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## Structured Quantum Devices

Quantum computers are designed to utilise quantum effects to achieve a (significant) computational advantage over conventional computers for important real world problems. Several small-scale quantum computing prototypes, employing a range of qubit technologies, are currently in development in laboratories worldwide. We research the development of algorithms for existing quantum computers, as well as the theoretical study of protocols to make future devices more robust and scalable. Our research covers continuous-time quantum information processing devices, such as the devices manufactured by D-Wave Systems Inc. and NTT, as well as digital circuit-model architectures such as those in development by NQIT, IBM, Google and Rigetti.

### Continuous-time quantum computing

Continuous-time quantum computing uses a continuous-time Hamiltonian evolution applied to qubits (or qudits) with, optionally, open quantum systems effects in the form of a low temperature bath or other forms of cooling. Adiabatic quantum computing, quantum annealing and computation by continuous-time quantum walk all fit into this model.

In particular we have recently demonstrated how interpolating between adiabatic and quantum walk protocols can still gain a quantum advantage when searching. The problem is encoded in the ground state of a Hamiltonian engineered from the natural interactions between the qubits. This type of hardware is also suitable for special purpose quantum simulators. We study these systems numerically, to understand how they work, optimise algorithms for specific hardware characteristics, and expand the range of problems that can be solved by such hardware.

#### Selected Continuous Time Quantum Computing Publications and Pre-Prints:

Morley, J. G. Chancellor, N. Bose, S. Kendon, V. Quantum search with hybrid adiabatic-quantum walk algorithms and realistic noise

### Digital quantum computing & quantum error correction

Classical bits are realised as semiconductor transistors, where the on/off states are differentiated by billions of electrons. In contrast, qubits are typically realised as single quantum systems, and as such are much more susceptible to error. Consequently, digitial circuit-model quantum computers must be made fault tolerant througth the incorporation of quantum error correction codes.

We are working on developing a class of quantum error correction codes which we term the Coherent Parity Check (CPC) framework. This framework is built around the gate operations used to actually construct a code, rather than abstract vector spaces. The design of these codes is greatly aided by the used of catagorical quantum mechanics, in particular the zx calculus. We have further studied how these methods can be used to optimise error correction codes on real devices via automated design techniques (Python and Octave programs to generate new CPC codes are available here). The CPC framework also facilitates development of error correction protocols based on the native interactions within a quantum device, rather than derived gates such as controlled-not (CNOT) operations. Our primary focus is on practical error correction for the types of small quantum processors currently in development.

#### Selected Quantum error correction publications and preprints

Roffe, J. Headley, D. Chancellor, N. Horsman, D. Kendon, V. Protecting quantum memories using coherent parity check codes
Chancellor, N. Kissinger, A. Roffe, J. Zohren, S. Horsman, D. Coherent Parity Check Construction for Quantum Error Correction (programs for making new CPC codes)

### Hybrid Quantum Annealing

We look at how to integrate already known information into quantum annealing protocols, such as those performed on the D-Wave devices. D-Wave have already developed a reverse annealing' feature along these lines (partially inspired by our work), which allows annealing around an initial guess' input state. We are looking into how to test this feature, build more sophisticated algorithms based on annealing subroutines, and take advantage of other classical controls, including how to include uncertaintly information along with a solution candidate. We are interested in how these methods can be expanded beyond quantum annealing to other continuous (and discrete) time computing techniques. One tool which we have developed to study algorithm design is the graphical inference primitive formalism, an example of which appears below:

#### Selected Hybrid Quantum Annealing Publications and Pre-prints:

Chancellor, N. Modernizing Quantum Annealing

### Quantum Annealing Experiments

Durham researchers have recently been given access to D-Wave devices for two experimentally driven projects. The first of which is to test the performance of the recently added reverse annealing feature on D-Wave devices, and is funded throught the Oxford NQIT quantum technologies hub. The example below shows some experimental results with an engieered energy landscape. For values of the parameter s' close to 1, the sytem is unable to search the solution space at all, while for intermediate values it searches locally and successfully finds the true solution to the problem with a high probability. Finally, for small s', the device gets trapped in a false minimum, which has been engineered to fool traditional quantum annealing in most cases:

Additionally, there is a project in collaboration with Simon Benjamin at Oxford funded by an industrial sponsor to explore how annealers may provide more robust solutions to optimization problems.

### Funding

Viv Kendon is funded by EPSRC grant ref: EP/L022303/1.

Nicholas Chancellor is funded by grant ref: EP/S00114X/1

Joschka Roffe is funded by a Durham Doctoral Studentship.