Towards a generic compilation approach for quantum circuits through resynthesis

In this paper, we propose a generic quantum circuit resynthesis approach for compilation. We use an intermediate representation consisting of Paulistrings over {Z, I} and {X, I} called a ``mixed ZX-phase polynomial``. From this universal representation, we generate a completely new circuit such that all multi-qubit gates (CNOTs) are satisfying a given quantum architecture. Moreover, we attempt to minimize the amount of generated gates. The proposed algorithms generate fewer CNOTs than similar previous methods on different connectivity graphs ranging from 5-20 qubits. In most cases, the CNOT counts are also lower than Qiskit's. For large circuits, containing >= 100 Paulistrings, our proposed algorithms even generate fewer CNOTs than the TKET compiler. Additionally, we give insight into the trade-off between compilation time and final CNOT count.Comment: 10 pages including references. 2 tables, 1 figur

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

QuantMark: A Benchmarking API for VQE Algorithms

Thanks to the rise of quantum computers, many variations of the variational quantum eigensolver (VQE) have been proposed in recent times. This is a promising development for real quantum algorithms, as the VQE is a promising algorithm that runs on current quantum hardware. However, the popular method of comparing your algorithm versus a classical baseline in a small basis set is not meaningful in the big picture. Moreover, many papers use a different molecular representation or a different quantum computer to test their algorithms such that the used baselines are different between different papers. Thus, it is almost impossible to compare the different algorithms to each other. As a solution, we have built a benchmarking framework to standardize the VQE performance metrics, such that they can be analyzed more easily. Using our framework, any researcher working on the VQE can easily test their own algorithms against previous ones on the leaderboard without the need to reproduce previous work themselves.Peer reviewe

Kvanttiohjelmien kääntämisen kehittäminen NISQ-aikakaudella

Recent advances in the development of quantum technology have made it possible to run small quantum programs on real quantum computers. This has created a need for compiling methods specific to these quantum computers. Unlike classical computers, if a quantum computation takes too long, the qubits might decohere and lose their information, making the computation useless. Hence, well-optimized quantum programs are a necessity. Like classical computers, quantum computers have registers for qubits that are generally sparsely connected. However, classical compilation methods that rely on copying data from one register to another do not apply to quantum computers because qubits cannot be copied. This problem is called the qubit routing problem. Following classical compilation, one could solve the connectivity constraints by moving the qubits to adjacent qubit registers. However, this requires the addition of SWAP gates throughout the quantum circuit, resulting in a strictly longer program. Additionally, a SWAP gate on qubits is not cheap and requires three CNOT gates each. Instead, in this thesis, we have defined a new method for quantum compilation that is based in the quantum nature of the program to be compiled. Instead of routing the qubits directly, we generate new machine code (in the form of quantum circuits) from an intermediate representation. We call this process quantum circuit synthesis. During synthesis, we make sure that all generated gates are supported by the target quantum hardware. Additionally, if the synthesis process is optimal, the resulting quantum circuit will also be optimal, although the methods proposed in this thesis are all heuristic in nature due to the computational complexity of optimal architecture-aware synthesis. We construct the nested intermediate representation starting from sequences of CNOT circuits interleaved with single qubit gates and incrementally generalize the intermediate representation to a universal representation. In particular, we propose two algorithms for synthesizing CNOT circuits from their parity matrix representation and one algorithm for synthesizing phase polynomials (i.e. CNOT+$R_z$ circuits). Additionally, we show that when combining these methods into the universal representation called Mixed ZX-phase polynomial, it is competitive with existing commercial quantum compilers IBM's Qiskit and Quantinuum's TKET for large circuits. This thesis additionally contains a proposal for a framework to benchmark the quality of circuits used in an algorithm called Variational Quantum Eigensolver (VQE). This framework attempts to measure how close the solution found by the VQE is to our best estimate of a real molecule (i.e. accuracy), rather than a classical simulation of the approximate molecule as given to the quantum computer (i.e. precision).Nykyään ensimmäiset kvanttitietokoneet ovat tutkijoiden ja harrastajien käytössä. Nykyiset kvanttitietokoneet ovat toistaiseksi rajoitettuja. Niissä on rajallinen määrä kvanttibittejä (kubitteja) tiedon tallentamiseen, ja näillä kubiteilla suoritetut laskutoimitukset voivat sisältää virheitä. Virheitä ei voida suoraan korjata, sillä kubitteja ei ole mahdollista lukea muuttamatta niiden tilaa. On olemassa tapoja kvanttitietokoneissa esiintyvien virheiden korjaamista varten mutta niiden toteuttaminen vaatii huomattavasti nykyistä enemmän kubitteja. Näistä syistä nykyistä aikakautta kutsutaan Noisy Intermediate-Scale Quantum (NISQ) aikakaudeksi. Tässä väitöskirjassa käsittelemme kvanttilaskennassa olevia haasteita NISQ-aikakaudella. Työn painopiste on kvanttiohjelmien kääntämisessä, jotta ne ovat ajettavissa nykyisillä NISQ-kvanttietokoneilla. NISQ-laitteiden korkean virheellisyyden vuoksi kvanttiohjelmien tulee olla huolellisesti optimoituja, jotta ylimääräisiä operaatioita ei tarvitse suorittaa. Lisäksi meidän tulee huomioida kubittien väliset kytkennät kvanttitietokoneissa. Esimerkiksi suprajohtavissa kvanttitietokoneissa jokainen kubitti on yhteydessä vain rajalliseen määrään kubitteja. Tästä syystä kvanttiohjelmat täytyy säätää niin että kubittien väliset suoritukset sopivat yhteen kubittien välisten yhteyksien kanssa. Tätä kubittien välisiin yhteyksiin liittyvää haastetta kutsutaan kubittien reititys -ongelmaksi. Nimi juontaa juurensa ongelman ratkaisusta, jossa kubitteja siirretään eli reititetään rekistereiden välillä. Tässä väitöskirjassa esitetään uusi strategia ongelman ratkaisuksi: ohjelman operaatioita muutetaan sen laskennallinen toiminnallisuus säilyttäen. Ratkaisussa ongelmaa lähestytään uudella ajatusmallilla, jossa kubittien sijoittelun sijaan kvanttioperaatioiden itsessään katsotaan olevan sopimattomia. Näin voimme luoda kvanttiohjelman uudelleen ottaen huomioon kvanttietokoneiden vaatimukset. Tätä kutsutaan kvanttiohjelmien kääntämiseksi. Kvanttiohjelmien kääntämisen vaikeus on siinä, että meidän tulee tietää riittävästi ohjelman toiminnoista, jotta voimme muotoilla sen uudelleen mutta samalla varmistua, että emme aja sitä. Muussa tapauksessa voisimme yksinkertaisesti ajaa kvanttiohjelman klassisella tietokoneella, mikä on yleensä liian vaativaa sille. Esitämme kvanttiohjelman sarjana laskennallisia välivaiheita, joista uusi ohjelma generoidaan. Olemme kehittäneet kokonaisuuden algoritmeja, joiden avulla näistä välivaiheista saadaan luotuun kvanttiohjelmia, joiden toiminnot ovat välittömästi tuettuja kvanttitietokoneella. Osoitamme, että tällä tavalla saadaan aikaiseksi lyhyempiä kvanttialgoritmeja, joita voidaan hyödyntää kvanttitietokoneilla jo lähitulevaisuudessa. Lisäksi, nämä algoritmit on toteutettu osana Quantinuum kvanttilaskentayrityksen TKET-ohjelmistoa (osana väitöskirjaa) sekä IBM:n Qiskit ympäristöä (itsenäisesti)

