Efficient approximation of diagonal unitaries over the Clifford+T basis

Welch, Jonathan; Bocharov, Alex; Svore, Krysta M.

doi:10.26421/qic16.1-2-6

Cited by 10 publications

(11 citation statements)

References 14 publications

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“…The complex permutation gate is of interest to the study of quantum computation, as it is a somewhat classical part of a quantum circuit; see its use in the definition of the Fourier hierarchy in [9]. The diagonal unitary, which is a special complex permutation matrix, can be efficiently simulated in terms of the Clifford+T basis by the algorithm in [24]. We define the controlled-permutation matrices to be bipartite controlled unitaries controlled in the computational basis of one system and with the terms on the controlled side being permutation matrices.…”

Section: A Decomposition Of Complex Permutation Matricesmentioning

confidence: 99%

Decomposition of bipartite and multipartite unitary gates into the product of controlled unitary gates

Chen

2015

Phys. Rev. A

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We show that any unitary operator on the dA x dB system (dA ^ 2) can be decomposed into the product of at most 4dA -5 controlled unitary operators. The number can be reduced to 2dA -1 when dA is a power of two. We also prove that three controlled unitaries can implement a bipartite complex permutation operator, and discuss the connection to an analogous result on classical reversible circuits. We further show that any n-partite unitary on the space C';' ® • • • Cdn is the product of at most [2 Y\"=\(2dj -2) -1] controlled unitary gates, each of which is controlled from n -1 systems. We also decompose any bipartite unitary into the product of a simple type of bipartite gate and some local unitaries. We derive dimension-independent upper bounds for the controlled-NOT gate cost or entanglement cost of bipartite permutation unitaries (with the help of ancillas of fixed size) as functions of the Schmidt rank of the unitary. It is shown that such costs under a simple protocol are related to the log-rank conjecture in communication complexity theory via the link of nonnegative rank.

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Section: A Decomposition Of Complex Permutation Matricesmentioning

confidence: 99%

Decomposition of bipartite and multipartite unitary gates into the product of controlled unitary gates

Chen

2015

Phys. Rev. A

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“…Walsh sequences can be used to provide timing information relevant to the sequencing of control operations on qubits at the physical level, with rising and falling edges employed to trigger the application of a desired operation. Generically this can be employed for logical or physical-layer algorithmic implementation or unitary gate construction [39,45,50], and of course it may also be advantageous to apply all physicallayer operations timed via Walsh sequences due to their discrete timing structure. We therefore refer generically to Walsh timing patterns.…”

Section: Discussionmentioning

confidence: 99%

“…1b) [40,46], Walsh-modulated (Fig. 1c) dynamically protected single-qubit gates (including well known composite pulses) [31,42,47], dynamically protected multiqubit gates [48,49], noise spectroscopy and real-time quantum signal reconstruction [43], the construction of quantum algorithms [39] (language therein refers to Hadamard matrices), and the construction of quantum circuits for the implementation of unitary operators [45,50]. Across various applications, the Walsh family of controls is shown to incorporate previously known sequences and protocols in a single unifying mathematical framework.…”

Section: Walsh Functions a Functional Programming Basis For Physical-...mentioning

confidence: 99%

Functional Basis for Efficient Physical Layer Classical Control in Quantum Processors

2016

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The rapid progress seen in the development of quantum coherent devices for information processing has motivated serious consideration of quantum computer architecture and organization. One topic which remains open for investigation and optimization relates to the design of the classical-quantum interface, where control operations on individual qubits are applied according to higher-level algorithms; accommodating competing demands on performance and scalability remains a major outstanding challenge. In this work we present a resource-efficient, scalable framework for the implementation of embedded physical-layer classical controllers for quantum information systems. Design drivers and key functionalities are introduced, leading to the selection of Walsh functions as an effective functional basis for both programming and controller hardware implementation. This approach leverages the simplicity of real-time Walsh-function generation in classical digital hardware, and the fact that a wide variety of physical-layer controls such as dynamic error suppression are known to fall within the Walsh family. We experimentally implement a real-time FPGA-based Walsh controller producing Walsh timing signals and Walsh-synthesized analog waveforms appropriate for critical tasks in error-resistant quantum control and noise characterization. These demonstrations represent the first step towards a unified framework for the realization of physical-layer controls compatible with large-scale quantum information processing.

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“…The runtimes presented in (8) and (9) stem from a so-called 'flawed' runtime analysis originally presented in [17]. Suppose we are searching for a collision in a space of size N , and that the available memory is full with w distinguished points.…”

Section: Appendixmentioning

confidence: 99%

“…where k represents the depth of the circuit. A myriad of algorithms currently exist to find such a decomposition [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. They are generally divided into two classes, those which synthesize approximately (i.e.…”

Section: Introductionmentioning

confidence: 99%

Parallelizing quantum circuit synthesis

Di Matteo,

Mosca

2016

Preprint

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Quantum circuit synthesis is the process in which an arbitrary unitary operation is decomposed into a sequence of gates from a universal set, typically one which a quantum computer can implement both efficiently and fault-tolerantly. As physical implementations of quantum computers improve, the need is growing for tools which can effectively synthesize components of the circuits and algorithms they will run. Existing algorithms for exact, multi-qubit circuit synthesis scale exponentially in the number of qubits and circuit depth, leaving synthesis intractable for circuits on more than a handful of qubits. Even modest improvements in circuit synthesis procedures may lead to significant advances, pushing forward the boundaries of not only the size of solvable circuit synthesis problems, but also in what can be realized physically as a result of having more efficient circuits.We present a method for quantum circuit synthesis using deterministic walks. Also termed pseudorandom walks, these are walks in which once a starting point is chosen, its path is completely determined. We apply our method to construct a parallel framework for circuit synthesis, and implement one such version performing optimal Tcount synthesis over the Clifford+T gate set. We use our software to present examples where parallelization offers a significant speedup on the runtime, as well as directly confirm that the 4-qubit 1-bit full adder has optimal T -count 7 and T -depth 3.

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Efficient approximation of diagonal unitaries over the Clifford+T basis

Cited by 10 publications

References 14 publications

Decomposition of bipartite and multipartite unitary gates into the product of controlled unitary gates

Decomposition of bipartite and multipartite unitary gates into the product of controlled unitary gates

Functional Basis for Efficient Physical Layer Classical Control in Quantum Processors

Parallelizing quantum circuit synthesis

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