Predicting the optimum SWAP depth of a quantum circuit is useful because it informs the compiler about the amount of necessary optimization. Fast prediction methods will prove essential to the compilation of practical quantum circuits. In this paper,
we propose that quantum circuits can be modeled as queuing networks, enabling efficient extraction of the parallelism and duration of SWAP circuits. To provide preliminary substantiation of this approach, we compile a quantum multiplier circuit and use a queuing network model to accurately determine the quantum circuit parallelism and duration. Our method is scalable and has the potential speed and precision necessary for large scale quantum circuit compilation.
Quantum circuit simulators have a long tradition of exploiting massive hardware parallelism. Most of the times, parallelism has been supported by special purpose libraries tailored specifically for the quantum circuits. Quantum circuit simulators are
integral part of quantum software stacks, which are mostly written in Python. Our focus has been on ease of use, implementation and maintainability within the Python ecosystem. We report the performance gains we obtained by using CuPy, a general purpose library (linear algebra) developed specifically for CUDA-based GPUs, to simulate quantum circuits. For supremacy circuits the speedup is around 2x, and for quantum multipliers almost 22x compared to state-of-the-art C++-based simulators.
We present an arithmetic circuit performing constant modular addition having $mathcal{O}(n)$ depth of Toffoli gates and using a total of $n+3$ qubits. This is an improvement by a factor of two compared to the width of the state-of-the-art Toffoli-bas
ed constant modular adder. The advantage of our adder, compared to the ones operating in the Fourier-basis, is that it does not require small angle rotations and their Clifford+T decomposition. Our circuit uses a recursive adder combined with the modular addition scheme proposed by Vedral et. al. The circuit is implemented and verified exhaustively with QUANTIFY, an open-sourced framework. We also report on the Clifford+T cost of the circuit.
We provide evidence that commonly held intuitions when designing quantum circuits can be misleading. In particular we show that: a) reducing the T-count can increase the total depth; b) it may be beneficial to trade CNOTs for measurements in NISQ cir
cuits; c) measurement-based uncomputation of relative phase Toffoli ancillae can make up to 30% of a circuits depth; d) area and volume cost metrics can misreport the resource analysis. Our findings assume that qubits are and will remain a very scarce resource. The results are applicable for both NISQ and QECC protected circuits. Our method uses multiple ways of decomposing Toffoli gates into Clifford+T gates. We illustrate our method on addition and multiplication circuits using ripple-carry. As a byproduct result we show systematically that for a practically significant range of circuit widths, ripple-carry addition circuits are more resource efficient than the carry-lookahead addition ones. The methods and circuits were implemented in the open-source QUANTIFY software.
The quantum circuit layout problem is to map a quantum circuit to a quantum computing device, such that the constraints of the device are satisfied. The optimality of a layout method is expressed, in our case, by the depth of the resulting circuits.
We introduce QXX, a novel search-based layout method, which includes a configurable Gaussian function used to: emph{i)} estimate the depth of the generated circuits; emph{ii)} determine the circuit region that influences most the depth. We optimize the parameters of the QXX model using an improved version of random search (weighted random search). To speed up the parameter optimization, we train and deploy QXX-MLP, an MLP neural network which can predict the depth of the circuit layouts generated by QXX. We experimentally compare the two approaches (QXX and QXX-MLP) with the baseline: exponential time exhaustive search optimization. According to our results: 1) QXX is on par with state-of-the-art layout methods, 2) the Gaussian function is a fast and accurate optimality estimator. We present empiric evidence for the feasibility of learning the layout method using approximation.