Dynamic qubit allocation and routing for constrained topologies by CNOT circuit re-synthesis

Many quantum computers have constraints regarding which two-qubit operations are locally allowed. To run a quantum circuit under those constraints, qubits need to be allocated to different quantum registers, and multi-qubit gates need to be routed accordingly. Recent developments have shown that Steiner-tree based compiling strategies provide a competitive tool to route CNOT gates. However, these algorithms require the qubit allocation to be decided before routing. Moreover, the allocation is fixed throughout the computation, i.e. the logical qubit will not move to a different qubit register. This is inefficient with respect to the CNOT count of the resulting circuit. In this paper, we propose the algorithm PermRowCol for routing CNOTs in a quantum circuit. It dynamically reallocates logical qubits during the computation, and thus results in fewer output CNOTs than the algorithms Steiner-Gauss[11] and RowCol [23]. Here we focus on circuits over CNOT only, but this method could be generalized to a routing and allocation strategy on Clifford+T circuits by slicing the quantum circuit into subcircuits composed of CNOTs and single-qubit gates. Additionally, PermRowCol can be used in place of Steiner-Gauss in the synthesis of phase polynomials as well as the extraction of quantum circuits from ZX-diagrams.Comment: 12+3 pages, 8+2 figures (second number refers to the appendix

From Bit-Parallelism to Quantum String Matching for Labelled Graphs

Publisher Copyright: © 2023 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.Many problems that can be solved in quadratic time have bit-parallel speed-ups with factor w, where w is the computer word size. A classic example is computing the edit distance of two strings of length n, which can be solved in O(n2/w) time. In a reasonable classical model of computation, one can assume w = Θ(log n), and obtaining significantly better speed-ups is unlikely in the light of conditional lower bounds obtained for such problems. In this paper, we study the connection of bit-parallelism to quantum computation, aiming to see if a bit-parallel algorithm could be converted to a quantum algorithm with better than logarithmic speed-up. We focus on string matching in labeled graphs, the problem of finding an exact occurrence of a string as the label of a path in a graph. This problem admits a quadratic conditional lower bound under a very restricted class of graphs (Equi et al. ICALP 2019), stating that no algorithm in the classical model of computation can solve the problem in time O(|P||E|1−ϵ) or O(|P|1−ϵ|E|). We show that a simple bit-parallel algorithm on such restricted family of graphs (level DAGs) can indeed be converted into a realistic quantum algorithm that attains subquadratic time complexity O(|E|p|P|).Peer reviewe