Quantum-state preparation with universal gate decompositions

Plesch, Martin; Brukner, Časlav

doi:10.1103/physreva.83.032302

Cited by 239 publications

(212 citation statements)

References 17 publications

(29 reference statements)

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“…In this section we combine the decomposition scheme for isometries of Knill [17] and the state preparation scheme described in [13]. The main result is as follows.…”

Section: A Notation For Controlled Gatesmentioning

confidence: 99%

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Quantum circuits for isometries

et al. 2016

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We consider the decomposition of arbitrary isometries into a sequence of single-qubit and Controlled-not (C-not) gates. In many experimental architectures, the C-not gate is relatively 'expensive' and hence we aim to keep the number of these as low as possible. We derive a theoretical lower bound on the number of C-not gates required to decompose an arbitrary isometry from m to n qubits, and give three explicit gate decompositions that achieve this bound up to a factor of about two in the leading order. We also perform some bespoke optimizations for certain cases where m and n are small. In addition, we show how to apply our result for isometries to give a decomposition scheme for an arbitrary quantum operation via Stinespring's theorem, and derive a lower bound on the number of C-nots in this case too. These results will have an impact on experimental efforts to build a quantum computer, enabling them to go further with the same resources.

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“…In this section we combine the decomposition scheme for isometries of Knill [17] and the state preparation scheme described in [13]. The main result is as follows.…”

Section: A Notation For Controlled Gatesmentioning

confidence: 99%

“…Similarly, in order to prepare a state of n qubits (starting from the state |0 ⊗n ), the best known construction requires 23 24 2 n C-nots to leading order if n is even [13], and 2 n to leading order if n is odd [16], which is again approximately twice the best known lower bound [13].…”

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confidence: 99%

Quantum circuits for isometries

et al. 2016

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“…In quantum circuit model, the circuit costs for generating arbitrary quantum states or simulating unitary gates are basically determined by the number of independent (real) parameters [24][25][26][27][28][29]. The dilated unitary operator for an arbitrary generalized extreme qudit channel is of dimension d 2 , which leads to O(d 4 ) gates, while the initial state of the ancilla is fixed as |0 , which would reduce the number of gates by order d, eventually resulting in O(d 3 ) gates.…”

Section: Extreme Qutrit-to-qubit and Qubit-to-qutrit Channelsmentioning

confidence: 99%

Convex decomposition of dimension-altering quantum channels

Wang

2016

Int. J. Quantum Inform.

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Quantum channels, which are completely positive and trace preserving mappings, can alter the dimension of a system; e.g., a quantum channel from a qubit to a qutrit. We study the convex set properties of dimension-altering quantum channels, and particularly the channel decomposition problem in terms of convex sum of extreme channels. We provide various quantum circuit representations of extreme and generalized extreme channels, which can be employed in an optimization to approximately decompose an arbitrary channel. Numerical simulations of low-dimensional channels are performed to demonstrate our channel decomposition scheme.

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“…1-b) vc ( If there is no connection to a with color c, the oracle returns the unique label invalid. In [6], this unique value is all 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 2-cycles for black edges: (7,16), (8,17), (9,15), (11,19), (12,22), (13,18), (14,20). In general, one needs l C k NOT gates to implement each minterm where l is the number of bits with value 1 in the binary representation of the minterm.…”

Section: Quantum Walk On Binary Welded Treementioning

confidence: 99%

“…(1) Without un-computation, each cofactor needs a new ancilla (qubit) and the number of available qubits is very restricted in current quantum technologies. (2) Constructing a zero state from an unknown quantum state generally needs an exponential number of gates [15].…”

Section: The Proposed Synthesis Algorithmmentioning

confidence: 99%

Reversible Logic Synthesis of k-Input, m-Output Lookup Tables

Shafaei

Saeedi

Pedram

2013

Design, Automation &Amp; Test in Europe Conference &Amp; Exhibition (DATE), 2013

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Abstract-Improving circuit realization of known quantum algorithms by CAD techniques has benefits for quantum experimentalists. In this paper, we address the problem of synthesizing a given k-input, m-output lookup table (LUT) by a reversible circuit. This problem has interesting applications in the Shor's number-factoring algorithm and in quantum walk on sparse graphs. For LUT synthesis, our approach targets the number of control lines in multiple-control Toffoli gates to reduce synthesis cost. To achieve this, we propose a multi-level optimization technique for reversible circuits to benefit from shared cofactors. To reuse output qubits and/or zero-initialized ancillae, we uncompute intermediate cofactors. Our simulations reveal that the proposed LUT synthesis has a significant impact on reducing the size of modular exponentiation circuits for Shor's quantum factoring algorithm, oracle circuits in quantum walk on sparse graphs, and the well-known MCNC benchmarks.

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Quantum-state preparation with universal gate decompositions

Cited by 239 publications

References 17 publications

Quantum circuits for isometries

Quantum circuits for isometries

Convex decomposition of dimension-altering quantum channels

Reversible Logic Synthesis of k-Input, m-Output Lookup Tables

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