Quantum resource analysis is crucial for designing quantum circuits as well as assessing the viability of arbitrary (error-corrected) quantum computations. To this end, we introduce QUANTIFY, which is an open-source framework for the quantitative ana
lysis of quantum circuits. It is based on Google Cirq and is developed with Clifford+T circuits in mind, and it includes the necessary methods to handle Toffoli+H and more generalised controlled quantum gates, too. Key features of QUANTIFY include: (1) analysis and optimisation methods which are compatible with the surface code, (2) choice between different automated (mixed polarity) Toffoli gate decompositions, (3) semi-automatic quantum circuit rewriting and quantum gate insertion methods that take into account known gate commutation rules, and (4) novel optimiser types that can be combined with different verification methods (e.g. truth table or circuit invariants like number of wires). For benchmarking purposes QUANTIFY includes quantum memory and quantum arithmetic circuits. Experimental results show that the frameworks performance scales to circuits with thousands of qubits.
Quantum algorithms often use quantum RAMs (QRAM) for accessing information stored in a database-like manner. QRAMs have to be fast, resource efficient and fault-tolerant. The latter is often influenced by access speeds, because shorter times introduc
e less exposure of the stored information to noise. The total execution time of an algorithm depends on the QRAM access time which includes: 1) address translation time, and 2) effective query time. The bucket brigade QRAMs were proposed to achieve faster addressing at the cost of exponentially many ancillae. We illustrate a systematic method to significantly reduce the effective query time by using Clifford+T gate parallelism. The method does not introduce any ancillae qubits. Our parallelisation method is compatible with the surface code quantum error correction. We show that parallelisation is a result of advantageous Toffoli gate decomposition in terms of Clifford+T gates, and after addresses have been translated, we achieve theoretical $mathcal{O}(1)$ parallelism for the effective queries. We conclude that, in theory: 1) fault-tolerant bucket brigade quantum RAM queries can be performed approximately with the speed of classical RAM; 2) the exponentially many ancillae from the bucket brigade addressing scheme are a trade-off cost for achieving exponential query speedup compared to quantum read-only memories whose queries are sequential by design. The methods to compile, parallelise and analyse the presented QRAM circuits were implemented in software which is available online.
Surface quantum error-correcting codes are the leading proposal for fault-tolerance within quantum computers. We present OpenSurgery, a scalable tool for the preparation of circuits protected by the surface code operated through lattice surgery. Latt
ice surgery is considered a resource efficient method to implement surface code computations. Resource efficiency refers to the number of physical qubits and the time necessary for executing a quantum computation. OpenSurgery is a first step towards methods that aid quantum algorithm design informed by the realities of the hardware architectures. OpenSurgery can: 1) lay out arbitrary quantum circuits, 2) estimate the quantum resources used for their execution, 3) visualise the resulting 3D topological assemblies. Source code is available at http://www.github.com/alexandrupaler/opensurgery.
Clifford gates play a role in the optimisation of Clifford+T circuits. Reducing the count and the depth of Clifford gates, as well as the optimal scheduling of T gates, influence the hardware and the time costs of executing quantum circuits. This wor
k focuses on circuits protected by the surface quantum error-correcting code. The result of compiling a quantum circuit for the surface code is called a topological assembly. We use queuing theory to model a part of the compiled assemblies, evaluate the models, and make the empiric observation that at least for certain Clifford+T circuits (e.g. adders), the assemblys execution time does not increase when the available hardware is restricted. This is an interesting property, because it shows that T gate scheduling and Clifford gate optimisation have the potential to save both hardware and execution time.
We introduce a data bus, for reducing the qubit counts within quantum computations (protected by surface codes). For general computations, an automated trade-off analysis (software tool and source code are open sourced and available online) is perfor
med to determine to what degree qubit counts are reduced by the data bus: is the time penalty worth the qubit count reductions? We provide two examples where the qubit counts are convincingly reduced: 1) interaction of two surface code patches on NISQ machines with 28 and 68 qubits, and 2) very large-scale circuits with a structure similar to state-of-the-art quantum chemistry circuits. The data bus has the potential to transform all layers of the quantum computing stack (e.g., as envisioned by Google, IBM, Riggeti, Intel), because it simplifies quantum computation layouts, hardware architectures and introduces lower qubits counts at the expense of a reasonable time penalty.
