The quantum computer race has been hot for a few years now, with drug discovery, materials science, optimization, machine learning, and cryptography being just a few of the areas that will be revolutionized by its advancements.
But despite all the progress, building quantum computers that solve real-world problems has been held back by three big challenges:
- Fragile quantum states
- Scaling up while maintaining control
- Preserving coherence
Now, a team at Chalmers University of Technology in Sweden has taken a significant step in addressing these challenges and accelerating the development of practical quantum computers. They recently published a new method in the journal Nature for manipulating quantum information using tunable nonlinearity in superconducting circuits. This allows for complex operations on multi-dimensional quantum states to be performed faster and more accurately than ever before.
Building Practical Quantum Computers
At the heart of quantum computing is the quantum bit, or qubit, the fundamental unit of quantum information. Unlike classical bits, which are either 0 or 1, qubits can be both 0 and 1 and everything in between. Qubits can also be entangled with each other, allowing quantum computers to perform some calculations much faster than classical computers.
However, reaching this capability has been a significant challenge. One of the biggest issues is the fragility of quantum states. Qubits are sensitive to their environment and quickly lose their quantum properties through decoherence, introducing errors into the quantum computation and limiting the depth of computations.
Another major problem is scaling. As more qubits are added to a quantum processor, it becomes harder to control the interactions between them and to implement the quantum gates. This is because the control systems and cross-talk between qubits become more complex.
And there’s a trade-off between coherence and controllability. Techniques that make qubits more coherent, like error correction codes, require more resources and limit some operations. Systems that have more control over individual qubits, like trapped ions or superconducting circuits, are noisier and more prone to decoherence.
“Think of a qubit as a blue lamp that, quantum mechanically, can be both switched on and off simultaneously. In contrast, a continuous variable quantum system is like an infinite rainbow, offering a seamless gradient of colors. This illustrates its ability to access a vast number of states, providing far richer possibilities than the qubit”s two states.”
– Axel Eriksson, researcher in quantum technology at Chalmers University of Technology and lead author of the study
Click here to learn about the current state of quantum computing.
Tunable Nonlinearities in Superconducting Circuits
The Chalmers University team, led by Drs. Axel M. Eriksson and Simone Gasparinetti have solved these problems by using superconducting circuits. They’ve developed a special component called a Superconducting Nonlinear Asymmetric Inductive eLement (SNAIL) resonator.
SNAILs are superconducting circuit elements with strong, tunable nonlinearity. It’s a superconducting loop with Josephson junctions, thin insulating barriers that allow Cooper pairs (bound pairs of electrons) to tunnel through. By arranging the junctions asymmetrically, they’ve made a circuit element with nonlinear inductance.
“We have made a system that does complex operations on a multi-state quantum system faster than ever before.”
– Senior author Dr. Simone Gasparinetti, leader of the 202Q-lab at Chalmers University
The key thing the Chalmers team did was to put a SNAIL resonator inside a superconducting microwave cavity, which is a bosonic mode for encoding quantum information. They applied microwave pulses to this hybrid system and activated and deactivated the nonlinearity in the SNAIL to perform all sorts of quantum operations fast and accurately.
Continuous-Variable Quantum Computing
One of the unique things about the Chalmers team’s approach is that it goes beyond the qubit paradigm and uses continuous-variable (CV) quantum states.
In a CV quantum system, information is encoded in the amplitude and phase quadratures of a harmonic oscillator, like a microwave cavity field. Those quadratures can take on a continuous range of values, not just 0 and 1 like qubits.
According to senior author Dr. Simone Gasparinetti, leader of the 202Q-lab at Chalmers University:
“We have created a system that enables extremely complex operations on a multi-state quantum system, at an unprecedented speed.”
The CV approach has advantages over discrete-variable quantum computing.
(i) One, a single CV mode can encode multiple qubits’ worth of information, which means less hardware for fault-tolerant quantum computing.
(ii) Two, the consciousness of CV states allows for better error correction codes, which are needed for quantum computing with noise and decoherence.
However, a big problem in CV quantum computing is non-Gaussian operations, which are needed for universal quantum computing. Gaussian operations like displacement and squeezing of the oscillator state can be done with linear optical elements or microwave circuits, but that’s not enough for quantum speedup because it can be classically simulated.
Non-Gaussian operations require nonlinear interactions, which are much harder to make and control. Previous attempts to combine CV modes with nonlinear elements have been foiled by the Kerr effect, which messes up the quantum information and reduces the operation fidelity.
The Chalmers team has solved this by engineering the nonlinearity inside the SNAIL resonator. They operate the SNAIL at a so-called “Kerr-free” point, where the unwanted Kerr nonlinearity is suppressed, and the third-order nonlinearity that’s needed for non-Gaussian operations is preserved.
“Our community has often tried to keep superconducting elements away from quantum oscillators, not to scramble the fragile quantum states. In this work, we have challenged this paradigm. By embedding a controlling device at the heart of the oscillator we were able to avoid scrambling the many quantum states while at the same time being able to control and manipulate them. As a result, we demonstrated a novel set of gate operations performed at very high speed.”
– Simone Gasparinetti
A Universal Gate Set
To show what they can do, they’ve made a universal gate set on their SNAIL-resonator platform. That includes Gaussian gates like displacement and squeezing and a cubic phase gate, which is non-Gaussian.
The Gaussian gates were made by applying microwave pulses at specific frequencies to the SNAIL circuit. Driving at the fundamental frequency gives displacement, and driving at twice the fundamental frequency gives squeezing. That’s for preparing and manipulating coherent and squeezed states, which are the blocks for CV quantum information processing.
The cubic phase gate was made by combining a “trisqueezing” interaction (driving at three times the fundamental frequency) with drives at lower frequencies. That applies a nonlinear phase shift to the oscillator state that’s proportional to the cube of the amplitude, hence the name “cubic phase.”
