an example of such a universal gate set.

This is what allows your computer to carry out such a wide range of seemingly very different tasks. A set consisting of AND, OR and NOT is an example of such a universal gate set.

Quantum logic gates

Quantum computers operate using qubits, not bits. Unlike traditional bits which can only be 0 or 1, a qubit can exist in a ‘superposition’ of 0 and 1. This ability to exist in multiple states at once gives quantum computers tremendous power.

But a qubit is useless unless you can use it to carry out a quantum calculation. And these quantum calculations are achieved by performing a series of fundamental operations, known as quantum logic gates.

There are lots of types of quantum gates. There are single-qubit gates, which can flip a qubit from 0 to 1 as well as allowing superposition states to be created.

Then there are also two-qubit gates. These allow the qubits to interact with each other and can be used to create quantum entanglement: a state of two or more qubits that are correlated in a way that can’t be explained by classical physics.

You may have heard of entanglement. It can lead to counterintuitive quantum phenomena. An example of a gate is the controlled-NOT (CNOT) gate. It’s a two-qubit operation where the first qubit is labelled the control qubit and the second one is the target qubit. If the control qubit is |1> then it will flip the target’s qubit state from |0> to |1>or vice versa.

(Note: the | and > used in the notation are just to remind us that we’re talking about vectors that represent the qubit states labelled 0 and 1.

Similar to traditional computers, quantum algorithms with many qubits can be broken down into a sequence of single and two-qubit quantum gates, forming a universal quantum gate set.

Therefore, if we can get these quantum gates to work in a reliable way that scales to many qubits, we can use them to run all possible algorithms on our quantum computer.

Quantum gates in trapped ions

Trapped ions (charged atoms) are one of the leading platforms for quantum computing.

Each ion can store a single qubit, which is encoded in two atomic states related to a uniquely quantum property of the particles making up the ion (electrons, protons and neutrons) called ‘spin’. These spin states are well isolated from the outside world, protecting them from any noise that could destroy the fragile qubit states.

So how do we implement the required quantum logic gates on these trapped-ion qubits?

For single-qubit gates, it’s actually quite straightforward: we apply a short pulse of microwave radiation. If the frequency of the microwave exactly matches the resonant frequency of the qubit, it will cause the qubit state to flip. We can also create superposition states in the same way by adjusting how long the pulse lasts.

For the two-qubit gate, things are not so easy, since the spin states used to store the qubits don’t naturally interact with one another. The ions themselves do interact, however — they repel each other due to both having a positive electric charge, in a similar way to the repulsion between two bar magnets with their north poles facing each other.

We can use this repulsion to engineer an artificial interaction between the qubits. This can be achieved in a few different ways, including using high-power lasers or using specially shaped magnetic fields combined with microwave pulses.

Techniques to improve quantum gates

As you’ve hopefully gathered from the previous sections, quantum gates are an essential part of quantum computers. Therefore, as we scale up to millions of qubits, it’s crucial that they work extremely reliably.

The reliability of quantum gates can be improved using so-called ‘quantum control methods’, which modify the microwave pulses to make the interaction more protected from noise in the environment. One of the methods is to unite a number of quantum control methods under a single framework, allowing their effect against different noise sources commonly encountered in the lab to be directly compared.

Towards larger trapped-ion quantum computers: Quantum Charged Coupled Device (QCCD)

A QCCD system is composed of a set of traps, each holding a small number of ions, instead of a single large trap.

Similar to single-trap architectures, gates can be performed on one or more ions that are co-located within a trap. To enable entanglement across traps, QCCD uses ion shuttling to communicate ions across the system. That is, when a two-qubit operation is to be performed on a pair of ions which are in different traps, one of the ions is physically moved to the other trap, co-locating the ions before the gate is executed. Over the last two decades, all operations required for building these systems have been developed and honed.

Architecting the next generation of QCCD systems

To build the next generation of QCCD systems with 50 to 100 qubits, hardware designers have to tackle a variety of conflicting design choices. How many ions should we place in each trap? What communication topologies work well for near-term QC applications? What are the best methods for implementing gates and shuttling operations in hardware? These are key design questions that our work seeks to answer. Although individual experiments have been performed to understand some of these choices, there are no studies on the impact of these choices on applications and their overall system-level performance and reliability tradeoffs. Furthermore, hardware designers have to contend with unreliable gates and other limitations of near-term systems and still support an evolving mix of quantum applications.

To study these design choices efficiently, a design tool flow which estimates the reliability, execution time and other metrics for a set of quantum programs on a specified QCCD device. This tool flow consists of two parts. The first part is a compiler which maps the program down to the primitive operations that will be available on QCCD systems. Since shuttling is error-prone and time-consuming, the compiler seeks to improve the overall application reliability and performance by minimizing the total amount of shuttling. The second part is a QCCD simulator which uses realistic performance and noise models for QCCD systems, derived from hardware characterization works, to estimate the quality of an application execution.

Tuning the architectural attributes of the system such as the number of ions in a trap and topology can impact the reliability of application executions by as much as three orders of magnitude. Optimizing the low-level gate implementations and shuttling methods can further improve the reliability by another order of magnitude.

Computer architecture and simulation-based design have been a key enabler of technology progress in classical computing. By leveraging these techniques for QC design and adopting a full system-view of the design space, rather than focusing on hardware alone, this study seeks to accelerate the progress towards the next major milestone of 50 to100 qubits. Currently the two most promising ideas for scaling to 1000s of ions are large QCCD systems and photonic interconnects between small QCCD systems. The architectural study of near-term QCCD devices has the potential to guide QC hardware design for both future directions.