On the Qubit Routing Problem

We introduce a new architecture-agnostic methodology for mapping abstract quantum circuits to realistic quantum computing devices with restricted qubit connectivity, as implemented by Cambridge Quantum Computing\u27s t|ket> compiler. We present empirical results showing the effectiveness of this method in terms of reducing two-qubit gate depth and two-qubit gate count, compared to other implementations

Improving Qubit Routing by Using Entanglement Mediated Remote Gates

Near-term quantum computers often have connectivity constraints, i.e. restrictions, on which pairs of qubits in the device can interact. Optimally mapping a quantum circuit to a hardware topology under these constraints is a difficult task. While numerous approaches have been proposed to optimize qubit routing, the resulting gate count and depth overheads of the compiled circuits remain high due to the short-range coupling of qubits in near-term devices. Resource states, such as Bell or Einstein-Podolsky-Rosen (EPR) pairs, can be used to mediate operations that facilitate long-range interactions between qubits. In this work, we studied some of the practical trade-offs involved in using resource states for qubit routing. We developed a method that leverages an existing state-of-the-art compiler to optimize the routing of circuits with both standard gates and EPR mediated remote controlled-NOT gates. This was then used to compile different benchmark circuits for a square grid topology, where a fraction of the qubits are used to store EPR pairs. We demonstrate that EPR-mediated operations can substantially reduce the total number of gates and depths of compiled circuits when used with an appropriate optimizing compiler. This advantage scales differently for different types of circuits, but nonetheless grows with the size of the architecture. Our results highlight the relevance of developing efficient compilation tools that can integrate EPR-mediated operations

SZX-Calculus: Scalable Graphical Quantum Reasoning

We introduce the Scalable ZX-calculus (SZX-calculus for short), a formal and compact graphical language for the design and verification of quantum computations. The SZX-calculus is an extension of the ZX-calculus, a powerful framework that captures graphically the fundamental properties of quantum mechanics through its complete set of rewrite rules. The ZX-calculus is, however, a low level language, with each wire representing a single qubit. This limits its ability to handle large and elaborate quantum evolutions. We extend the ZX-calculus to registers of qubits and allow compact representation of sub-diagrams via binary matrices. We show soundness and completeness of the SZX-calculus and provide two examples of applications, for graph states and error correcting codes

Global Synthesis of CNOT Circuits with Holes

A common approach to quantum circuit transformation is to use the properties of a specific gate set to create an efficient representation of a given circuit's unitary, such as a parity matrix or stabiliser tableau, and then resynthesise an improved circuit, e.g. with fewer gates or respecting connectivity constraints. Since these methods rely on a restricted gate set, generalisation to arbitrary circuits usually involves slicing the circuit into pieces that can be resynthesised and working with these separately. The choices made about what gates should go into each slice can have a major effect on the performance of the resynthesis. In this paper we propose an alternative approach to generalising these resynthesis algorithms to general quantum circuits. Instead of cutting the circuit into slices, we "cut out" the gates we can't resynthesise leaving holes in our quantum circuit. The result is a second-order process called a quantum comb, which can be resynthesised directly. We apply this idea to the RowCol algorithm, which resynthesises CNOT circuits for topologically constrained hardware, explaining how we were able to extend it to work for quantum combs. We then compare the generalisation of RowCol using our method to the naive "slice and build" method empirically on a variety of circuit sizes and hardware topologies. Finally, we outline how quantum combs could be used to help generalise other resynthesis algorithms.Comment: In Proceedings QPL 2023, arXiv:2308.1548

Cnot circuit extraction for topologically-constrained quantum memories

Funding Information: We gratefully acknowledge support from the Unitary Fund (http://unitary.fund) for this work. We would also like to thank Will Zeng, Ross Duncan, and John van de Wetering for fruitful discussions about circuit mapping for NISQ as well as the authors of [22] for clarifying some points about their approach. Publisher Copyright: © Rinton Press.Many physical implementations of quantum computers impose stringent memory constraints in which 2-qubit operations can only be performed between qubits which are nearest neighbours in a lattice or graph structure. Hence, before a computation can be run on such a device, it must be mapped onto the physical architecture. That is, logical qubits must be assigned physical locations in the quantum memory, and the circuit must be replaced by an equivalent one containing only operations between nearest neighbours. In this paper, we give a new technique for quantum circuit mapping (a.k.a. routing), based on Gaussian elimination constrained to certain optimal spanning trees called Steiner trees. We give a reference implementation of the technique for CNOT circuits and show that it significantly out-performs general-purpose routines on CNOT circuits. We then comment on how the technique can be extended straightforwardly to the synthesis of CNOT+Rz circuits and as a modification to a recently-proposed circuit simplification/extraction procedure for generic circuits based on the ZX-calculus.Peer reviewe

Cnot circuit extraction for topologically-constrained quantum memories

Funding Information: We gratefully acknowledge support from the Unitary Fund (http://unitary.fund) for this work. We would also like to thank Will Zeng, Ross Duncan, and John van de Wetering for fruitful discussions about circuit mapping for NISQ as well as the authors of [22] for clarifying some points about their approach. Publisher Copyright: © Rinton Press.Many physical implementations of quantum computers impose stringent memory constraints in which 2-qubit operations can only be performed between qubits which are nearest neighbours in a lattice or graph structure. Hence, before a computation can be run on such a device, it must be mapped onto the physical architecture. That is, logical qubits must be assigned physical locations in the quantum memory, and the circuit must be replaced by an equivalent one containing only operations between nearest neighbours. In this paper, we give a new technique for quantum circuit mapping (a.k.a. routing), based on Gaussian elimination constrained to certain optimal spanning trees called Steiner trees. We give a reference implementation of the technique for CNOT circuits and show that it significantly out-performs general-purpose routines on CNOT circuits. We then comment on how the technique can be extended straightforwardly to the synthesis of CNOT+Rz circuits and as a modification to a recently-proposed circuit simplification/extraction procedure for generic circuits based on the ZX-calculus.Peer reviewe

Peptide Binding Classification on Quantum Computers

We conduct an extensive study on using near-term quantum computers for a task in the domain of computational biology. By constructing quantum models based on parameterised quantum circuits we perform sequence classification on a task relevant to the design of therapeutic proteins, and find competitive performance with classical baselines of similar scale. To study the effect of noise, we run some of the best-performing quantum models with favourable resource requirements on emulators of state-of-the-art noisy quantum processors. We then apply error mitigation methods to improve the signal. We further execute these quantum models on the Quantinuum H1-1 trapped-ion quantum processor and observe very close agreement with noiseless exact simulation. Finally, we perform feature attribution methods and find that the quantum models indeed identify sensible relationships, at least as well as the classical baselines. This work constitutes the first proof-of-concept application of near-term quantum computing to a task critical to the design of therapeutic proteins, opening the route toward larger-scale applications in this and related fields, in line with the hardware development roadmaps of near-term quantum technologies