Controlled gates for multi-level quantum computation (original) (raw)
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Two-Qubit Quantum Gates to Reduce the Quantum Cost of Reversible Circuit
2011
This paper presents a quantum gate library that consists of all possible two-qubit quantum gates which do not produce entangled states. The quantum cost of each two-qubit gate in the proposed library is one. Therefore, these gates can be used to reduce the quantum costs of reversible circuits. Experimental results show a significant reduction of quantum cost in benchmark circuits. The resulting circuits could be further optimized with existing tools, such as quantum template matching.
Dancing the Quantum Waltz: Compiling Three-Qubit Gates on Four Level Architectures
Proceedings of the 50th Annual International Symposium on Computer Architecture
Superconducting quantum devices are a leading technology for quantum computation, but they suffer from several challenges. Gate errors, coherence errors and a lack of connectivity all contribute to low fidelity results. In particular, connectivity restrictions enforce a gate set that requires three-qubit gates to be decomposed into one-or two-qubit gates. This substantially increases the number of two-qubit gates that need to be executed. However, many quantum devices have access to higher energy levels. We can expand the qubit abstraction of |0⟩ and |1⟩ to a ququart which has access to the |2⟩ and |3⟩ state, but with shorter coherence times. This allows for two qubits to be encoded in one ququart, enabling increased virtual connectivity between physical units from two adjacent qubits to four fully connected qubits. This connectivity scheme allows us to more efficiently execute three-qubit gates natively between two physical devices. We present direct-to-pulse implementations of several threequbit gates, synthesized via optimal control, for compilation of three-qubit gates onto a superconducting-based architecture with access to four-level devices with the first experimental demonstration of four-level ququart gates designed through optimal control. We demonstrate strategies that temporarily use higher level states to perform Toffoli gates and always use higher level states to improve fidelities for quantum circuits. We find that these methods improve expected fidelities with increases of 2x across circuit sizes using intermediate encoding, and increases of 3x for fully-encoded ququart compilation.
Asymptotically Optimal Quantum Circuits for d-Level Systems
Physical Review Letters, 2005
As a qubit is a two-level quantum system whose state space is spanned by |0 , |1 , so a qudit is a d-level quantum system whose state space is spanned by |0 , · · · , |d − 1 . Quantum computation has stimulated much recent interest in algorithms factoring unitary evolutions of an n-qubit state space into component two-particle unitary evolutions. In the absence of symmetry, Shende, Markov and Bullock use Sard's theorem to prove that at least C4 n two-qubit unitary evolutions are required, while Vartiainen, Möttönen, and Salomaa (VMS) use the QR matrix factorization and Gray codes in an optimal order construction involving two-particle evolutions. In this work, we note that Sard's theorem demands Cd 2n two-qudit unitary evolutions to construct a generic (symmetryless) n-qudit evolution. However, the VMS result applied to virtual-qubits only recovers optimal order in the case that d is a power of two. We further construct a QR decomposition for d-multi-level quantum logics, proving a sharp asymptotic of Θ(d 2n ) two-qudit gates and thus closing the complexity question for all d-level systems (d finite.) Gray codes are not required, and the optimal Θ(d 2n ) asymptotic also applies to gate libraries where two-qudit interactions are restricted by a choice of certain architectures.
Synthesis of quantum-logic circuits
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2006
The pressure of fundamental limits on classical computation and the promise of exponential speedups from quantum effects have recently brought quantum circuits [10] to the attention of the Electronic Design Automation community . We discuss efficient quantum logic circuits which perform two tasks: (i) implementing generic quantum computations and (ii) initializing quantum registers. In contrast to conventional computing, the latter task is nontrivial because the state-space of an n-qubit register is not finite and contains exponential superpositions of classical bit strings. Our proposed circuits are asymptotically optimal for respective tasks and improve earlier published results by at least a factor of two.
Efficient Implementation of Controlled Operations for Multivalued Quantum Logic
2009 39th International Symposium on Multiple-Valued Logic, 2009
This paper presents a new quantum array that can be used to control a single-qudit hermitian operator for an odd radix r > 2 by n controls using Θ n log 2 r+2 single-qudit controlled gates with one control and no ancilla qudits. This quantum array is more practical than existing quantum arrays of the same complexity because it does not require the use of small roots of the operation that is being implemented. Another quantum array is also presented that implements a single-qudit operator with n controls for any radix r > 2 using log r−1 n ancilla qudits and Θ n log r−1 2+1 single-qudit gates with one control.
Results on two-bit gate design for quantum computers
Proceedings Workshop on Physics and Computation. PhysComp '94
We present numerical results which show how twobit logic gates can be used in the design of a quantum computer. We show that the Toffoli gate, which is a universal gate for all classical reversible computation, can be implemented using a particular sequence of exactly five two-bit gates. An arbitrary three-bit unitary gate, which can be used to build up any arbitrary quantum computation, can be implemented exactly with six two-bit gates. The ease of implementation of any particular quantum operation is dependent upon a very non-classical feature of the operation, its exact quantum phase factor.
Elementary gates for quantum computation
Physical Review A, 1995
We show that a set of gates that consists of all one-bit quantum gates (U(2)) and the two-bit exclusive-or gate (that maps Boolean values (x, y) to (x, x ⊕ y)) is universal in the sense that all unitary operations on arbitrarily many bits n (U(2 n )) can be expressed as compositions of these gates. We investigate the number of the above gates required to implement other gates, such as generalized Deutsch-Toffoli gates, that apply a specific U(2) transformation to one input bit if and only if the logical AND of all remaining input bits is satisfied. These gates play a central role in many proposed constructions of quantum computational networks. We derive upper and lower bounds on the exact number of elementary gates required to build up a variety of two-and three-bit quantum gates, the asymptotic number required for n-bit Deutsch-Toffoli gates, and make some observations about the number required for arbitrary n-bit unitary operations.
A Hierarchical Approach to Computer-Aided Design of Quantum Circuits
… and Methodology of …, 2003
A new approach to synthesis of permutation class of quantum logic circuits has been proposed in this paper. This approach produces better results than the previous approaches based on classical reversible logic and can be easier tuned to any particular quantum technology such as nuclear magnetic resonance (NMR). First we synthesize a library of permutation (pseudo- binary) gates using a
The pressure of fundamental limits on classical computation and the promise of exponential speedups from quantum effects have recently brought quantum circuits [10] to the attention of the Electronic Design Automation community . We discuss efficient quantum logic circuits which perform two tasks: (i) implementing generic quantum computations and (ii) initializing quantum registers. In contrast to conventional computing, the latter task is nontrivial because the state-space of an n-qubit register is not finite and contains exponential superpositions of classical bit strings. Our proposed circuits are asymptotically optimal for respective tasks and improve earlier published results by at least a factor of two.
Multibit gates for quantum computing
Physical Review Letters, 2001
We present a general technique to implement products of many qubit operators communicating via a joint harmonic oscillator degree of freedom in a quantum computer. By conditional displacements and rotations we can implement Hamiltonians which are trigonometric functions of qubit operators. With such operators we can effectively implement higher order gates such as Toffoli gates and C n -NOT gates, and we show that the entire Grover search algorithm can be implemented in a direct way.