The cubic phase gate is needed for universal CV quantum computing because it makes highly non-classical states like Gottesman-Kitaev-Preskill (GKP) states, which are for fault-tolerant quantum error correction. The cubic phase gate with Gaussian gates makes a deterministic non-Gaussian state called the “cubic phase state.”
The gates made by the Chalmers team were made with pulses as short as tens of nanoseconds. That’s 10-100 times faster than previous implementations with dispersive qubit-oscillator couplings. That’s because of the strong nonlinearity in the SNAIL resonator.
Deterministic Cubic Phase State Preparation
Another example is the Chalmers team using their universal gate set to make a highly non-classical quantum state called a cubic phase state. Cubic phase states are needed for quantum error correction, quantum metrology, and CV measurement-based quantum computing.
Cubic phase state preparation was made by applying gates to the ground state (vacuum) of the SNAIL resonator. First, a 20-ns squeezing gate was applied to make a squeezed vacuum state. Then, a 40-ns cubic phase gate was applied to that squeezed state, and voilà, a cubic phase state with a cubicity of 0.11.
The state was characterized with Wigner tomography, which makes a phase-space distribution of the quantum state. The Wigner function was strongly negative, which is non-classical and cannot be seen in any classical oscillator state.
The fidelity of the cubic phase state with respect to the target state was 92%. They showed that the cubicity of the state can be increased by just extending the cubic phase gate duration. That’s much better than previous state preparation methods, which required a full re-optimization of the control sequence for each cubicity value.
Room for Improvement and Future Work
While what the Chalmers team has done is already commendable, there’s still more to be done:
SNAIL Resonator
One limitation of the quantum operations is the coherence time of the SNAIL resonator. They have coherence times of a few microseconds, which is enough for now, but longer coherence times will allow for more complex and deeper quantum circuits. Optimizing the SNAIL circuit parameters to reduce flux noise and shielding and filtering the microwave environment are ways to improve coherence.
This includes:
- Coherence time of the SNAIL resonator (a few microseconds is enough for now, but longer will allow for more complex circuits)
- Optimizing SNAIL circuit parameters to reduce flux noise
- Shielding and filtering the microwave environment
Click here to learn how quantum emitters and infrared lasers can help us build the next generation of quantum computers.
Scalability
Another area to improve is scalability. The experiment was done with one SNAIL, but a large-scale quantum computer needs multiple SNAILs. To scale up, one could use multiple SNAILs, each connected to its own microwave cavity. This setup allows for the creation of multi-qubit gates and entangled states by designing the coupling between the cavities. However, that requires control over the fabrication and tuning of the SNAILs to be homogeneous and reproducible.
- Scalability (one SNAIL now, but a large-scale quantum computer needs multiple)
- An array of SNAILs, each with its own microwave cavity
- Multi-qubit gates and entangled states across the array by coupling between cavities
- Control over fabrication and tuning of SNAILs to be homogeneous and reproducible
Besides scaling up the number of CV modes, we also need to scale up the number of photons in each mode. The SNAIL resonator’s nonlinearity deviates from its ideal behavior at higher photon numbers, which limits the size of the computational Hilbert space.
One way to fix that is to use a multi-SNAIL design in which the nonlinearity of each SNAIL is engineered to cancel out at higher orders while preserving the lower-order interactions.
Other plausible advancements include:
- More CV modes
- More photons in each mode
- Nonlinearity in the SNAIL resonator makes it deviate from ideal behavior at higher photon numbers
- Limits size of computational Hilbert space
- Multi-SNAIL design: nonlinearity of each SNAIL cancels out at higher orders while preserving lower-order interactions
Looking ahead, the Chalmers team wants to integrate their SNAIL-resonator platform with other quantum computing architectures to make hybrid systems. For example, SNAIL-mediated interactions can be used to entangle superconducting qubits and CV modes to make complex multi-qubit states. The fast and efficient CV gates in this work can be used for quantum error correction on encoded qubits, and that will make more robust and scalable quantum processors.
One exciting prospect to look forward to is integrating the SNAIL-resonator platform with optical quantum systems. Superconducting circuits are good for quantum computing, which operate at microwave frequencies and cryogenic temperatures, are good for quantum computing. In contrast, optical quantum systems, which function at room temperature, are ideal for long-distance quantum communication. By developing a quantum frequency converter, we can combine the best of both worlds to create a scalable and networked quantum computer.
Wrap Up
What the Chalmers team has achieved is a major advancement for practical quantum computers. They’ve used tunable nonlinearity in superconducting circuits to develop a hardware-efficient and controllable quantum computer capable of rapidly and accurately performing complex operations on multidimensional quantum states.
This represents a new paradigm in CV-NISQ computing. SNAIL resonators can solve hard problems in quantum chemistry, optimization, and machine learning. As this technology matures and scales, it will open up applications that are not possible with classical computers.
However, building large-scale, fault-tolerant quantum computers still presents substantial challenges, including the coherence time of superconducting circuits, the number of qubits and CV modes, and interfaces between quantum computing platforms.
Despite these challenges, quantum computing as an applied science has come a long way, and the Chalmers team has played an instrumental role in pushing its barriers. They’ve added to the quantum computing toolbox and shown us new ways to use quantum mechanics. Now, we’re one step closer to accessible quantum computing.
As theory and experiments move faster, the future of quantum computing has never looked better. Quantum computers will deliver exponential speedups for a wide range of computational tasks in fields such as drug discovery, materials design, cryptography, and artificial intelligence. Coupled with advances in technologies like AI, these developments assure us that the world is on the brink of transformative changes that are hard to fully envision.
Click here for a list of the five best quantum computing companies.