303 research outputs found
Phase gadget synthesis for shallow circuits
We give an overview of the circuit optimisation methods used by tket, a compiler system for quantum software developed by Cambridge Quantum Computing Ltd. We focus on a novel technique based around phase gadgets, a family of multi-qubit quantum operations which occur naturally in a wide range of quantum circuits of practical interest. The phase gadgets have a simple presentation in the ZX-calculus, which makes it easy to reason about them. Taking advantage of this, we present an efficient method to translate the phase gadgets back to CNOT gates and single qubit operations suitable for execution on a quantum computer with significant reductions in gate count and circuit depth. We demonstrate the effectiveness of these methods on a quantum chemistry benchmarking set based on variational circuits for ground state estimation of small molecules
Annealing Optimisation of Mixed ZX Phase Circuits
We present a topology-aware optimisation technique for circuits of mixed ZX
phase gadgets, based on conjugation by CX gates and simulated annealing.Comment: In Proceedings QPL 2022, arXiv:2311.0837
Constructing quantum circuits with global gates
There are various gate sets that can be used to describe a quantum
computation. A particularly popular gate set in the literature on quantum
computing consists of arbitrary single-qubit gates and 2-qubit CNOT gates. A
CNOT gate is however not always the natural multi-qubit interaction that can be
implemented on a given physical quantum computer, necessitating a compilation
step that transforms these CNOT gates to the native gate set. A particularly
interesting case where compilation is necessary is for ion trap quantum
computers, where the natural entangling operation can act on more than 2 qubits
and can even act globally on all qubits at once. This calls for an entirely
different approach to constructing efficient circuits. In this paper we study
the problem of converting a given circuit that uses 2-qubit gates to one that
uses global gates. Our three main contributions are as follows. First, we find
an efficient algorithm for transforming an arbitrary circuit consisting of
Clifford gates and arbitrary phase gates into a circuit consisting of
single-qubit gates and a number of global interactions proportional to the
number of non-Clifford phases present in the original circuit. Second, we find
a general strategy to transform a global gate that targets all qubits into one
that targets only a subset of the qubits. This approach scales linearly with
the number of qubits that are not targeted, in contrast to the exponential
scaling reported in (Maslov & Nam, N. J. Phys. 2018). Third, we improve on the
number of global gates required to synthesise an arbitrary n-qubit Clifford
circuit from the 12n-18 reported in (Maslov & Nam, N. J. Phys. 2018) to 6n-8.Comment: 13 pages. v2: added some more figures and fixed a number of
(mathematical) typo
Building Qutrit Diagonal Gates from Phase Gadgets
Phase gadgets have proved to be an indispensable tool for reasoning about
ZX-diagrams, being used in optimisation and simulation of quantum circuits and
the theory of measurement-based quantum computation. In this paper we study
phase gadgets for qutrits. We present the flexsymmetric variant of the original
qutrit ZX-calculus, which allows for rewriting that is closer in spirit to the
original (qubit) ZX-calculus. In this calculus phase gadgets look as you would
expect, but there are non-trivial differences in their properties. We devise
new qutrit-specific tricks to extend the graphical Fourier theory of qubits,
resulting in a translation between the 'additive' phase gadgets and a
'multiplicative' counterpart we dub phase multipliers.
This enables us to generalise the qubit notion of multiple-control to qutrits
in two ways. The first type is controlling on a single tritstring, while the
second type applies the gate a number of times equal to the tritwise
multiplication modulo 3 of the control qutrits.We show how both types of
control can be implemented for any qutrit Z or X phase gate, ancilla-free, and
using only Clifford and phase gates. The first requires a polynomial number of
gates and exponentially small phases, while the second requires an exponential
number of gates, but constant sized phases. This is interesting, because such a
construction is not possible in the qubit setting.
