### Table 4 - Circuits to implement the QFT for n = 1-4 qubits

"... In PAGE 4: ... Each of these circuits implements an exact QFT for that system size. Table4 shows the circuits produced by this algorithm for quantum systems of 1 - 4 qubits. Table 4 - Circuits to implement the QFT for n = 1-4 qubits ... In PAGE 5: ... (Hand-Optimised) circuit generated by the evolved solution to QFT(3) This circuit has 10 gates. Although the best known circuit to generate QFT(3) can be implemented in 7 gates (see Table4 ), that circuit requires the use of a SWAP gate, which was not available as an allele to Q-PACE III in this particular GP run. The most efficient known circuit to implement QFT(3) using the alleles given to Q-PACE III in this GP run has 9 gates, just one less than the solution evolved here.... ..."

### Table 2: Simplification of the benchmark circuits from [15]. Circuit name appears in column Name and is taken directly from [15], Size indicates the number of qubits in the circuit. NCV GC lists the quantum NCV gate count when the Toffoli gates in the corresponding circuit are substituted with their quantum implementations. Optimized NCV GC and Levels show the quantum gate count and the number of logic levels after reversible gates are substituted with their quantum circuits and the resulting circuit is run through the template simplification and then level compaction processes. We do not report the runtimes in this table because all circuits were computed almost instantaneously. Name Size NCV GC Optimized NCV GC Levels

2006

"... In PAGE 9: ... Since [15] do not compact levels in their circuits, we have no comparisons for the number of levels. Table2 summaries the results. Let us describe the simplification procedure for one of these benchmark circuits: the 5-qubit oracle function mod5.... In PAGE 9: ... It leaves the first four inputs unchanged and inverts the last one if, and only if, the first four represent an integer divisible by 5. We first found a Toffoli gate realization (circuit mod5mils in Table2 ). We then applied the template... ..."

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### Table I. Qubit Technology Basic Characteristics (Question marks under QIO indicate that experimental verification has not yet been shown. JJ: Josephson junction, LOQC: linear optics quantum computing.) Stationary/ Single/

2006

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### Table 2: Overhead of recursive error correction for a sin- gle qubit operation

"... In PAGE 5: ...CJCJBGBLBN BDBN BJCLCL, CJCJBFBGBFBN BDBN BDBHCLCL, etc.). The reason for this is the relative ease with which most quantum primitives are per- formed on this code. Table2 depicts the storage and op- erational overhead of using these codes. The numbers are for a single logical qubit, with rows depicting increased levels of concatenation, and thus additional error correc- tion capability.... ..."

### Table 2: Overhead of recursive error correction for a sin- gle qubit operation

"... In PAGE 52: ... For instance, instead of decoding a full 56 bit DES encryption, it would be possible to execute test runs on smaller key size to make sure the error profiles are acceptable and the program is correct. # of bits Runtime (secs) 4 27 8 126 16 1306 32 15348 Table2 - Runtime of Minimal Set Cover Program Discussion/Future Work In this section, we will discuss the lessons learned about DNA computation from this project and present ideas for future work in this area such as improvements to the machine architecture, the compiler algorithms, etc. One of the aspects of the language design that seems particularly lacking is the semantics of the = operator when dealing with tubes.... In PAGE 66: ...CJCJBGBLBN BDBN BJCLCL, CJCJBFBGBFBN BDBN BDBHCLCL, etc.). The reason for this is the relative ease with which most quantum primitives are per- formed on this code. Table2 depicts the storage and op- erational overhead of using these codes. The numbers are for a single logical qubit, with rows depicting increased levels of concatenation, and thus additional error correc- tion capability.... ..."

### Table 2: Overhead of recursive error correction for a sin- gle qubit operation

2002

"... In PAGE 52: ... For instance, instead of decoding a full 56 bit DES encryption, it would be possible to execute test runs on smaller key size to make sure the error profiles are acceptable and the program is correct. # of bits Runtime (secs) 4 27 8 126 16 1306 32 15348 Table2 - Runtime of Minimal Set Cover Program Discussion/Future Work In this section, we will discuss the lessons learned about DNA computation from this project and present ideas for future work in this area such as improvements to the machine architecture, the compiler algorithms, etc. One of the aspects of the language design that seems particularly lacking is the semantics of the = operator when dealing with tubes.... In PAGE 66: ...CJCJBGBLBN BDBN BJCLCL, CJCJBFBGBFBN BDBN BDBHCLCL, etc.). The reason for this is the relative ease with which most quantum primitives are per- formed on this code. Table2 depicts the storage and op- erational overhead of using these codes. The numbers are for a single logical qubit, with rows depicting increased levels of concatenation, and thus additional error correc- tion capability.... ..."

### Table 2. Average decrease in entanglement h E1i between one qubit and the rest during the IQFT.

2005

"... In PAGE 9: ... In these cases, though we cannot easily calculate a full entanglement analysis, we have calculated the entropy between one qubit and the rest of the qubits in both registers, this corre- sponds to the quantities in the top line of Table 1. The di erence in the average entropy E1 before and after the IQFT (corresponding to the last column in Table 1), is shown in Table2 grouped by the period r. There is a clear pattern for E1: the closer the period r is to a power of 2, the smaller the value of E1.... ..."

### TABLE 3 Representation of the Quantum Gate V (a; c) in a Circuit with Lines a, b, c

2007

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### Table 2: Power estimation for dynamic circuits

1992

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### Table 3: Power estimation for combinational circuits

1992

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