As an application of these results we find a construction for emulating
arbitrary qubit diagonal unitaries, and specifically find an ancilla-free
emulation for the qubit CCZ gate that only requires three single-qutrit
non-Clifford gates, provably lower than the four T gates needed for qubits with
ancilla.Comment: In Proceedings QPL 2022, arXiv:2311.0837
Non-stabilizerness and entanglement from cat-state injection
Recently, cat states have been used to heuristically improve the runtime of a
classical simulator of quantum circuits based on the diagrammatic ZX-calculus.
Here we investigate the use of cat-state injection within the quantum circuit
model. We explore a family of cat states, ,
and describe circuit gadgets using them to concurrently inject
non-stabilizerness (also known as magic) and entanglement into any quantum
circuit. We provide numerical evidence that cat-state injection does not lead
to speed-up in classical simulation. On the other hand, we show that our
gadgets can be used to widen the scope of compelling applications of cat
states. Specifically, we show how to leverage them to achieve savings in the
number of injected qubits, and also to induce scrambling dynamics in otherwise
non-entangling Clifford circuits in a controlled manner.Comment: 20 pages, 5 figure
The Qudit ZH-Calculus: Generalised Toffoli+Hadamard and Universality
We introduce the qudit ZH-calculus and show how to generalise all the
phase-free qubit rules to qudits. We prove that for prime dimensions d, the
phase-free qudit ZH-calculus is universal for matrices over the ring
Z[e^2(pi)i/d]. For qubits, there is a strong connection between phase-free
ZH-diagrams and Toffoli+Hadamard circuits, a computationally universal fragment
of quantum circuits. We generalise this connection to qudits, by finding that
the two-qudit |0>-controlled X gate can be used to construct all classical
reversible qudit logic circuits in any odd qudit dimension, which for qubits
requires the three-qubit Toffoli gate. We prove that our construction is
asymptotically optimal up to a logarithmic term. Twenty years after the
celebrated result by Shi proving universality of Toffoli+Hadamard for qubits,
we prove that circuits of |0>-controlled X and Hadamard gates are approximately
universal for qudit quantum computing for any odd prime d, and moreover that
phase-free ZH-diagrams correspond precisely to such circuits allowing
post-selections.Comment: In Proceedings QPL 2023, arXiv:2308.1548
t|ket> : A retargetable compiler for NISQ devices
We present t|ket>, a quantum software development platform produced by Cambridge Quantum Computing Ltd. The heart of t|ket> is a language-agnostic optimising compiler designed to generate code for a variety of NISQ devices, which has several features designed to minimise the influence of device error. The compiler has been extensively benchmarked and outperforms most competitors in terms of circuit optimisation and qubit routing
Diagrammatic Analysis for Parameterized Quantum Circuits
Diagrammatic representations of quantum algorithms and circuits offer novel
approaches to their design and analysis. In this work, we describe extensions
of the ZX-calculus especially suitable for parameterized quantum circuits, in
particular for computing observable expectation values as functions of or for
fixed parameters, which are important algorithmic quantities in a variety of
applications ranging from combinatorial optimization to quantum chemistry. We
provide several new ZX-diagram rewrite rules and generalizations for this
setting. In particular, we give formal rules for dealing with linear
combinations of ZX-diagrams, where the relative complex-valued scale factors of
each diagram must be kept track of, in contrast to most previously studied
single-diagram realizations where these coefficients can be effectively
ignored. This allows us to directly import a number useful relations from the
operator analysis to ZX-calculus setting, including causal cone and quantum
gate commutation rules. We demonstrate that the diagrammatic approach offers
useful insights into algorithm structure and performance by considering several
ans\"atze from the literature including realizations of hardware-efficient
ans\"atze and QAOA. We find that by employing a diagrammatic representation,
calculations across different ans\"atze can become more intuitive and
potentially easier approach systematically than by alternative means. Finally,
we outline how diagrammatic approaches may aid in the design and study of new
and more effective quantum circuit ans\"atze
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